[cig-commits] r20402 - in short/3D/PyLith/branches/v1.7-stable/doc/userguide: runpylith tutorials/3dhex8/dike tutorials/3dhex8/surfload tutorials/3dtet4 tutorials/greensfns2d tutorials/shearwave tutorials/subduction tutorials/twohex8 tutorials/twoquad4 tutorials/twotet4 tutorials/twotet4-geoproj tutorials/twotri3
sue at geodynamics.org
sue at geodynamics.org
Sun Jun 24 21:33:45 PDT 2012
Author: sue
Date: 2012-06-24 21:33:44 -0700 (Sun, 24 Jun 2012)
New Revision: 20402
Modified:
short/3D/PyLith/branches/v1.7-stable/doc/userguide/runpylith/runpylith.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dhex8/dike/dike.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dhex8/surfload/surfload.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dtet4/3dtet4.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/greensfns2d/greensfns2d.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/hex8.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/quad4.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/shearwave.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/tet4.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/tri3.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/subduction/subduction.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twohex8/twohex8.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twoquad4/twoquad4.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotet4-geoproj/twotet4-geoproj.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotet4/twotet4.lyx
short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotri3/twotri3.lyx
Log:
fixed typos and format problems
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/runpylith/runpylith.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/runpylith/runpylith.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/runpylith/runpylith.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1308,7 +1308,7 @@
\begin_layout Standard
The refiner is used to decrease node spacing by a factor of two by subdividing
each cell.
- In a 2-D triangular mesh a node is inserted at the midpoint of each edge,
+ In a 2D triangular mesh a node is inserted at the midpoint of each edge,
splitting each cell into four cells (see Figure
\begin_inset CommandInset ref
LatexCommand ref
@@ -1317,11 +1317,11 @@
\end_inset
).
- In a 2-D quadrilateral mesh a node is inserted at the midpoint of each
- edge and at the centroid of the cell, splitting each cell into four cells.
- In a 3-D tetrahedral mesh a node is inserted at the midpoint of each edge,
+ In a 2D quadrilateral mesh a node is inserted at the midpoint of each edge
+ and at the centroid of the cell, splitting each cell into four cells.
+ In a 3D tetrahedral mesh a node is inserted at the midpoint of each edge,
splitting each cell into eight cells.
- In a 3-D hexahedral mesh a node is inserted at the midpoint of each edge,
+ In a 3D hexahedral mesh a node is inserted at the midpoint of each edge,
the centroid of each face, and at the centroid of the cell, splitting each
cell into eight cells.
\end_layout
@@ -1351,7 +1351,7 @@
\begin_inset Caption
\begin_layout Plain Layout
-Global uniform mesh refinement of 2-D and 3-D linear cells.
+Global uniform mesh refinement of 2D and 3D linear cells.
The blue lines and orange circles identify the edges and vertices in the
original cells.
The purple lines and green circles identify the new edges and vertices
@@ -1383,8 +1383,8 @@
the simulation setup phase, such as, adjusting the topology to insert cohesive
cells and distribution of the mesh among processors uses this much smaller
coarse mesh.
- For 2-D problems the global mesh refinement increases the maximum problem
- size by a factor of four, and for 3-D problems it increases the maximum
+ For 2D problems the global mesh refinement increases the maximum problem
+ size by a factor of four, and for 3D problems it increases the maximum
problem size by a factor of eight.
\end_layout
@@ -4885,6 +4885,12 @@
\end_layout
\begin_layout Subsection
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:HDF5/Xdmf-Output"
+
+\end_inset
+
HDF5/Xdmf Output
\end_layout
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dhex8/dike/dike.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dhex8/dike/dike.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dhex8/dike/dike.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,286 +1,290 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
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-\maintain_unincluded_children false
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-\font_tt_scale 100
-
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-\default_output_format default
-\output_sync 0
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-\spacing single
-\use_hyperref false
-\papersize default
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-\use_amsmath 0
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-\use_bibtopic false
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-\shortcut idx
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-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Subsection
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-3d-hex8-dike"
-
-\end_inset
-
-Dike Intrusion Example
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Fault opening via prescribed tractions to mimic a dike instrusion
-\end_layout
-
-\begin_layout Itemize
-Dirichlet boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Elastic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Subsubsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This set of examples describes a problem where prescribed tensile tractions
- are imposed on a fault to mimic a dike intrusion.
- The example is contained in the directory
-\family typewriter
-examples/3d/hex8
-\family default
-, and the corresponding
-\family typewriter
-.cfg
-\family default
- file is
-\family typewriter
-step20.cfg
-\family default
-.
- The example may be run as follows:
-\end_layout
-
-\begin_layout LyX-Code
-pylith step20.cfg
-\end_layout
-
-\begin_layout Standard
-This will cause PyLith to read the default parameters in
-\family typewriter
-pylithapp.cfg
-\family default
-, and then override or augment them with the additional parameters in the
-
-\family typewriter
-step20.cfg
-\family default
- file.
- The
-\family typewriter
-.cfg
-\family default
- file is extensively documented, to provide detailed information on the
- various parameters.
-\end_layout
-
-\begin_layout Subsubsection
-Step20 - Static dike intrusion
-\end_layout
-
-\begin_layout Standard
-The
-\family typewriter
-step20.cfg
-\family default
- file defines a problem with spatially varying tensile normal tractions
- on the fault surface associated with a fluid intrusion.
- The lateral sides and bottom of the domain are fixed using Dirichlet (roller)
- boundary conditions.
- As in the other examples, we also setup output for the ground surface.
-\end_layout
-
-\begin_layout Standard
-We use the FaultCohesiveDyn object to impose tractions on the fault surface.
- We must include a fault constitutive model so we choose static friction
- with a coefficient of friction of 0.1.
- The coefficient of friction is irrelevant for the center of the fault where
- we impose uniform tensile tractions (10 MPa) and the fault opens, but it
- facilitates clamping the edges of the fault via compressive normal tractions
- (-100 MPa).
- Note that we must set the property
-\family typewriter
-open_free_surface
-\family default
- to True in order for the tractions to be imposed when the fault is open;
- the default behavior for fault opening is a free surface (the two sides
- of the fault are completely uncoupled).
- The most important fault parameters for prescribing the tensile fault tractions
- are
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.interfaces.fault]
-\end_layout
-
-\begin_layout LyX-Code
-open_free_surface = True
-\begin_inset Newline newline
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-traction_perturbation = pylith.faults.TractPerturbation
-\begin_inset Newline newline
-\end_inset
-
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.interfaces.fault.traction_perturbation]
-\end_layout
-
-\begin_layout LyX-Code
-db_initial = spatialdata.spatialdb.SimpleDB
-\end_layout
-
-\begin_layout LyX-Code
-db_initial.label = Initial fault tractions
-\end_layout
-
-\begin_layout LyX-Code
-db_initial.iohandler.filename = spatialdb/tractions_opening.spatialdb
-\end_layout
-
-\begin_layout LyX-Code
-db_initial.query_type = nearest
-\end_layout
-
-\begin_layout Standard
-When we have run the simulation, the output VTK files will be contained
- in
-\family typewriter
-examples/3d/hex8/output
-\family default
- (all with a prefix of
-\family typewriter
-step
-\family default
-20).
- Results using ParaView are shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:step20-disp"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step20_disp.png
- lyxscale 50
- width 10cm
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Displacement magnitude for example step20 visualized using ParaView.
-
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:step20-disp"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 2in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Subsection
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-3d-hex8-dike"
+
+\end_inset
+
+Dike Intrusion Example
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Fault opening via prescribed tractions to mimic a dike instrusion
+\end_layout
+
+\begin_layout Itemize
+Dirichlet boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Elastic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Subsubsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This set of examples describes a problem where prescribed tensile tractions
+ are imposed on a fault to mimic a dike intrusion.
+ The example is contained in the directory
+\family typewriter
+examples/3d/hex8
+\family default
+, and the corresponding
+\family typewriter
+.cfg
+\family default
+ file is
+\family typewriter
+step20.cfg
+\family default
+.
+ The example may be run as follows:
+\end_layout
+
+\begin_layout LyX-Code
+pylith step20.cfg
+\end_layout
+
+\begin_layout Standard
+This will cause PyLith to read the default parameters in
+\family typewriter
+pylithapp.cfg
+\family default
+, and then override or augment them with the additional parameters in the
+
+\family typewriter
+step20.cfg
+\family default
+ file.
+ The
+\family typewriter
+.cfg
+\family default
+ file is extensively documented, to provide detailed information on the
+ various parameters.
+\end_layout
+
+\begin_layout Subsubsection
+Step20 - Static Dike Intrusion
+\end_layout
+
+\begin_layout Standard
+The
+\family typewriter
+step20.cfg
+\family default
+ file defines a problem with spatially varying tensile normal tractions
+ on the fault surface associated with a fluid intrusion.
+ The lateral sides and bottom of the domain are fixed using Dirichlet (roller)
+ boundary conditions.
+ As in the other examples, we also setup output for the ground surface.
+\end_layout
+
+\begin_layout Standard
+We use the FaultCohesiveDyn object to impose tractions on the fault surface.
+ We must include a fault constitutive model so we choose static friction
+ with a coefficient of friction of 0.1.
+ The coefficient of friction is irrelevant for the center of the fault where
+ we impose uniform tensile tractions (10 MPa) and the fault opens, but it
+ facilitates clamping the edges of the fault via compressive normal tractions
+ (-100 MPa).
+ Note that we must set the property
+\family typewriter
+open_free_surface
+\family default
+ to True in order for the tractions to be imposed when the fault is open;
+ the default behavior for fault opening is a free surface (the two sides
+ of the fault are completely uncoupled).
+ The most important fault parameters for prescribing the tensile fault tractions
+ are
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.interfaces.fault]
+\end_layout
+
+\begin_layout LyX-Code
+open_free_surface = True
+\begin_inset Newline newline
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+traction_perturbation = pylith.faults.TractPerturbation
+\begin_inset Newline newline
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.interfaces.fault.traction_perturbation]
+\end_layout
+
+\begin_layout LyX-Code
+db_initial = spatialdata.spatialdb.SimpleDB
+\end_layout
+
+\begin_layout LyX-Code
+db_initial.label = Initial fault tractions
+\end_layout
+
+\begin_layout LyX-Code
+db_initial.iohandler.filename = spatialdb/tractions_opening.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+db_initial.query_type = nearest
+\end_layout
+
+\begin_layout Standard
+When we have run the simulation, the output VTK files will be contained
+ in
+\family typewriter
+examples/3d/hex8/output
+\family default
+ (all with a prefix of
+\family typewriter
+step20
+\family default
+).
+ Results using ParaView are shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:step20-disp"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step20_disp.png
+ lyxscale 50
+ width 10cm
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Displacement magnitude for example
+\family typewriter
+step20
+\family default
+ visualized using ParaView.
+
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:step20-disp"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dhex8/surfload/surfload.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dhex8/surfload/surfload.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dhex8/surfload/surfload.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -153,7 +153,7 @@
\end_layout
\begin_layout Subsubsection
-Step18 - Static surface load
+Step18 - Static Surface Load
\end_layout
\begin_layout Standard
@@ -389,7 +389,7 @@
\end_layout
\begin_layout Subsubsection
-Step19 - Time-dependent surface load
+Step19 - Time-Dependent Surface Load
\end_layout
\begin_layout Standard
@@ -497,7 +497,14 @@
for a discussion of the output parameters.
This type of output is designed for comparison against observations and
- inversions and output via HDF5 files (see Section ??).
+ inversions and output via HDF5 files (see Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:HDF5/Xdmf-Output"
+
+\end_inset
+
+).
\end_layout
\begin_layout Standard
@@ -522,8 +529,11 @@
\begin_inset Caption
\begin_layout Plain Layout
-Stress field (zz-component) for example step19 at t = 200 years visualized
- using ParaView.
+Stress field (zz-component) for example
+\family typewriter
+step19
+\family default
+ at t = 200 years visualized using ParaView.
The stresses appear as 4 layers since we have used
\family typewriter
CellFilterAvgMesh
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dtet4/3dtet4.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dtet4/3dtet4.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/3dtet4/3dtet4.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,1954 +1,1954 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
-\use_default_options false
-\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding latin1
-\fontencoding global
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\use_non_tex_fonts false
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
-\graphics default
-\default_output_format default
-\output_sync 0
-\bibtex_command default
-\index_command default
-\paperfontsize default
-\spacing single
-\use_hyperref false
-\papersize default
-\use_geometry true
-\use_amsmath 0
-\use_esint 0
-\use_mhchem 1
-\use_mathdots 1
-\cite_engine basic
-\use_bibtopic false
-\use_indices false
-\paperorientation portrait
-\suppress_date false
-\use_refstyle 0
-\index Index
-\shortcut idx
-\color #008000
-\end_index
-\leftmargin 1in
-\topmargin 1in
-\rightmargin 1in
-\bottommargin 2in
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\paragraph_indentation default
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-3d-tet4"
-
-\end_inset
-
-Tutorial Using Tetrahedral Mesh Created by LaGriT
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Quasi-static solution
-\end_layout
-
-\begin_layout Itemize
-LaGriT mesh format
-\end_layout
-
-\begin_layout Itemize
-Dirichlet boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Linearly elastic isotropic material
-\end_layout
-
-\begin_layout Itemize
-Maxwell linear viscoelastic material
-\end_layout
-
-\begin_layout Itemize
-Specifying more than one material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Linear tetrahedral cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Itemize
-Custom algebraic multigrid preconditioner with split fields
-\end_layout
-
-\begin_layout Itemize
-Global uniform mesh refinement
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/3d/tet4.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial is a simple 3D example of a quasi-static finite element problem.
- It is a mesh composed of 852 linear tetrahedra subject to displacement
- boundary conditions.
- This example demonstrates the usage of the LaGriT mesh generation package
-
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-lagrit.lanl.gov
-\end_layout
-
-\end_inset
-
- to create a mesh, as well as describing how to use a LaGriT-generated mesh
- in PyLith.
- In this tutorial, we will walk through the steps necessary to construct,
- run, and visualize the results for two problems that use the same mesh.
- For each of these problems we also consider a simulation using a custom
- algebraic multigrid preconditioner with a globally uniformly refined mesh
- that reduces the node spacing by a factor of two.
- In addition to this manual, each of the files for the example problems
- includes extensive comments.
-\end_layout
-
-\begin_layout Subsection
-Mesh Generation and Description
-\end_layout
-
-\begin_layout Standard
-The mesh for these examples is a simple rectangular prism (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:3dtet4-mesh"
-
-\end_inset
-
-).
- This mesh would be quite difficult to generate by hand, so we use the LaGriT
- mesh generation package.
- For this example, we provide a documented command file in
-\family typewriter
-examples/3d/tet4.
-
-\family default
- Examination of this command file should provide some insight into how to
- use LaGriT with PyLith.
- For more detailed information refer to the LaGriT web site
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-lagrit.lanl.gov
-\end_layout
-
-\end_inset
-
-.
- If you have LaGriT installed on your machine, you can use the command file
- to create your own mesh.
- Otherwise, you can use the mesh that has already been created.
-\end_layout
-
-\begin_layout Standard
-There are two ways to use the command file.
- The simplest method is to go to the
-\family sans
-
-\family default
-examples directory (
-\family typewriter
-examples/3d/tet4
-\family default
-), start LaGriT, and then type:
-\end_layout
-
-\begin_layout LyX-Code
-input mesh_tet4_1000m.lagrit
-\end_layout
-
-\begin_layout Standard
-This will run the commands in that file, which will produce the necessary
- files to run the example.
- This method will create the mesh, but you will gain very little insight
- into what is being done.
- A more informative approach is to input each command directly.
- That way, you will see what each command does.
- You can simply copy and paste the commands from
-\family typewriter
-mesh_tet4_1000m.lagrit
-\family default
-.
- For example, the first six commands, which define the block shape, are
-\end_layout
-
-\begin_layout LyX-Code
-define / domain_xm / -3.0e+3
-\end_layout
-
-\begin_layout LyX-Code
-define / domain_xp / 3.0e+3
-\end_layout
-
-\begin_layout LyX-Code
-define / domain_ym / -3.0e+3
-\end_layout
-
-\begin_layout LyX-Code
-define / domain_yp / 3.0e+3
-\end_layout
-
-\begin_layout LyX-Code
-define / domain_zm / -4.0e+3
-\end_layout
-
-\begin_layout LyX-Code
-define / domain_zp / 0.0e+3
-\end_layout
-
-\begin_layout Standard
-Continuing through the remainder of the commands in
-\family typewriter
-mesh_tet4_1000m.lagrit
-\family default
-, you will eventually end up with the files
-\family typewriter
-tet4_1000m_binary.gmv
-\family default
-,
-\family typewriter
-tet4_1000m_ascii.gmv
-\family default
-,
-\family typewriter
-tet4_1000m_ascii.pset
-\family default
-, and
-\family typewriter
-tet4_1000m_binary.pset
-\family default
-.
- The ASCII files are not actually needed, but we create them so users can
- see what is contained in the files.
- These files may also be used instead of the binary versions, if desired.
- The
-\family typewriter
-.gmv
-\family default
- files define the mesh information, and they may be read directly by the
- GMV
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-laws.lanl.gov/XCM/gmv/GMVHome.html
-\end_layout
-
-\end_inset
-
- mesh visualization package.
- The
-\family typewriter
-.pset
-\family default
- files specify the vertices corresponding to each set of vertices on a surface
- used in the problem, including the fault as well as external boundaries
- to which boundary conditions are applied.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/tet4-mesh.jpg
- lyxscale 50
- scale 45
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of linear tetrahedral cells generated by LaGriT used for the
- example problems.
- The different colors represent the different materials.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:3dtet4-mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Additional Common Information
-\end_layout
-
-\begin_layout Standard
-In addition to the mesh, the example problems share additional information.
- In such cases it is generally useful to create a file named
-\family typewriter
-pylithapp.cfg
-\family default
- in the run directory, since this file is read automatically every time
- PyLith is run.
- Settings specific to a particular problem may be placed in other
-\family typewriter
-.cfg
-\family default
- files, as described later, and then those files are placed on the command
- line.
- The settings contained in
-\family typewriter
-pylithapp.cfg
-\family default
- for this problem consist of:
-\end_layout
-
-\begin_layout Description
-pylithapp.journal.info Settings that control the verbosity of the output for
- the different components.
-\end_layout
-
-\begin_layout Description
-pylithapp.mesh_generator Settings that control mesh importing, such as the
- importer type, the filenames, and the spatial dimension of the mesh.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Settings that control the problem, such as the total
- time, time step size, and number of entries in the material array.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials Settings that control the material type,
- specify which material IDs are to be associated with a particular material
- type, and give the name of the spatial database containing material parameters
- for the mesh.
- The quadrature information is also given.
-\end_layout
-
-\begin_layout Description
-pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
- type.
-\end_layout
-
-\begin_layout Standard
-Since these examples use a mesh from LaGriT, we set the importer to
-\family typewriter
-MeshIO
-\family default
-Lagrit:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.mesh_generator]
-\end_layout
-
-\begin_layout LyX-Code
-reader = pylith.meshio.MeshIOLagrit
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.mesh_generator.reader]
-\end_layout
-
-\begin_layout LyX-Code
-filename_gmv = mesh/tet4_1000m_binary.gmv
-\end_layout
-
-\begin_layout LyX-Code
-filename_pset = mesh/tet4_1000m_binary.pset
-\end_layout
-
-\begin_layout LyX-Code
-flip_endian = True
-\end_layout
-
-\begin_layout LyX-Code
-# record_header_32bit = False
-\end_layout
-
-\begin_layout Standard
-Notice that there are a couple of settings pertinent to binary files.
- The first flag (
-\family typewriter
-flip_endian
-\family default
-) is used if the binary files were produced on a machine with a different
- endianness than the machine on which they are being read.
- If you get an error when attempting to run an example, you may need to
- change the setting of this flag.
- The second flag (
-\family typewriter
-record_header_32bit
-\family default
-) may need to be set to
-\family typewriter
-False
-\family default
- if the version of LaGriT being used has 64-bit Fortran record headers.
-
-\end_layout
-
-\begin_layout Standard
-This example differs from previous examples, because we specify two material
- groups:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent]
-\end_layout
-
-\begin_layout LyX-Code
-materials = [elastic,viscoelastic]
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.materials.elastic]
-\end_layout
-
-\begin_layout LyX-Code
-label = Elastic material
-\end_layout
-
-\begin_layout LyX-Code
-id = 1
-\end_layout
-
-\begin_layout LyX-Code
-db.iohandler.filename = spatialdb/mat_elastic.spatialdb
-\end_layout
-
-\begin_layout LyX-Code
-quadrature.cell = pylith.feassemble.FIATSimplex
-\end_layout
-
-\begin_layout LyX-Code
-quadrature.cell.shape = tetrahedron
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.materials.viscoelastic]
-\end_layout
-
-\begin_layout LyX-Code
-label = Viscoelastic material
-\end_layout
-
-\begin_layout LyX-Code
-id = 2
-\end_layout
-
-\begin_layout LyX-Code
-db.iohandler.filename = spatialdb/mat_viscoelastic.spatialdb
-\end_layout
-
-\begin_layout LyX-Code
-quadrature.cell = pylith.feassemble.FIATSimplex
-\end_layout
-
-\begin_layout LyX-Code
-quadrature.cell.shape = tetrahedron
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout Standard
-The two materials correspond to the two different colors in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:3dtet4-mesh"
-
-\end_inset
-
-.
- Each material uses a different spatial database because the physical parameters
- are different.
- In generating the mesh within LaGriT, the mesh contains four materials
- as a result of how LaGriT handles materials and interior interfaces.
- Near the end of the LaGriT command file, we merge the materials on each
- side of the fault into a single material to simplify the input and output
- from PyLith.
- For this example, values describing three-dimensional elastic material
- properties are given by the single point in the spatial databases, resulting
- in uniform physical properties within each material.
-\end_layout
-
-\begin_layout Subsection
-Shear Displacement Example
-\end_layout
-
-\begin_layout Standard
-The first example problem is shearing of the mesh along the y-direction,
- with displacement boundary conditions applied on the planes corresponding
- to the minimum and maximum x-values.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step01.cfg
-\family default
-.
- These settings are:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies an implicit formulation for the problem
- and specifies the array of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.implicit Specifies an array of two output managers,
- one for the full domain, and another for a subdomain corresponding to the
- ground surface.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- right side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
- and
-\family typewriter
-y
-\family default
-), providing the label (defined in
-\family typewriter
-tet4_1000m_binary.pset
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database defining the boundary
- conditions (
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
- and
-\family typewriter
-y
-\family default
-), providing the label (defined in
-\family typewriter
-tet4_1000m_binary.
-\family default
-pset) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database defining the boundary
- conditions (
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.z_neg Specifies the boundary conditions for the
- bottom of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
- and
-\family typewriter
-y
-\family default
-), providing the label (defined in
-\family typewriter
-tet4_1000m_binary.
-\family default
-pset) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database defining the boundary
- conditions (
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain.writer Gives the base filename for
- VTK output over the entire domain (
-\family typewriter
-shearxy.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.subdomain Gives the label of the nodeset
- defining the subdomain and gives the base filename for VTK output over
- the subdomain corresponding to the ground surface (
-\family typewriter
-step01-groundsurf.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.elastic.output Gives the base filename for
- state variable output files for the
-\family typewriter
-elastic
-\family default
- material set (
-\family typewriter
-step01-elastic.vtk
-\family default
-), and causes state variables to be averaged over all quadrature points
- in each cell.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.viscoelastic.output Gives the base filename
- for state variable output files for the
-\family typewriter
-viscoelastic
-\family default
- material set (
-\family typewriter
-step01-viscoelastic.vtk
-\family default
-), and causes state variables to be averaged over all quadrature points
- in each cell.
-\end_layout
-
-\begin_layout Standard
-The values for the Dirichlet boundary conditions are described in the file
-
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-, as specified in
-\family typewriter
-step01.cfg
-\family default
-.
- The format of all spatial database files is similar.
- Because data are being specified using two control points (rather than
- being uniform over the mesh, for example), the data dimension is one.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-\size small
-tet4_1000m_binary.gmv
-\family default
-,
-\family typewriter
-tet4_1000m_binary.pset
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-mat_elastic.spatialdb
-\family default
-\size default
-, and
-\family typewriter
-mat_viscoelastic.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-\size small
-step01.cfg
-\family default
- and
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step01.cfg
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, six files will be produced.
- The first file is named
-\family typewriter
-step01_t0000000.vtk
-\family default
-.
- The
-\family typewriter
-t0000000
-\family default
- indicates that the output is for the first (and only) time step, corresponding
- to an elastic solution.
- This file contains mesh information as well as displacement values at the
- mesh vertices.
- The second file is named
-\family typewriter
-step01-statevars-elastic_t0000000.vtk
-\family default
-.
- This file contains the state variables for each cell in the material group
-
-\family typewriter
-elastic
-\family default
-.
- The default fields are the total strain and stress fields.
- These values are computed at each quadrature point in the cell.
- We have requested that the values be averaged over all quadrature points
- for each cell; however, since we only have a single quadrature point for
- each linear tetrahedron, this will have no effect.
- The third file (
-\family typewriter
-step01-statevars-viscoelastic_info.vtk
-\family default
-) gives the material properties used for the
-\family typewriter
-viscoelastic
-\family default
- material set.
- Since we have not specified which properties to write, the default properties
- (
-\family typewriter
-mu
-\family default
-,
-\family typewriter
-lambda
-\family default
-,
-\family typewriter
-density
-\family default
-) are written.
- There are two additional files containing the state variables for each
- of the material sets.
- The final file (
-\family typewriter
-step01-groundsurf_t0000000.vtk
-\family default
-) is analogous to
-\family typewriter
-step01_t0000000.vtk
-\family default
-, but in this case the results are only given for a subset of the mesh correspon
-ding to the ground surface.
- Also, the cells in this file are one dimension lower than the cells described
- in
-\family typewriter
-step01_t0000000.vtk
-\family default
-, so they are triangles rather than tetrahedra.
- All of the
-\family typewriter
-.vtk
-\family default
- files may be used with a number of visualization packages.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:3dtet4-shear"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/shear.jpg
- lyxscale 50
- scale 45
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the axial displacement example
- using a mesh composed of linear tetrahedral cells generated by LaGriT.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:3dtet4-shear"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Alternative Solver and Discretization Settings
-\end_layout
-
-\begin_layout Standard
-Example
-\family typewriter
-step01.cfg
-\family default
- uses the additive Schwarz preconditioner in conjunction with a classical
- Gram-Schmidt orthogonalization iterative solver.
- This preconditioner works reasonably well but the number of iterations
- generally scales with problem size.
- Even this small, simple problem requires 24 iterations.
- In this example (
-\family typewriter
-step02.cfg
-\family default
-), we use a more sophisticated preconditioner that preconditions the degrees
- of freedom associated with the three Cartesian coordinates separately while
- using an algebraic multigrid algorithm (see Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:petsc:options"
-
-\end_inset
-
- for details).
- Additionally, we illustrate the use of global uniform mesh refinement to
- increase the resolution of the solution by a factor of two.
- Because the mesh is refined in parallel after distribution, this technique
- can be used to run a larger problem than would be possible if the full
- resolution mesh had to be generated by the mesh generator.
- LaGriT runs only in serial and CUBIT has extremely limited parallel mesh
- generation capabilities.
- Table
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "tab:3dtet4:solver:cmp"
-
-\end_inset
-
- shows the improved efficiency of the solver using the split fields with
- the algebraic multigrid preconditioner, especially as the problem size
- becomes larger.
- We have found similar results for other problems.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Caption
-
-\begin_layout Plain Layout
-\begin_inset CommandInset label
-LatexCommand label
-name "tab:3dtet4:solver:cmp"
-
-\end_inset
-
-Number of iterations in linear solve for the Shear Displacement and Kinematic
- Fault Slip problems discussed in this section.
- The preconditioner using split fields and an algebraic multigrid algorithm
- solves the linear system with fewer iterations with only a small to moderate
- increase as the problem size grows.
-\end_layout
-
-\end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="9" columns="4">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="1.5in">
-<column alignment="center" valignment="middle" width="1.25in">
-<column alignment="center" valignment="top" width="1.5in">
-<column alignment="center" valignment="top" width="1in">
-<row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\series bold
-Problem
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\series bold
-Preconditioner
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\series bold
-Refinement
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\series bold
-# Iterations in Solve
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Shear Displacement
-\end_layout
-
-\end_inset
-</cell>
-<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-additive Schwarz
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-none (546 DOF)
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-24 (step01)
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell multirow="4" alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-2x refinement
-\end_layout
-
-\begin_layout Plain Layout
-(3890 DOF)
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-48
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-split fields with algebraic multigrid
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-none (546 DOF)
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-12
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell multirow="4" alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-2x refinement
-\end_layout
-
-\begin_layout Plain Layout
-(3890 DOF)
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-17 (step02)
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell multirow="3" alignment="left" valignment="middle" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Kinematic Fault Slip
-\end_layout
-
-\end_inset
-</cell>
-<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-additive Schwarz
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-none (735 DOF)
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-35 (step03)
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell multirow="4" alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-2x refinement
-\end_layout
-
-\begin_layout Plain Layout
-(4527 DOF)
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-83
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell multirow="3" alignment="left" valignment="middle" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-split fields with algebraic multigrid
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-none (735 DOF)
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-33
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell multirow="4" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell multirow="4" alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-2x refinement
-\end_layout
-
-\begin_layout Plain Layout
-(4527 DOF)
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-53 (step04)
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The field splitting and algebraic multigrid preconditioning are set up in
-
-\family typewriter
-step02.cfg
-\family default
- with the following parameters:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.formulation]
-\end_layout
-
-\begin_layout LyX-Code
-split_fields = True
-\end_layout
-
-\begin_layout LyX-Code
-matrix_type = aij
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.petsc]
-\end_layout
-
-\begin_layout LyX-Code
-fs_pc_type = fieldsplit
-\end_layout
-
-\begin_layout LyX-Code
-fs_pc_fieldsplit_real_diagonal =
-\end_layout
-
-\begin_layout LyX-Code
-fs_pc_fieldsplit_type = multiplicative
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_0_pc_type = ml
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_1_pc_type = ml
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_2_pc_type = ml
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_0_ksp_type = preonly
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_1_ksp_type = preonly
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_2_ksp_type = preonly
-\end_layout
-
-\begin_layout Standard
-The uniform global refinement requires changing just a single parameter:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.mesh_generator]
-\end_layout
-
-\begin_layout LyX-Code
-refiner = pylith.topology.RefineUniform
-\end_layout
-
-\begin_layout Subsection
-Kinematic Fault Slip Example
-\end_layout
-
-\begin_layout Standard
-The next example problem is a right-lateral fault slip applied on the vertical
- fault defined by
-\family typewriter
-x = 0
-\family default
-.
- The left and right sides of the mesh are fixed in the
-\family typewriter
-x
-\family default
-,
-\family typewriter
-y
-\family default
-, and
-\family typewriter
-z
-\family default
- directions.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step03.cfg
-\family default
-.
- These settings are:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies an implicit formulation for the problem,
- the array of boundary conditions, and the array of interfaces.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.implicit Specifies an array of two output managers,
- one for the full domain, and another for a subdomain corresponding to the
- ground surface.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- right side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
-,
-\family typewriter
-y
-\family default
-, and
-\family typewriter
-z
-\family default
-), providing the label (defined in
-\family typewriter
-tet4_1000m_binary.
-\family default
-pset) defining the points desired, and assigning a label to the boundary
- condition set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
-,
-\family typewriter
-y
-\family default
-, and
-\family typewriter
-z
-\family default
-), providing the label (defined in
-\family typewriter
-tet4_1000m_binary.
-\family default
-pset) defining the points desired, and assigning a label to the boundary
- condition set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces Gives the label (defined in
-\family typewriter
-tet4_1000m_binary.
-\family default
-pset) defining the points on the fault, provides quadrature information,
- and then gives database names for material properties (needed for conditioning)
-, fault slip, peak fault slip rate, and fault slip time.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain.writer Gives the base filename for
- VTK output over the entire domain (
-\family typewriter
-step03.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.subdomain Gives the label of the nodeset
- defining the subdomain and gives the base filename for VTK output over
- the subdomain corresponding to the ground surface (
-\family typewriter
-step03-groundsurf.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces.fault.output.writer Gives the base filename
- for cohesive cell output files (
-\family typewriter
-step03-fault.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.elastic.output Gives the base filename for
- state variable output files for the
-\family typewriter
-elastic
-\family default
- material set (
-\family typewriter
-step03-statevars-elastic.vtk
-\family default
-), and causes state variables to be averaged over all quadrature points
- in each cell.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.viscoelastic.output Gives the base filename
- for state variable output files for the
-\family typewriter
-viscoelastic
-\family default
- material set (
-\family typewriter
-step03-statevars-viscoelastic.vtk
-\family default
-), and causes state variables to be averaged over all quadrature points
- in each cell.
-\end_layout
-
-\begin_layout Standard
-The fault example requires three additional database files that were not
- needed for the simple displacement example.
- The first file (
-\family typewriter
-finalslip.spatialdb
-\family default
-) specifies a constant value of 2 m of right-lateral fault slip that then
- tapers linearly to zero from 2 km to 4 km depth, and a linearly-varying
- amount of reverse slip, with a maximum of 0.25 m at the surface, linearly
- tapering to 0 m at 2 km depth.
- The data dimension is one since the data vary linearly along a vertical
- line.
- The default slip time function is a step-function, so we also must provide
- the time at which slip begins.
- The elastic solution is associated with advancing from
-\begin_inset Formula $t=-dt$
-\end_inset
-
- to
-\begin_inset Formula $t=0$
-\end_inset
-
-, so we set the slip initiation time for the step-function to 0 in
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-\size small
-tet4_1000m_binary.gmv
-\family default
-,
-\family typewriter
-tet4_1000m_binary.pset
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-mat_elastic.spatialdb
-\family default
-\size default
-, and
-\family typewriter
-mat_viscoelastic.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-\size small
-step03.cfg
-\family default
-,
-\family typewriter
-finalslip.spatialdb
-\family default
-, and
-\family typewriter
-sliptime.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step03.cfg
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, eight files will be produced.
- The first file is named
-\family typewriter
-step03_t0000000.vtk
-\family default
-.
- The
-\family typewriter
-t0000000
-\family default
- indicates that the output is for the first (and only) time step, corresponding
- to an elastic solution.
- This file contains mesh information as well as displacement values at the
- mesh vertices.
- The second file is named
-\family typewriter
-step03-statevars-elastic_t0000000.vtk
-\family default
-.
- This file contains the state variables for each cell in the material group
-
-\family typewriter
-elastic
-\family default
-.
- The default fields are the total strain and stress fields.
- We have requested that the values be averaged over all quadrature points
- for each cell; however, since we only have a single quadrature point for
- each linear tetrahedron, this will have no effect.
- The third file (
-\family typewriter
-step03-statevars-viscoelastic_info.vtk
-\family default
-) gives the material properties used for the
-\family typewriter
-viscoelastic
-\family default
- material set.
- Since we have not specified which properties to write, the default properties
- (
-\family typewriter
-mu
-\family default
-,
-\family typewriter
-lambda
-\family default
-,
-\family typewriter
-density
-\family default
-) are written.
- There are two additional files containing the state variables for each
- of the material sets.
- The file
-\family typewriter
-step03-groundsurf_t0000000.vtk
-\family default
- is analogous to
-\family typewriter
-step03_t0000000.vtk
-\family default
-, but in this case the results are only given for a subset of the mesh correspon
-ding to the ground surface.
- Also, the cells in this file are one dimension lower than the cells described
- in
-\family typewriter
-step03_t0000000.vtk
-\family default
-, so they are triangles rather than tetrahedra.
- The file
-\family typewriter
-step03-fault_t0000000.vtk
-\family default
- gives the specified fault slip for each vertex on the fault, along with
- the computed traction change for the cohesive cell.
- The final file,
-\family typewriter
-step03-fault_info.vtk
-\family default
-, provides information such as the normal direction, final slip, and slip
- time for each vertex on the fault.
- All of the
-\family typewriter
-.vtk
-\family default
- files may be used with a number of visualization packages.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:3dtet-disloc"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/dislocation.jpg
- lyxscale 50
- scale 45
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the kinematic fault example
- using a mesh composed of linear tetrahedral cells generated by LaGriT.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:3dtet-disloc"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Alternative Solver and Discretization Settings
-\end_layout
-
-\begin_layout Standard
-As we did for the Shear Dislocation examples, in
-\family typewriter
-step04.cfg
-\family default
- we switch to using the split fields and algebraic multigrid preconditioner
- along with global uniform mesh refinement.
- Because PyLith implements fault slip using Lagrange multipliers, we make
- a few small adjusments to the solver settings.
- As discussed in Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:petsc:options"
-
-\end_inset
-
-, we use a custom preconditioner for the Lagrange multiplier degrees of
- freedom when preconditioning with field splitting.
- Within
-\family typewriter
-step04.cfg
-\family default
- we turn on the use of the custom preconditioner for the Lagrange multiplier
- degrees of freedom and add the corresponding settings for the fourth field
- for the algebraic multigrid algorithm,
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.formulation]
-\end_layout
-
-\begin_layout LyX-Code
-split_fields = True
-\end_layout
-
-\begin_layout LyX-Code
-use_custom_constraint_pc = True
-\end_layout
-
-\begin_layout LyX-Code
-matrix_type = aij
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.petsc]
-\end_layout
-
-\begin_layout LyX-Code
-fs_pc_type = fieldsplit
-\end_layout
-
-\begin_layout LyX-Code
-fs_pc_fieldsplit_real_diagonal =
-\end_layout
-
-\begin_layout LyX-Code
-fs_pc_fieldsplit_type = multiplicative
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_0_pc_type = ml
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_1_pc_type = ml
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_2_pc_type = ml
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_3_pc_type = ml
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_0_ksp_type = preonly
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_1_ksp_type = preonly
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_2_ksp_type = preonly
-\end_layout
-
-\begin_layout LyX-Code
-fs_fieldsplit_3_ksp_type = preonly
-\end_layout
-
-\begin_layout Standard
-Table
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "tab:3dtet4:solver:cmp"
-
-\end_inset
-
- shows the improved efficiency of the solver using the split fields with
- the algebraic multigrid preconditioner.
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 2in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-3d-tet4"
+
+\end_inset
+
+Tutorial Using Tetrahedral Mesh Created by LaGriT
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Quasi-static solution
+\end_layout
+
+\begin_layout Itemize
+LaGriT mesh format
+\end_layout
+
+\begin_layout Itemize
+Dirichlet boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Linearly elastic isotropic material
+\end_layout
+
+\begin_layout Itemize
+Maxwell linear viscoelastic material
+\end_layout
+
+\begin_layout Itemize
+Specifying more than one material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Linear tetrahedral cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Itemize
+Custom algebraic multigrid preconditioner with split fields
+\end_layout
+
+\begin_layout Itemize
+Global uniform mesh refinement
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/3d/tet4.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial is a simple 3D example of a quasi-static finite element problem.
+ It is a mesh composed of 852 linear tetrahedra subject to displacement
+ boundary conditions.
+ This example demonstrates the usage of the LaGriT mesh generation package
+
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+lagrit.lanl.gov
+\end_layout
+
+\end_inset
+
+ to create a mesh, as well as describing how to use a LaGriT-generated mesh
+ in PyLith.
+ In this tutorial, we will walk through the steps necessary to construct,
+ run, and visualize the results for two problems that use the same mesh.
+ For each of these problems we also consider a simulation using a custom
+ algebraic multigrid preconditioner with a globally uniformly refined mesh
+ that reduces the node spacing by a factor of two.
+ In addition to this manual, each of the files for the example problems
+ includes extensive comments.
+\end_layout
+
+\begin_layout Subsection
+Mesh Generation and Description
+\end_layout
+
+\begin_layout Standard
+The mesh for these examples is a simple rectangular prism (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:3dtet4-mesh"
+
+\end_inset
+
+).
+ This mesh would be quite difficult to generate by hand, so we use the LaGriT
+ mesh generation package.
+ For this example, we provide a documented command file in
+\family typewriter
+examples/3d/tet4.
+
+\family default
+ Examination of this command file should provide some insight into how to
+ use LaGriT with PyLith.
+ For more detailed information refer to the LaGriT website
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+lagrit.lanl.gov
+\end_layout
+
+\end_inset
+
+.
+ If you have LaGriT installed on your machine, you can use the command file
+ to create your own mesh.
+ Otherwise, you can use the mesh that has already been created.
+\end_layout
+
+\begin_layout Standard
+There are two ways to use the command file.
+ The simplest method is to go to the
+\family sans
+
+\family default
+examples directory (
+\family typewriter
+examples/3d/tet4
+\family default
+), start LaGriT, and then type:
+\end_layout
+
+\begin_layout LyX-Code
+input mesh_tet4_1000m.lagrit
+\end_layout
+
+\begin_layout Standard
+This will run the commands in that file, which will produce the necessary
+ files to run the example.
+ This method will create the mesh, but you will gain very little insight
+ into what is being done.
+ A more informative approach is to input each command directly.
+ That way, you will see what each command does.
+ You can simply copy and paste the commands from
+\family typewriter
+mesh_tet4_1000m.lagrit
+\family default
+.
+ For example, the first six commands, which define the block shape, are
+\end_layout
+
+\begin_layout LyX-Code
+define / domain_xm / -3.0e+3
+\end_layout
+
+\begin_layout LyX-Code
+define / domain_xp / 3.0e+3
+\end_layout
+
+\begin_layout LyX-Code
+define / domain_ym / -3.0e+3
+\end_layout
+
+\begin_layout LyX-Code
+define / domain_yp / 3.0e+3
+\end_layout
+
+\begin_layout LyX-Code
+define / domain_zm / -4.0e+3
+\end_layout
+
+\begin_layout LyX-Code
+define / domain_zp / 0.0e+3
+\end_layout
+
+\begin_layout Standard
+Continuing through the remainder of the commands in
+\family typewriter
+mesh_tet4_1000m.lagrit
+\family default
+, you will eventually end up with the files
+\family typewriter
+tet4_1000m_binary.gmv
+\family default
+,
+\family typewriter
+tet4_1000m_ascii.gmv
+\family default
+,
+\family typewriter
+tet4_1000m_ascii.pset
+\family default
+, and
+\family typewriter
+tet4_1000m_binary.pset
+\family default
+.
+ The ASCII files are not actually needed, but we create them so users can
+ see what is contained in the files.
+ These files may also be used instead of the binary versions, if desired.
+ The
+\family typewriter
+.gmv
+\family default
+ files define the mesh information, and they may be read directly by the
+ GMV
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+laws.lanl.gov/XCM/gmv/GMVHome.html
+\end_layout
+
+\end_inset
+
+ mesh visualization package.
+ The
+\family typewriter
+.pset
+\family default
+ files specify the vertices corresponding to each set of vertices on a surface
+ used in the problem, including the fault as well as external boundaries
+ to which boundary conditions are applied.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/tet4-mesh.jpg
+ lyxscale 50
+ scale 45
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of linear tetrahedral cells generated by LaGriT used for the
+ example problems.
+ The different colors represent the different materials.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:3dtet4-mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Additional Common Information
+\end_layout
+
+\begin_layout Standard
+In addition to the mesh, the example problems share additional information.
+ In such cases it is generally useful to create a file named
+\family typewriter
+pylithapp.cfg
+\family default
+ in the run directory, since this file is read automatically every time
+ PyLith is run.
+ Settings specific to a particular problem may be placed in other
+\family typewriter
+.cfg
+\family default
+ files, as described later, and then those files are placed on the command
+ line.
+ The settings contained in
+\family typewriter
+pylithapp.cfg
+\family default
+ for this problem consist of:
+\end_layout
+
+\begin_layout Description
+pylithapp.journal.info Settings that control the verbosity of the output for
+ the different components.
+\end_layout
+
+\begin_layout Description
+pylithapp.mesh_generator Settings that control mesh importing, such as the
+ importer type, the filenames, and the spatial dimension of the mesh.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Settings that control the problem, such as the total
+ time, time-step size, and number of entries in the material array.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials Settings that control the material type,
+ specify which material IDs are to be associated with a particular material
+ type, and give the name of the spatial database containing material parameters
+ for the mesh.
+ The quadrature information is also given.
+\end_layout
+
+\begin_layout Description
+pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
+ type.
+\end_layout
+
+\begin_layout Standard
+Since these examples use a mesh from LaGriT, we set the importer to
+\family typewriter
+MeshIO
+\family default
+Lagrit:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.mesh_generator]
+\end_layout
+
+\begin_layout LyX-Code
+reader = pylith.meshio.MeshIOLagrit
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.mesh_generator.reader]
+\end_layout
+
+\begin_layout LyX-Code
+filename_gmv = mesh/tet4_1000m_binary.gmv
+\end_layout
+
+\begin_layout LyX-Code
+filename_pset = mesh/tet4_1000m_binary.pset
+\end_layout
+
+\begin_layout LyX-Code
+flip_endian = True
+\end_layout
+
+\begin_layout LyX-Code
+# record_header_32bit = False
+\end_layout
+
+\begin_layout Standard
+Notice that there are a couple of settings pertinent to binary files.
+ The first flag (
+\family typewriter
+flip_endian
+\family default
+) is used if the binary files were produced on a machine with a different
+ endianness than the machine on which they are being read.
+ If you get an error when attempting to run an example, you may need to
+ change the setting of this flag.
+ The second flag (
+\family typewriter
+record_header_32bit
+\family default
+) may need to be set to
+\family typewriter
+False
+\family default
+ if the version of LaGriT being used has 64-bit Fortran record headers.
+
+\end_layout
+
+\begin_layout Standard
+This example differs from previous examples, because we specify two material
+ groups:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent]
+\end_layout
+
+\begin_layout LyX-Code
+materials = [elastic,viscoelastic]
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials.elastic]
+\end_layout
+
+\begin_layout LyX-Code
+label = Elastic material
+\end_layout
+
+\begin_layout LyX-Code
+id = 1
+\end_layout
+
+\begin_layout LyX-Code
+db.iohandler.filename = spatialdb/mat_elastic.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+quadrature.cell = pylith.feassemble.FIATSimplex
+\end_layout
+
+\begin_layout LyX-Code
+quadrature.cell.shape = tetrahedron
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials.viscoelastic]
+\end_layout
+
+\begin_layout LyX-Code
+label = Viscoelastic material
+\end_layout
+
+\begin_layout LyX-Code
+id = 2
+\end_layout
+
+\begin_layout LyX-Code
+db.iohandler.filename = spatialdb/mat_viscoelastic.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+quadrature.cell = pylith.feassemble.FIATSimplex
+\end_layout
+
+\begin_layout LyX-Code
+quadrature.cell.shape = tetrahedron
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout Standard
+The two materials correspond to the two different colors in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:3dtet4-mesh"
+
+\end_inset
+
+.
+ Each material uses a different spatial database because the physical parameters
+ are different.
+ In generating the mesh within LaGriT, the mesh contains four materials
+ as a result of how LaGriT handles materials and interior interfaces.
+ Near the end of the LaGriT command file, we merge the materials on each
+ side of the fault into a single material to simplify the input and output
+ from PyLith.
+ For this example, values describing three-dimensional elastic material
+ properties are given by the single point in the spatial databases, resulting
+ in uniform physical properties within each material.
+\end_layout
+
+\begin_layout Subsection
+Shear Displacement Example
+\end_layout
+
+\begin_layout Standard
+The first example problem is shearing of the mesh along the y-direction,
+ with displacement boundary conditions applied on the planes corresponding
+ to the minimum and maximum x-values.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step01.cfg
+\family default
+.
+ These settings are:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies an implicit formulation for the problem
+ and specifies the array of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.implicit Specifies an array of two output managers,
+ one for the full domain, and another for a subdomain corresponding to the
+ ground surface.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
+ right side of the mesh, defining which degrees of freedom are being constrained
+ (
+\family typewriter
+x
+\family default
+ and
+\family typewriter
+y
+\family default
+), providing the label (defined in
+\family typewriter
+tet4_1000m_binary.pset
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database defining the boundary
+ conditions (
+\family typewriter
+fixeddisp_shear.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (
+\family typewriter
+x
+\family default
+ and
+\family typewriter
+y
+\family default
+), providing the label (defined in
+\family typewriter
+tet4_1000m_binary.
+\family default
+pset) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database defining the boundary
+ conditions (
+\family typewriter
+fixeddisp_shear.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.z_neg Specifies the boundary conditions for the
+ bottom of the mesh, defining which degrees of freedom are being constrained
+ (
+\family typewriter
+x
+\family default
+ and
+\family typewriter
+y
+\family default
+), providing the label (defined in
+\family typewriter
+tet4_1000m_binary.
+\family default
+pset) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database defining the boundary
+ conditions (
+\family typewriter
+fixeddisp_shear.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain.writer Gives the base filename for
+ VTK output over the entire domain (
+\family typewriter
+shearxy.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.subdomain Gives the label of the nodeset
+ defining the subdomain and gives the base filename for VTK output over
+ the subdomain corresponding to the ground surface (
+\family typewriter
+step01-groundsurf.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials.elastic.output Gives the base filename for
+ state variable output files for the
+\family typewriter
+elastic
+\family default
+ material set (
+\family typewriter
+step01-elastic.vtk
+\family default
+), and causes state variables to be averaged over all quadrature points
+ in each cell.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials.viscoelastic.output Gives the base filename
+ for state variable output files for the
+\family typewriter
+viscoelastic
+\family default
+ material set (
+\family typewriter
+step01-viscoelastic.vtk
+\family default
+), and causes state variables to be averaged over all quadrature points
+ in each cell.
+\end_layout
+
+\begin_layout Standard
+The values for the Dirichlet boundary conditions are described in the file
+
+\family typewriter
+fixeddisp_shear.spatialdb
+\family default
+, as specified in
+\family typewriter
+step01.cfg
+\family default
+.
+ The format of all spatial database files is similar.
+ Because data are being specified using two control points (rather than
+ being uniform over the mesh, for example), the data dimension is one.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+\size small
+tet4_1000m_binary.gmv
+\family default
+,
+\family typewriter
+tet4_1000m_binary.pset
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+mat_elastic.spatialdb
+\family default
+\size default
+, and
+\family typewriter
+mat_viscoelastic.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+\size small
+step01.cfg
+\family default
+ and
+\family typewriter
+fixeddisp_shear.spatialdb
+\family default
+\size default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step01.cfg
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, six files will be produced.
+ The first file is named
+\family typewriter
+step01_t0000000.vtk
+\family default
+.
+ The
+\family typewriter
+t0000000
+\family default
+ indicates that the output is for the first (and only) time step, corresponding
+ to an elastic solution.
+ This file contains mesh information as well as displacement values at the
+ mesh vertices.
+ The second file is named
+\family typewriter
+step01-statevars-elastic_t0000000.vtk
+\family default
+.
+ This file contains the state variables for each cell in the material group
+
+\family typewriter
+elastic
+\family default
+.
+ The default fields are the total strain and stress fields.
+ These values are computed at each quadrature point in the cell.
+ We have requested that the values be averaged over all quadrature points
+ for each cell; however, since we only have a single quadrature point for
+ each linear tetrahedron, this will have no effect.
+ The third file (
+\family typewriter
+step01-statevars-viscoelastic_info.vtk
+\family default
+) gives the material properties used for the
+\family typewriter
+viscoelastic
+\family default
+ material set.
+ Since we have not specified which properties to write, the default properties
+ (
+\family typewriter
+mu
+\family default
+,
+\family typewriter
+lambda
+\family default
+,
+\family typewriter
+density
+\family default
+) are written.
+ There are two additional files containing the state variables for each
+ of the material sets.
+ The final file (
+\family typewriter
+step01-groundsurf_t0000000.vtk
+\family default
+) is analogous to
+\family typewriter
+step01_t0000000.vtk
+\family default
+, but in this case the results are only given for a subset of the mesh correspon
+ding to the ground surface.
+ Also, the cells in this file are one dimension lower than the cells described
+ in
+\family typewriter
+step01_t0000000.vtk
+\family default
+, so they are triangles rather than tetrahedra.
+ All of the
+\family typewriter
+.vtk
+\family default
+ files may be used with a number of visualization packages.
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:3dtet4-shear"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/shear.jpg
+ lyxscale 50
+ scale 45
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the axial displacement example
+ using a mesh composed of linear tetrahedral cells generated by LaGriT.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:3dtet4-shear"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Alternative Solver and Discretization Settings
+\end_layout
+
+\begin_layout Standard
+Example
+\family typewriter
+step01.cfg
+\family default
+ uses the additive Schwarz preconditioner in conjunction with a classical
+ Gram-Schmidt orthogonalization iterative solver.
+ This preconditioner works reasonably well but the number of iterations
+ generally scales with problem size.
+ Even this small, simple problem requires 24 iterations.
+ In this example (
+\family typewriter
+step02.cfg
+\family default
+), we use a more sophisticated preconditioner that preconditions the degrees
+ of freedom associated with the three Cartesian coordinates separately while
+ using an algebraic multigrid algorithm (see Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:petsc:options"
+
+\end_inset
+
+ for details).
+ Additionally, we illustrate the use of global uniform mesh refinement to
+ increase the resolution of the solution by a factor of two.
+ Because the mesh is refined in parallel after distribution, this technique
+ can be used to run a larger problem than would be possible if the full
+ resolution mesh had to be generated by the mesh generator.
+ LaGriT runs only in serial and CUBIT has extremely limited parallel mesh
+ generation capabilities.
+ Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tab:3dtet4:solver:cmp"
+
+\end_inset
+
+ shows the improved efficiency of the solver using the split fields with
+ the algebraic multigrid preconditioner, especially as the problem size
+ becomes larger.
+ We have found similar results for other problems.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Caption
+
+\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "tab:3dtet4:solver:cmp"
+
+\end_inset
+
+Number of iterations in linear solve for the Shear Displacement and Kinematic
+ Fault Slip problems discussed in this section.
+ The preconditioner using split fields and an algebraic multigrid algorithm
+ solves the linear system with fewer iterations with only a small to moderate
+ increase as the problem size grows.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="4">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="1.5in">
+<column alignment="center" valignment="middle" width="1.25in">
+<column alignment="center" valignment="top" width="1.5in">
+<column alignment="center" valignment="top" width="1in">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Problem
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Preconditioner
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Refinement
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+# Iterations in Solve
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Shear Displacement
+\end_layout
+
+\end_inset
+</cell>
+<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+additive Schwarz
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+none (546 DOF)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+24 (step01)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multirow="4" alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2x refinement
+\end_layout
+
+\begin_layout Plain Layout
+(3890 DOF)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+48
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+split fields with algebraic multigrid
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+none (546 DOF)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+12
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multirow="4" alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2x refinement
+\end_layout
+
+\begin_layout Plain Layout
+(3890 DOF)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+17 (step02)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multirow="3" alignment="left" valignment="middle" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Kinematic Fault Slip
+\end_layout
+
+\end_inset
+</cell>
+<cell multirow="3" alignment="left" valignment="middle" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+additive Schwarz
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+none (735 DOF)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+35 (step03)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multirow="4" alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2x refinement
+\end_layout
+
+\begin_layout Plain Layout
+(4527 DOF)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+83
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multirow="4" alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multirow="3" alignment="left" valignment="middle" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+split fields with algebraic multigrid
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+none (735 DOF)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+33
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell multirow="4" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell multirow="4" alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+2x refinement
+\end_layout
+
+\begin_layout Plain Layout
+(4527 DOF)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+53 (step04)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The field splitting and algebraic multigrid preconditioning are set up in
+
+\family typewriter
+step02.cfg
+\family default
+ with the following parameters:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.formulation]
+\end_layout
+
+\begin_layout LyX-Code
+split_fields = True
+\end_layout
+
+\begin_layout LyX-Code
+matrix_type = aij
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.petsc]
+\end_layout
+
+\begin_layout LyX-Code
+fs_pc_type = fieldsplit
+\end_layout
+
+\begin_layout LyX-Code
+fs_pc_fieldsplit_real_diagonal =
+\end_layout
+
+\begin_layout LyX-Code
+fs_pc_fieldsplit_type = multiplicative
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_0_pc_type = ml
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_1_pc_type = ml
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_2_pc_type = ml
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_0_ksp_type = preonly
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_1_ksp_type = preonly
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_2_ksp_type = preonly
+\end_layout
+
+\begin_layout Standard
+The uniform global refinement requires changing just a single parameter:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.mesh_generator]
+\end_layout
+
+\begin_layout LyX-Code
+refiner = pylith.topology.RefineUniform
+\end_layout
+
+\begin_layout Subsection
+Kinematic Fault Slip Example
+\end_layout
+
+\begin_layout Standard
+The next example problem is a right-lateral fault slip applied on the vertical
+ fault defined by
+\family typewriter
+x = 0
+\family default
+.
+ The left and right sides of the mesh are fixed in the
+\family typewriter
+x
+\family default
+,
+\family typewriter
+y
+\family default
+, and
+\family typewriter
+z
+\family default
+ directions.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step03.cfg
+\family default
+.
+ These settings are:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies an implicit formulation for the problem,
+ the array of boundary conditions, and the array of interfaces.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.implicit Specifies an array of two output managers,
+ one for the full domain, and another for a subdomain corresponding to the
+ ground surface.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
+ right side of the mesh, defining which degrees of freedom are being constrained
+ (
+\family typewriter
+x
+\family default
+,
+\family typewriter
+y
+\family default
+, and
+\family typewriter
+z
+\family default
+), providing the label (defined in
+\family typewriter
+tet4_1000m_binary.pset
+\family default
+) defining the points desired, and assigning a label to the boundary condition
+ set.
+ Rather than specifying a spatial database file to define the boundary condition
+s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
+ condition, which sets the displacements to zero.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (
+\family typewriter
+x
+\family default
+,
+\family typewriter
+y
+\family default
+, and
+\family typewriter
+z
+\family default
+), providing the label (defined in
+\family typewriter
+tet4_1000m_binary.pset
+\family default
+) defining the points desired, and assigning a label to the boundary condition
+ set.
+ Rather than specifying a spatial database file to define the boundary condition
+s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
+ condition, which sets the displacements to zero.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces Gives the label (defined in
+\family typewriter
+tet4_1000m_binary.pset
+\family default
+) defining the points on the fault, provides quadrature information, and
+ then gives database names for material properties (needed for conditioning),
+ fault slip, peak fault slip rate, and fault slip time.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.output.writer Gives the base filename for
+ VTK output over the entire domain (
+\family typewriter
+step03.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.subdomain Gives the label of the nodeset
+ defining the subdomain and gives the base filename for VTK output over
+ the subdomain corresponding to the ground surface (
+\family typewriter
+step03-groundsurf.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces.fault.output.writer Gives the base filename
+ for cohesive cell output files (
+\family typewriter
+step03-fault.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials.elastic.output Gives the base filename for
+ state variable output files for the
+\family typewriter
+elastic
+\family default
+ material set (
+\family typewriter
+step03-statevars-elastic.vtk
+\family default
+), and causes state variables to be averaged over all quadrature points
+ in each cell.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials.viscoelastic.output Gives the base filename
+ for state variable output files for the
+\family typewriter
+viscoelastic
+\family default
+ material set (
+\family typewriter
+step03-statevars-viscoelastic.vtk
+\family default
+), and causes state variables to be averaged over all quadrature points
+ in each cell.
+\end_layout
+
+\begin_layout Standard
+The fault example requires three additional database files that were not
+ needed for the simple displacement example.
+ The first file (
+\family typewriter
+finalslip.spatialdb
+\family default
+) specifies a constant value of 2 m of right-lateral fault slip that then
+ tapers linearly to zero from 2 km to 4 km depth, and a linearly-varying
+ amount of reverse slip, with a maximum of 0.25 m at the surface, linearly
+ tapering to 0 m at 2 km depth.
+ The data dimension is one since the data vary linearly along a vertical
+ line.
+ The default slip time function is a step-function, so we also must provide
+ the time at which slip begins.
+ The elastic solution is associated with advancing from
+\begin_inset Formula $t=-dt$
+\end_inset
+
+ to
+\begin_inset Formula $t=0$
+\end_inset
+
+, so we set the slip initiation time for the step-function to 0 in
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+\size small
+tet4_1000m_binary.gmv
+\family default
+,
+\family typewriter
+tet4_1000m_binary.pset
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+mat_elastic.spatialdb
+\family default
+\size default
+, and
+\family typewriter
+mat_viscoelastic.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+\size small
+step03.cfg
+\family default
+,
+\family typewriter
+finalslip.spatialdb
+\family default
+, and
+\family typewriter
+sliptime.spatialdb
+\family default
+\size default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step03.cfg
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, eight files will be produced.
+ The first file is named
+\family typewriter
+step03_t0000000.vtk
+\family default
+.
+ The
+\family typewriter
+t0000000
+\family default
+ indicates that the output is for the first (and only) time step, corresponding
+ to an elastic solution.
+ This file contains mesh information as well as displacement values at the
+ mesh vertices.
+ The second file is named
+\family typewriter
+step03-statevars-elastic_t0000000.vtk
+\family default
+.
+ This file contains the state variables for each cell in the material group
+
+\family typewriter
+elastic
+\family default
+.
+ The default fields are the total strain and stress fields.
+ We have requested that the values be averaged over all quadrature points
+ for each cell; however, since we only have a single quadrature point for
+ each linear tetrahedron, this will have no effect.
+ The third file (
+\family typewriter
+step03-statevars-viscoelastic_info.vtk
+\family default
+) gives the material properties used for the
+\family typewriter
+viscoelastic
+\family default
+ material set.
+ Since we have not specified which properties to write, the default properties
+ (
+\family typewriter
+mu
+\family default
+,
+\family typewriter
+lambda
+\family default
+,
+\family typewriter
+density
+\family default
+) are written.
+ There are two additional files containing the state variables for each
+ of the material sets.
+ The file
+\family typewriter
+step03-groundsurf_t0000000.vtk
+\family default
+ is analogous to
+\family typewriter
+step03_t0000000.vtk
+\family default
+, but in this case the results are only given for a subset of the mesh correspon
+ding to the ground surface.
+ Also, the cells in this file are one dimension lower than the cells described
+ in
+\family typewriter
+step03_t0000000.vtk
+\family default
+, so they are triangles rather than tetrahedra.
+ The file
+\family typewriter
+step03-fault_t0000000.vtk
+\family default
+ gives the specified fault slip for each vertex on the fault, along with
+ the computed traction change for the cohesive cell.
+ The final file,
+\family typewriter
+step03-fault_info.vtk
+\family default
+, provides information such as the normal direction, final slip, and slip
+ time for each vertex on the fault.
+ All of the
+\family typewriter
+.vtk
+\family default
+ files may be used with a number of visualization packages.
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:3dtet-disloc"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/dislocation.jpg
+ lyxscale 50
+ scale 45
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the kinematic fault example
+ using a mesh composed of linear tetrahedral cells generated by LaGriT.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:3dtet-disloc"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Alternative Solver and Discretization Settings
+\end_layout
+
+\begin_layout Standard
+As we did for the Shear Dislocation examples, in
+\family typewriter
+step04.cfg
+\family default
+ we switch to using the split fields and algebraic multigrid preconditioner
+ along with global uniform mesh refinement.
+ Because PyLith implements fault slip using Lagrange multipliers, we make
+ a few small adjusments to the solver settings.
+ As discussed in Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:petsc:options"
+
+\end_inset
+
+, we use a custom preconditioner for the Lagrange multiplier degrees of
+ freedom when preconditioning with field splitting.
+ Within
+\family typewriter
+step04.cfg
+\family default
+ we turn on the use of the custom preconditioner for the Lagrange multiplier
+ degrees of freedom and add the corresponding settings for the fourth field
+ for the algebraic multigrid algorithm,
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.formulation]
+\end_layout
+
+\begin_layout LyX-Code
+split_fields = True
+\end_layout
+
+\begin_layout LyX-Code
+use_custom_constraint_pc = True
+\end_layout
+
+\begin_layout LyX-Code
+matrix_type = aij
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.petsc]
+\end_layout
+
+\begin_layout LyX-Code
+fs_pc_type = fieldsplit
+\end_layout
+
+\begin_layout LyX-Code
+fs_pc_fieldsplit_real_diagonal =
+\end_layout
+
+\begin_layout LyX-Code
+fs_pc_fieldsplit_type = multiplicative
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_0_pc_type = ml
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_1_pc_type = ml
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_2_pc_type = ml
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_3_pc_type = ml
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_0_ksp_type = preonly
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_1_ksp_type = preonly
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_2_ksp_type = preonly
+\end_layout
+
+\begin_layout LyX-Code
+fs_fieldsplit_3_ksp_type = preonly
+\end_layout
+
+\begin_layout Standard
+Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "tab:3dtet4:solver:cmp"
+
+\end_inset
+
+ shows the improved efficiency of the solver using the split fields with
+ the algebraic multigrid preconditioner.
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/greensfns2d/greensfns2d.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/greensfns2d/greensfns2d.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/greensfns2d/greensfns2d.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,1018 +1,1010 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
-\use_default_options false
-\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding latin1
-\fontencoding global
-\font_roman default
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-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
-\graphics default
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-\output_sync 0
-\bibtex_command default
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-\spacing single
-\use_hyperref false
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-\use_mhchem 1
-\use_mathdots 1
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-\use_bibtopic false
-\use_indices false
-\paperorientation portrait
-\suppress_date false
-\use_refstyle 0
-\index Index
-\shortcut idx
-\color #008000
-\end_index
-\leftmargin 1in
-\topmargin 1in
-\rightmargin 1in
-\bottommargin 1in
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\paragraph_indentation default
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-Greensfns-2d"
-
-\end_inset
-
-Tutorial Generating and Using Green's Functions in Two Dimensions
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Green's functions
-\end_layout
-
-\begin_layout Itemize
-HDF5 output
-\end_layout
-
-\begin_layout Itemize
-HDF5 point output
-\end_layout
-
-\begin_layout Itemize
-Reading HDF5 output using h5py
-\end_layout
-
-\begin_layout Itemize
-Simple inversion procedure
-\end_layout
-
-\begin_layout Itemize
-Plotting results using matplotlib
-\end_layout
-
-\begin_layout Itemize
-Cubit mesh generation
-\end_layout
-
-\begin_deeper
-\begin_layout Itemize
-Variable mesh resolution
-\end_layout
-
-\begin_layout Itemize
-APREPRO programming language
-\end_layout
-
-\end_deeper
-\begin_layout Itemize
-Static solution
-\end_layout
-
-\begin_layout Itemize
-Linear triangular cells
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Plane strain linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Itemize
-UniformDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained under the directory
-
-\family typewriter
-examples/2d/greensfns.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial examines the steps necessary to generate Green's functions
- using PyLith and how they may be used in a linear inversion.
- For simplicity we discuss strike-slip and reverse faulting examples in
- the context of 2-D simulations.
- In each example, we first compute surface displacement at a set of points,
- and these computed displacements provide the
-\begin_inset Quotes eld
-\end_inset
-
-data
-\begin_inset Quotes erd
-\end_inset
-
- for our inversion.
- Second, we compute a set of Green's functions using the same fault geometries,
- and output the results at the same set of points.
- Third, we perform a simple linear inversion.
- An important aspect for both the forward problem and the Green's function
- problem is that the computed solution is output at a set of user-specified
- points (not necessarily coincident with mesh vertices), rather than over
- a mesh or sub-mesh as for other types of output.
- To do this, PyLith internally performs the necessary interpolation.
- There is a README file in the top-level directory that explains how to
- perform the each step in the two problems.
-\end_layout
-
-\begin_layout Subsection
-Mesh Description
-\end_layout
-
-\begin_layout Standard
-We use linear triangular cells for the meshes in each of the two problems.
- We construct the mesh in CUBIT following the same techniques used in the
- 2-D subduction zone example.
- The main driver is in the journal file
-\family typewriter
-mesh_tri3.jou
-\family default
-.
- It calls the journal file
-\family typewriter
-geometry.jou
-\family default
- to construct the geometry.
- It then calls the journal file
-\family typewriter
-gradient.jou
-\family default
- to set the variable discretization sizes used in this mesh.
- Finally, the
-\family typewriter
-createbc.jou
-\family default
- file is called to setup the groups associated with boundary conditions
- and materials.
- The mesh used for the strike-slip example is shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:greensfns2d-strikeslip-mesh"
-
-\end_inset
-
- The journal files are documented and describe the various steps outlined
- below.
-\end_layout
-
-\begin_layout Enumerate
-Create the geometry defining the domain.
-\end_layout
-
-\begin_layout Enumerate
-Create fault surface by splitting domain across the given locations.
-\end_layout
-
-\begin_layout Enumerate
-Define meshing scheme and cell size variation.
-\end_layout
-
-\begin_deeper
-\begin_layout Enumerate
-Define cell size along curves near fault.
-\end_layout
-
-\begin_layout Enumerate
-Increase cell size away from fault at a geometric rate (bias).
-\end_layout
-
-\end_deeper
-\begin_layout Enumerate
-Generate mesh.
-\end_layout
-
-\begin_layout Enumerate
-Create blocks for materials and nodesets for boundary conditions.
-\end_layout
-
-\begin_layout Enumerate
-Export mesh.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/strikeslip_ydispl2.jpg
- width 4in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh used for both forward and Green's function computations for strike-slip
- problem.
- Computed y-displacements for the forward problem are shown with the color
- scale.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:greensfns2d-strikeslip-mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Additional Common Information
-\end_layout
-
-\begin_layout Standard
-As in the examples discussed in previous sections of these tutorials, we
- place parameters common to the forward model and Green's function computation
- in the
-\family typewriter
-pylithapp.cfg
-\family default
- file so that we do not have to duplicate them for the two procedures.
- The settings contained in
-\family typewriter
-pylithapp.cfg
-\family default
- for this problem consist of:
-\end_layout
-
-\begin_layout Description
-pylithapp.journal.info Settings that control the verbosity of the output written
- to stdout for the different components.
-\end_layout
-
-\begin_layout Description
-pylithapp.mesh_generator Settings that control mesh importing, such as the
- importer type, the filename, and the spatial dimension of the mesh.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem Settings that control the problem, such as the total time,
- time step size, and spatial dimension.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.materials Settings that control the material type, specify
- which material IDs are to be associated with a particular material type,
- and give the name of the spatial database containing the physical properties
- for the material.
- The quadrature information is also given.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.bc Settings that control the applied boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.interfaces Settings that control the specification of faults,
- including quadrature information.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output Settings related to output of the solution
- over the domain and points (surface observation locations).
-\end_layout
-
-\begin_layout Description
-pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
- type.
-\end_layout
-
-\begin_layout Standard
-One aspect that has not been covered previously is the specification of
- output at discrete points, rather than over a mesh or sub-mesh.
- We do this using the
-\family typewriter
-OutputSolnPoints
-\family default
- output type:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.problem.formulation]
-\end_layout
-
-\begin_layout LyX-Code
-output = [domain,points]
-\end_layout
-
-\begin_layout LyX-Code
-output.points = pylith.meshio.OutputSolnPoints
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.problem.formulation.output.points]
-\end_layout
-
-\begin_layout LyX-Code
-coordsys.space_dim = 2
-\end_layout
-
-\begin_layout LyX-Code
-coordsys.units = km
-\end_layout
-
-\begin_layout LyX-Code
-writer = pylith.meshio.DataWriterHDF5Mesh
-\end_layout
-
-\begin_layout LyX-Code
-reader.filename = output_points.txt
-\end_layout
-
-\begin_layout Standard
-We provide the number of spatial dimensions and the units of the point coordinat
-es, and then the coordinates are given in a simple ASCII file (
-\family typewriter
-output_points.txt
-\family default
-).
- These same points are used for both the forward model computation and the
- generation of the Green's functions.
-\end_layout
-
-\begin_layout Subsection
-Step 1: Solution of the Forward Problem
-\end_layout
-
-\begin_layout Standard
-For both the strike-slip problem and the reverse fault problem, we first
- run a static simulation to generate our synthetic data.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-eqsim.cfg
-\family default
-.
- These settings are:
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.interfaces Give the type of fault interface condition and
- provide the slip distribution to use.
- Linear interpolation is used for the slip distribution.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output Gives the output file names for domain
- output, fault output, point output, and material output.
- All output uses HDF5 format.
-\end_layout
-
-\begin_layout Standard
-The applied fault slip is given in the file
-\family typewriter
-eqslip.spatialdb
-\family default
-.
- For both the strike-slip and reverse problems, no fault opening is given,
- so only the left-lateral component is nonzero.
- We run the forward models by typing (in the appropriate directory)
-\end_layout
-
-\begin_layout LyX-Code
-pylith eqsim.cfg
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, four HDF5 files will be produced.
- The file named
-\family typewriter
-eqsim.h5
-\family default
- (and the associated XDMF file) contains the solution for the entire domain.
- This corresponds to the solution shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:greensfns2d-strikeslip-mesh"
-
-\end_inset
-
-.
- The
-\family typewriter
-eqsim-fault.h5
-\family default
- file contains the applied fault slip and the change in fault tractions,
- while the
-\family typewriter
-eqsim-fault_info.h5
-\family default
- file contains the final slip, the fault normal, and the slip time.
- The final file (
-\family typewriter
-eqsim-points.h5
-\family default
-) contains the solution computed at the point locations provided in the
-
-\family typewriter
-output_points.txt
-\family default
- file.
- These are the results that will be used as synthetic data for our inversion.
- One the problem has run, the results may be viewed with a visualization
- package such as ParaView.
- In Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:greensfns2d-strikeslip-forward"
-
-\end_inset
-
- we show the applied fault slip (from
-\family typewriter
-eqsim-fault.h5
-\family default
-) and the resulting x-displacements (from
-\family typewriter
-eqsim-points.h5
-\family default
-) for our strike-slip forward problem.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/strikeslip_forward_points.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Applied fault slip for the strike-slip forward problem as well as computed
- x-displacements at a set of points.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:greensfns2d-strikeslip-forward"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Step 2: Generation of Green's Functions
-\end_layout
-
-\begin_layout Standard
-The next step is to generate Green's functions that may be used in an inversion.
- The procedure is similar to that for running the forward problem; however,
- it is necessary to change the problem type from the default
-\family typewriter
-timedependent
-\family default
- to
-\family typewriter
-greensfns
-\family default
-.
- This is accomplished by simply typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith --problem=pylith.problems.GreensFns
-\end_layout
-
-\begin_layout Standard
-This changes the problem type and it also causes PyLith to read the file
-
-\family typewriter
-greensfns.cfg
-\family default
- by default, in addition to
-\family typewriter
-pylithapp.cfg
-\family default
-.
- These additional parameter settings provide the information necessary to
- generate the Green's functions:
-\end_layout
-
-\begin_layout LyX-Code
-[greensfns]
-\end_layout
-
-\begin_layout LyX-Code
-fault_id = 100
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-# Set the type of fault interface condition.
-\end_layout
-
-\begin_layout LyX-Code
-[greensfns.interfaces]
-\end_layout
-
-\begin_layout LyX-Code
-fault = pylith.faults.FaultCohesiveImpulses
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-# Set the parameters for the fault interface condition.
-\end_layout
-
-\begin_layout LyX-Code
-[greensfns.interfaces.fault]
-\end_layout
-
-\begin_layout LyX-Code
-# Generate impulses for lateral slip only, no fault opening.
-\end_layout
-
-\begin_layout LyX-Code
-# Fault DOF 0 corresponds to left-lateral slip.
-\end_layout
-
-\begin_layout LyX-Code
-impulse_dof = [0]
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-# Set the amplitude of the slip impulses (amplitude is nonzero on only
-\end_layout
-
-\begin_layout LyX-Code
-# a subset of the fault)
-\end_layout
-
-\begin_layout LyX-Code
-db_impulse_amplitude.label = Amplitude of slip impulses
-\end_layout
-
-\begin_layout LyX-Code
-db_impulse_amplitude.iohandler.filename = impulse_amplitude.spatialdb
-\end_layout
-
-\begin_layout LyX-Code
-db_impulse_amplitude.query_type = nearest
-\end_layout
-
-\begin_layout Standard
-Note that the top-level identifier is now
-\family typewriter
-greensfns
-\family default
- rather than
-\family typewriter
-pylithapp
-\family default
-.
- We first set the fault interface condition type to
-\family typewriter
-FaultCohesiveImpulses
-\family default
-, and then specify the slip component to use.
- The amplitude of the fault slip and the fault vertices to use are provided
- in the
-\family typewriter
-impulse_amplitude.spatialdb
-\family default
- file.
- Fault vertices for which zero slip is specified will not have associated
- Green's functions generated.
- The remainder of the
-\family typewriter
-greensfns.cfg
-\family default
- file provides output information, which is exactly analogous to the settings
- in
-\family typewriter
-eqsim.cfg
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-The generation of Green's functions is somewhat similar to the solution
- of a time-dependent problem with multiple time steps.
- In this case, each 'time step' corresponds to the solution computed for
- a slip impulse at a particular fault vertex.
- The output files contain the solution for each separate impulse (slip on
- a single fault vertex).
- The
-\family typewriter
-greensfns-fault_info.h5
-\family default
- file simply contains the slip amplitude and fault normal.
- In Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:greensfns2d-strikeslip-gf6"
-
-\end_inset
-
- we show the applied impulse (from file
-\family typewriter
-greensfns-fault.h5
-\family default
-) and associated point responses (from file
-\family typewriter
-greensfns-points.h5
-\family default
-) for the seventh generated Green's function in the strike-slip example.
- In the next section we will show how to read these Green's functions and
- use them to perform a simple linear inversion.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/strikeslip_gf6.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Applied fault slip and computed responses (at points) for the seventh Green's
- function generated for the strike-slip fault example.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:greensfns2d-strikeslip-gf6"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Step 3: Simple Inversion Using PyLith-generated Green's Functions
-\end_layout
-
-\begin_layout Standard
-In the previous two steps we generated a set of synthetic data as well as
- a set of Green's functions.
- Both are stored in HDF5 files.
- To make use of them, we provide a simple Python script that reads the HDF5
- results using the h5py Python package.
- Once we have read the necessary information, we will perform a simple least-squ
-ares inversion using the penalty method.
- We will be solving the equation:
-\begin_inset Formula
-\begin{equation}
-G_{a}m=d_{a}\:,
-\end{equation}
-
-\end_inset
-
-where
-\begin_inset Formula $m$
-\end_inset
-
- are the model parameters (slip),
-\begin_inset Formula $G_{a}$
-\end_inset
-
- is the augmented set of Green's functions, and
-\begin_inset Formula $d_{a}$
-\end_inset
-
- is the augmented data vector.
- The Green's functions are augmented by the addition of a penalty function:
-
-\begin_inset Formula
-\begin{equation}
-G_{a}=\left[\begin{array}{c}
-G\\
-\lambda D
-\end{array}\right]\:,
-\end{equation}
-
-\end_inset
-
-and the data vector is augmented by the addition of the
-\shape italic
-a priori
-\shape default
- model parameter values:
-\begin_inset Formula
-\begin{equation}
-d_{a}=\left[\begin{array}{c}
-d\\
-m_{ap}
-\end{array}\right]\:.
-\end{equation}
-
-\end_inset
-
-The matrix
-\begin_inset Formula $D$
-\end_inset
-
- is the penalty function, and
-\begin_inset Formula $\lambda$
-\end_inset
-
- is the penalty parameter.
- The solution is obtained using the generalized inverse (e.g.,
-\begin_inset CommandInset citation
-LatexCommand cite
-key "Menke:1984"
-
-\end_inset
-
-):
-\begin_inset Formula
-\begin{equation}
-G^{-g}=\left(G_{a}^{T}G_{a}\right)^{-1}G_{a}^{T}\:,
-\end{equation}
-
-\end_inset
-
-and the estimated solution is then:
-\begin_inset Formula
-\begin{equation}
-m_{est}=G^{-g}d_{a}\:.
-\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-The code to read the synthetic data and Green's functions and to perform
- the inversion is contained in the file
-\family typewriter
-invert_slip.py
-\family default
-, which is contained in the top-level directory.
- For this simple example, we have simply used a diagonal matrix as the penalty
- funtion, and the
-\shape italic
-a priori
-\shape default
- parameter values are assumed to be zero.
- The solution is performed for a range of values of the penalty parameter,
- which are contained in the file
-\family typewriter
-penalty_params.txt
-\family default
- within each subdirectory.
- The inversion is performed by running the script in the top-level directory
- from each subdirectory.
- To run an inversion, type:
-\end_layout
-
-\begin_layout LyX-Code
-../invert_slip.py --impulses=output/greensfns-fault.h5 --responses=output/greensfns-
-points.h5 --data=output/eqsim-points.h5 --penalty=penalty_params.txt --output=outpu
-t/slip_inverted.txt
-\end_layout
-
-\begin_layout Standard
-This will produce an ASCII file (
-\family typewriter
-slip_inverted.txt
-\family default
-), which will contain the estimated solution.
-\end_layout
-
-\begin_layout Subsection
-Step 4: Visualization of Estimated and True Solutions
-\end_layout
-
-\begin_layout Standard
-Once we have computed the solution, we would then like to visualize the
- results.
- We do this using another Python script that requires the matplotlib plotting
- package (this package is not included in the PyLith binary).
- We also use the h5py package again to read the applied slip for the forward
- problem.
- The Python code to plot the results is contained in the
-\family typewriter
-plot_invresults.py
-\family default
- file contained within each subdirectory.
- To plot the results, type:
-\end_layout
-
-\begin_layout LyX-Code
-plot_invresults.py --solution=output/eqsim-fault.h5 --predicted=output/slip_invert
-ed.txt
-\end_layout
-
-\begin_layout Standard
-The script will produce an interactive matplotlib window that shows the
- estimated solution compared to the true solution (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:greensfns-invresults"
-
-\end_inset
-
-).
- As the penalty parameter is increased, the solution is progressively damped.
- In a real inversion we would also include the effects of data uncertainties,
- and the penalty parameter would represent a factor controlling the tradeoff
- between solution simplicity and fitting the noise in the data.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/strikeslip_inversion.pdf
- lyxscale 50
- width 3in
-
-\end_inset
-
-
-\begin_inset Graphics
- filename figs/reverse_inversion.pdf
- width 3in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Inversion results from running Python plotting script.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:greensfns-invresults"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 1in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-Greensfns-2d"
+
+\end_inset
+
+Tutorial Generating and Using Green's Functions in Two Dimensions
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Green's functions
+\end_layout
+
+\begin_layout Itemize
+HDF5 output
+\end_layout
+
+\begin_layout Itemize
+HDF5 point output
+\end_layout
+
+\begin_layout Itemize
+Reading HDF5 output using h5py
+\end_layout
+
+\begin_layout Itemize
+Simple inversion procedure
+\end_layout
+
+\begin_layout Itemize
+Plotting results using matplotlib
+\end_layout
+
+\begin_layout Itemize
+Cubit mesh generation
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Variable mesh resolution
+\end_layout
+
+\begin_layout Itemize
+APREPRO programming language
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Static solution
+\end_layout
+
+\begin_layout Itemize
+Linear triangular cells
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Plane strain linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Itemize
+UniformDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained under the directory
+
+\family typewriter
+examples/2d/greensfns.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial examines the steps necessary to generate Green's functions
+ using PyLith and how they may be used in a linear inversion.
+ For simplicity we discuss strike-slip and reverse faulting examples in
+ the context of 2D simulations.
+ In each example, we first compute surface displacement at a set of points,
+ and these computed displacements provide the ``data'' for our inversion.
+ Second, we compute a set of Green's functions using the same fault geometries,
+ and output the results at the same set of points.
+ Third, we perform a simple linear inversion.
+ An important aspect for both the forward problem and the Green's function
+ problem is that the computed solution is output at a set of user-specified
+ points (not necessarily coincident with mesh vertices), rather than over
+ a mesh or sub-mesh as for other types of output.
+ To do this, PyLith internally performs the necessary interpolation.
+ There is a README file in the top-level directory that explains how to
+ perform each step in the two problems.
+\end_layout
+
+\begin_layout Subsection
+Mesh Description
+\end_layout
+
+\begin_layout Standard
+We use linear triangular cells for the meshes in each of the two problems.
+ We construct the mesh in CUBIT following the same techniques used in the
+ 2D subduction zone example.
+ The main driver is in the journal file
+\family typewriter
+mesh_tri3.jou
+\family default
+.
+ It calls the journal file
+\family typewriter
+geometry.jou
+\family default
+ to construct the geometry.
+ It then calls the journal file
+\family typewriter
+gradient.jou
+\family default
+ to set the variable discretization sizes used in this mesh.
+ Finally, the
+\family typewriter
+createbc.jou
+\family default
+ file is called to set up the groups associated with boundary conditions
+ and materials.
+ The mesh used for the strike-slip example is shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:greensfns2d-strikeslip-mesh"
+
+\end_inset
+
+ The journal files are documented and describe the various steps outlined
+ below.
+\end_layout
+
+\begin_layout Enumerate
+Create the geometry defining the domain.
+\end_layout
+
+\begin_layout Enumerate
+Create fault surface by splitting domain across the given locations.
+\end_layout
+
+\begin_layout Enumerate
+Define meshing scheme and cell size variation.
+\end_layout
+
+\begin_deeper
+\begin_layout Enumerate
+Define cell size along curves near fault.
+\end_layout
+
+\begin_layout Enumerate
+Increase cell size away from fault at a geometric rate (bias).
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Generate mesh.
+\end_layout
+
+\begin_layout Enumerate
+Create blocks for materials and nodesets for boundary conditions.
+\end_layout
+
+\begin_layout Enumerate
+Export mesh.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/strikeslip_ydispl2.jpg
+ width 4in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh used for both forward and Green's function computations for the strike-slip
+ problem.
+ Computed y-displacements for the forward problem are shown with the color
+ scale.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:greensfns2d-strikeslip-mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Additional Common Information
+\end_layout
+
+\begin_layout Standard
+As in the examples discussed in previous sections of these tutorials, we
+ place parameters common to the forward model and Green's function computation
+ in the
+\family typewriter
+pylithapp.cfg
+\family default
+ file so that we do not have to duplicate them for the two procedures.
+ The settings contained in
+\family typewriter
+pylithapp.cfg
+\family default
+ for this problem consist of:
+\end_layout
+
+\begin_layout Description
+pylithapp.journal.info Settings that control the verbosity of the output written
+ to stdout for the different components.
+\end_layout
+
+\begin_layout Description
+pylithapp.mesh_generator Settings that control mesh importing, such as the
+ importer type, the filename, and the spatial dimension of the mesh.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem Settings that control the problem, such as the total time,
+ time-step size, and spatial dimension.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.materials Settings that control the material type, specify
+ which material IDs are to be associated with a particular material type,
+ and give the name of the spatial database containing the physical properties
+ for the material.
+ The quadrature information is also given.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.bc Settings that control the applied boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.interfaces Settings that control the specification of faults,
+ including quadrature information.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output Settings related to output of the solution
+ over the domain and points (surface observation locations).
+\end_layout
+
+\begin_layout Description
+pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
+ type.
+\end_layout
+
+\begin_layout Standard
+One aspect that has not been covered previously is the specification of
+ output at discrete points, rather than over a mesh or sub-mesh.
+ We do this using the
+\family typewriter
+OutputSolnPoints
+\family default
+ output type:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.formulation]
+\end_layout
+
+\begin_layout LyX-Code
+output = [domain,points]
+\end_layout
+
+\begin_layout LyX-Code
+output.points = pylith.meshio.OutputSolnPoints
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.formulation.output.points]
+\end_layout
+
+\begin_layout LyX-Code
+coordsys.space_dim = 2
+\end_layout
+
+\begin_layout LyX-Code
+coordsys.units = km
+\end_layout
+
+\begin_layout LyX-Code
+writer = pylith.meshio.DataWriterHDF5Mesh
+\end_layout
+
+\begin_layout LyX-Code
+reader.filename = output_points.txt
+\end_layout
+
+\begin_layout Standard
+We provide the number of spatial dimensions and the units of the point coordinat
+es, and then the coordinates are given in a simple ASCII file (
+\family typewriter
+output_points.txt
+\family default
+).
+ These same points are used for both the forward model computation and the
+ generation of the Green's functions.
+\end_layout
+
+\begin_layout Subsection
+Step 1: Solution of the Forward Problem
+\end_layout
+
+\begin_layout Standard
+For both the strike-slip problem and the reverse fault problem, we first
+ run a static simulation to generate our synthetic data.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+eqsim.cfg
+\family default
+.
+ These settings are:
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.interfaces Give the type of fault interface condition and
+ provide the slip distribution to use.
+ Linear interpolation is used for the slip distribution.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output Gives the output filenames for domain
+ output, fault output, point output, and material output.
+ All output uses HDF5 format.
+\end_layout
+
+\begin_layout Standard
+The applied fault slip is given in the file
+\family typewriter
+eqslip.spatialdb
+\family default
+.
+ For both the strike-slip and reverse problems, no fault opening is given,
+ so only the left-lateral component is nonzero.
+ We run the forward models by typing (in the appropriate directory)
+\end_layout
+
+\begin_layout LyX-Code
+pylith eqsim.cfg
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, four HDF5 files will be produced.
+ The file named
+\family typewriter
+eqsim.h5
+\family default
+ (and the associated XDMF file) contains the solution for the entire domain.
+ This corresponds to the solution shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:greensfns2d-strikeslip-mesh"
+
+\end_inset
+
+.
+ The
+\family typewriter
+eqsim-fault.h5
+\family default
+ file contains the applied fault slip and the change in fault tractions,
+ while the
+\family typewriter
+eqsim-fault_info.h5
+\family default
+ file contains the final slip, the fault normal, and the slip time.
+ The final file (
+\family typewriter
+eqsim-points.h5
+\family default
+) contains the solution computed at the point locations provided in the
+
+\family typewriter
+output_points.txt
+\family default
+ file.
+ These are the results that will be used as synthetic data for our inversion.
+ One the problem has run, the results may be viewed with a visualization
+ package such as ParaView.
+ In Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:greensfns2d-strikeslip-forward"
+
+\end_inset
+
+ we show the applied fault slip (from
+\family typewriter
+eqsim-fault.h5
+\family default
+) and the resulting x-displacements (from
+\family typewriter
+eqsim-points.h5
+\family default
+) for our strike-slip forward problem.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/strikeslip_forward_points.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Applied fault slip for the strike-slip forward problem as well as computed
+ x-displacements at a set of points.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:greensfns2d-strikeslip-forward"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Step 2: Generation of Green's Functions
+\end_layout
+
+\begin_layout Standard
+The next step is to generate Green's functions that may be used in an inversion.
+ The procedure is similar to that for running the forward problem; however,
+ it is necessary to change the problem type from the default
+\family typewriter
+timedependent
+\family default
+ to
+\family typewriter
+greensfns
+\family default
+.
+ This is accomplished by simply typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith --problem=pylith.problems.GreensFns
+\end_layout
+
+\begin_layout Standard
+This changes the problem type and it also causes PyLith to read the file
+
+\family typewriter
+greensfns.cfg
+\family default
+ by default, in addition to
+\family typewriter
+pylithapp.cfg
+\family default
+.
+ These additional parameter settings provide the information necessary to
+ generate the Green's functions:
+\end_layout
+
+\begin_layout LyX-Code
+[greensfns]
+\end_layout
+
+\begin_layout LyX-Code
+fault_id = 100
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+# Set the type of fault interface condition.
+\end_layout
+
+\begin_layout LyX-Code
+[greensfns.interfaces]
+\end_layout
+
+\begin_layout LyX-Code
+fault = pylith.faults.FaultCohesiveImpulses
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+# Set the parameters for the fault interface condition.
+\end_layout
+
+\begin_layout LyX-Code
+[greensfns.interfaces.fault]
+\end_layout
+
+\begin_layout LyX-Code
+# Generate impulses for lateral slip only, no fault opening.
+\end_layout
+
+\begin_layout LyX-Code
+# Fault DOF 0 corresponds to left-lateral slip.
+\end_layout
+
+\begin_layout LyX-Code
+impulse_dof = [0]
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+# Set the amplitude of the slip impulses (amplitude is nonzero on only
+\end_layout
+
+\begin_layout LyX-Code
+# a subset of the fault)
+\end_layout
+
+\begin_layout LyX-Code
+db_impulse_amplitude.label = Amplitude of slip impulses
+\end_layout
+
+\begin_layout LyX-Code
+db_impulse_amplitude.iohandler.filename = impulse_amplitude.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+db_impulse_amplitude.query_type = nearest
+\end_layout
+
+\begin_layout Standard
+Note that the top-level identifier is now
+\family typewriter
+greensfns
+\family default
+ rather than
+\family typewriter
+pylithapp
+\family default
+.
+ We first set the fault interface condition type to
+\family typewriter
+FaultCohesiveImpulses
+\family default
+, and then specify the slip component to use.
+ The amplitude of the fault slip and the fault vertices to use are provided
+ in the
+\family typewriter
+impulse_amplitude.spatialdb
+\family default
+ file.
+ Fault vertices for which zero slip is specified will not have associated
+ Green's functions generated.
+ The remainder of the
+\family typewriter
+greensfns.cfg
+\family default
+ file provides output information, which is exactly analogous to the settings
+ in
+\family typewriter
+eqsim.cfg
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The generation of Green's functions is somewhat similar to the solution
+ of a time-dependent problem with multiple time steps.
+ In this case, each `time step' corresponds to the solution computed for
+ a slip impulse at a particular fault vertex.
+ The output files contain the solution for each separate impulse (slip on
+ a single fault vertex).
+ The
+\family typewriter
+greensfns-fault_info.h5
+\family default
+ file simply contains the slip amplitude and fault normal.
+ In Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:greensfns2d-strikeslip-gf6"
+
+\end_inset
+
+ we show the applied impulse (from file
+\family typewriter
+greensfns-fault.h5
+\family default
+) and associated point responses (from file
+\family typewriter
+greensfns-points.h5
+\family default
+) for the seventh generated Green's function in the strike-slip example.
+ In the next section we will show how to read these Green's functions and
+ use them to perform a simple linear inversion.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/strikeslip_gf6.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Applied fault slip and computed responses (at points) for the seventh Green's
+ function generated for the strike-slip fault example.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:greensfns2d-strikeslip-gf6"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Step 3: Simple Inversion Using PyLith-generated Green's Functions
+\end_layout
+
+\begin_layout Standard
+In the previous two steps we generated a set of synthetic data as well as
+ a set of Green's functions.
+ Both are stored in HDF5 files.
+ To make use of them, we provide a simple Python script that reads the HDF5
+ results using the h5py Python package.
+ Once we have read the necessary information, we will perform a simple least-squ
+ares inversion using the penalty method.
+ We will be solving the equation:
+\begin_inset Formula
+\begin{equation}
+G_{a}m=d_{a}\:,
+\end{equation}
+
+\end_inset
+
+where
+\begin_inset Formula $m$
+\end_inset
+
+ are the model parameters (slip),
+\begin_inset Formula $G_{a}$
+\end_inset
+
+ is the augmented set of Green's functions, and
+\begin_inset Formula $d_{a}$
+\end_inset
+
+ is the augmented data vector.
+ The Green's functions are augmented by the addition of a penalty function:
+
+\begin_inset Formula
+\begin{equation}
+G_{a}=\left[\begin{array}{c}
+G\\
+\lambda D
+\end{array}\right]\:,
+\end{equation}
+
+\end_inset
+
+and the data vector is augmented by the addition of the
+\shape italic
+a priori
+\shape default
+ model parameter values:
+\begin_inset Formula
+\begin{equation}
+d_{a}=\left[\begin{array}{c}
+d\\
+m_{ap}
+\end{array}\right]\:.
+\end{equation}
+
+\end_inset
+
+The matrix
+\begin_inset Formula $D$
+\end_inset
+
+ is the penalty function, and
+\begin_inset Formula $\lambda$
+\end_inset
+
+ is the penalty parameter.
+ The solution is obtained using the generalized inverse (e.g.,
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Menke:1984"
+
+\end_inset
+
+):
+\begin_inset Formula
+\begin{equation}
+G^{-g}=\left(G_{a}^{T}G_{a}\right)^{-1}G_{a}^{T}\:,
+\end{equation}
+
+\end_inset
+
+and the estimated solution is then:
+\begin_inset Formula
+\begin{equation}
+m_{est}=G^{-g}d_{a}\:.
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The code to read the synthetic data and Green's functions and to perform
+ the inversion is contained in the file
+\family typewriter
+invert_slip.py
+\family default
+, which is contained in the top-level directory.
+ For this simple example, we have simply used a diagonal matrix as the penalty
+ funtion, and the
+\shape italic
+a priori
+\shape default
+ parameter values are assumed to be zero.
+ The solution is performed for a range of values of the penalty parameter,
+ which are contained in the file
+\family typewriter
+penalty_params.txt
+\family default
+ within each subdirectory.
+ The inversion is performed by running the script in the top-level directory
+ from each subdirectory.
+ To run an inversion, type:
+\end_layout
+
+\begin_layout LyX-Code
+../invert_slip.py --impulses=output/greensfns-fault.h5 --responses=output/greensfns-
+points.h5 --data=output/eqsim-points.h5 --penalty=penalty_params.txt --output=outpu
+t/slip_inverted.txt
+\end_layout
+
+\begin_layout Standard
+This will produce an ASCII file (
+\family typewriter
+slip_inverted.txt
+\family default
+), which will contain the estimated solution.
+\end_layout
+
+\begin_layout Subsection
+Step 4: Visualization of Estimated and True Solutions
+\end_layout
+
+\begin_layout Standard
+Once we have computed the solution, we would then like to visualize the
+ results.
+ We do this using another Python script that requires the matplotlib plotting
+ package (this package is not included in the PyLith binary).
+ We also use the h5py package again to read the applied slip for the forward
+ problem.
+ The Python code to plot the results is contained in the
+\family typewriter
+plot_invresults.py
+\family default
+ file contained within each subdirectory.
+ To plot the results, type:
+\end_layout
+
+\begin_layout LyX-Code
+plot_invresults.py --solution=output/eqsim-fault.h5 --predicted=output/slip_invert
+ed.txt
+\end_layout
+
+\begin_layout Standard
+The script will produce an interactive matplotlib window that shows the
+ estimated solution compared to the true solution (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:greensfns-invresults"
+
+\end_inset
+
+).
+ As the penalty parameter is increased, the solution is progressively damped.
+ In a real inversion we would also include the effects of data uncertainties,
+ and the penalty parameter would represent a factor controlling the tradeoff
+ between solution simplicity and fitting the noise in the data.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/strikeslip_inversion.pdf
+ lyxscale 50
+ width 3in
+
+\end_inset
+
+
+\begin_inset Graphics
+ filename figs/reverse_inversion.pdf
+ width 3in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Inversion results from running Python plotting script.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:greensfns-invresults"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/hex8.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/hex8.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/hex8.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,284 +1,288 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
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-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:tutorial:shearwave:hex8"
-
-\end_inset
-
-3-D Bar Discretized with Hexahedra
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Dynamic solution
-\end_layout
-
-\begin_layout Itemize
-CUBIT mesh format
-\end_layout
-
-\begin_layout Itemize
-Absorbing dampers boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Elastic isotropic linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Linear hexahedral cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/bar_shearwave/hex8.
-\end_layout
-
-\begin_layout Subsection
-Mesh Generation
-\end_layout
-
-\begin_layout Standard
-The mesh is a simple rectangular prism 8 km by 400 m by 400m (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:hex8:mesh"
-
-\end_inset
-
-).
- This mesh could be generated via a simple script, but it is even easier
- to generate this mesh using CUBIT.
- We provide documented CUBIT journal files in
-\family typewriter
-examples/bar_shearwave/hex8.
-
-\family default
- We first create the geometry, mesh the domain using hexahedral cells, and
- then create blocks and nodesets associated with the materials and boundary
- conditions.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/hex8mesh.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of hexahedral cells generated by CUBIT used for the example
- problem.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:hex8:mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Simulation Parameters
-\end_layout
-
-\begin_layout Standard
-The simulation parameters match those in the tri3 and tet4 examples.
- As in the tet4 example, we fix both the longitudinal degree of freedom
- and the out-of-plane transverse degree of freedom.
- Using eight-point quadrature permits use of a time step of 1/20 s, which
- is slightly larger than the time step of 1/30 s used in the tri3 and tet4
- simulations.
- All of the parameters are set in the pylithapp.cfg file.
- To run the problem, simply run PyLith without any command line arguments:
-\end_layout
-
-\begin_layout LyX-Code
-pylith
-\end_layout
-
-\begin_layout Standard
-The VTK files will be written to the
-\family typewriter
-output
-\family default
- directory.
- The output includes the displacement and velocity fields over the entire
- domain at every other time step (0.10 s), the slip and change in traction
- vectors on the fault surface in along-strike and normal directions at every
- other time step (0.10 s), and the strain and stress tensors for each cell
- at every 20th time step (1.0 s).
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:hex8:deform"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/hex8deform30.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Displacement field in the bar at 3.0 s.
- Deformation has been exaggerated by a factor of 800.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:hex8:deform"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
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+\lyxformat 413
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+\begin_header
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+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:tutorial:shearwave:hex8"
+
+\end_inset
+
+3-D Bar Discretized with Hexahedra
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Dynamic solution
+\end_layout
+
+\begin_layout Itemize
+CUBIT mesh format
+\end_layout
+
+\begin_layout Itemize
+Absorbing dampers boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Elastic isotropic linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Linear hexahedral cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/bar_shearwave/hex8.
+\end_layout
+
+\begin_layout Subsection
+Mesh Generation
+\end_layout
+
+\begin_layout Standard
+The mesh is a simple rectangular prism 8 km by 400 m by 400 m (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:hex8:mesh"
+
+\end_inset
+
+).
+ This mesh could be generated via a simple script, but it is even easier
+ to generate this mesh using CUBIT.
+ We provide documented CUBIT journal files in
+\family typewriter
+examples/bar_shearwave/hex8.
+
+\family default
+ We first create the geometry, mesh the domain using hexahedral cells, and
+ then create blocks and nodesets associated with the materials and boundary
+ conditions.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/hex8mesh.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of hexahedral cells generated by CUBIT used for the example
+ problem.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:hex8:mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Simulation Parameters
+\end_layout
+
+\begin_layout Standard
+The simulation parameters match those in the tri3 and tet4 examples.
+ As in the tet4 example, we fix both the longitudinal degree of freedom
+ and the out-of-plane transverse degree of freedom.
+ Using eight-point quadrature permits use of a time step of 1/20 s, which
+ is slightly larger than the time step of 1/30 s used in the tri3 and tet4
+ simulations.
+ All of the parameters are set in the
+\family typewriter
+pylithapp.cfg
+\family default
+ file.
+ To run the problem, simply run PyLith without any command line arguments:
+\end_layout
+
+\begin_layout LyX-Code
+pylith
+\end_layout
+
+\begin_layout Standard
+The VTK files will be written to the
+\family typewriter
+output
+\family default
+ directory.
+ The output includes the displacement and velocity fields over the entire
+ domain at every other time step (0.10 s), the slip and change in traction
+ vectors on the fault surface in along-strike and normal directions at every
+ other time step (0.10 s), and the strain and stress tensors for each cell
+ at every 20th time step (1.0 s).
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:hex8:deform"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/hex8deform30.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Displacement field in the bar at 3.0 s.
+ Deformation has been exaggerated by a factor of 800.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:hex8:deform"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/quad4.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/quad4.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/quad4.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,704 +1,704 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
-\use_default_options false
-\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding latin1
-\fontencoding global
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\use_non_tex_fonts false
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
-\graphics default
-\default_output_format default
-\output_sync 0
-\bibtex_command default
-\index_command default
-\paperfontsize default
-\spacing single
-\use_hyperref false
-\papersize default
-\use_geometry true
-\use_amsmath 0
-\use_esint 0
-\use_mhchem 1
-\use_mathdots 1
-\cite_engine basic
-\use_bibtopic false
-\use_indices false
-\paperorientation portrait
-\suppress_date false
-\use_refstyle 0
-\index Index
-\shortcut idx
-\color #008000
-\end_index
-\leftmargin 1in
-\topmargin 1in
-\rightmargin 1in
-\bottommargin 1in
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\paragraph_indentation default
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:tutorial:shearwave:quad4"
-
-\end_inset
-
-3-D Bar Discretized with Quadrilaterals
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Dynamic solution
-\end_layout
-
-\begin_layout Itemize
-CUBIT mesh format
-\end_layout
-
-\begin_layout Itemize
-Absorbing dampers boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Dynamic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Plane strain linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Linear quadrilateral cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Itemize
-UniformDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/bar_shearwave/quad4.
-\end_layout
-
-\begin_layout Subsection
-Mesh Generation
-\end_layout
-
-\begin_layout Standard
-The mesh is a simple rectangular prism 8 km by 400 m by 400m (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:quad4:mesh"
-
-\end_inset
-
-).
- We provide documented CUBIT journal files in
-\family typewriter
-examples/bar_shearwave/quad4.
-
-\family default
- We first create the geometry, mesh the domain using quadrilateral cells,
- and then create blocks and nodesets associated with the materials and boundary
- conditions.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/quad4mesh.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of hexahedral cells generated by CUBIT used for the example
- problem.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:quad4:mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Kinematic Fault
-\end_layout
-
-\begin_layout Standard
-The simulation parameters match those in the tri3, tet4, and hex8 examples.
- Using four-point quadrature permits use of a time step of 1/20 s, which
- is slightly larger than the time step of 1/30 s used in the tri3 and tet4
- simulations.
- In contrast to the tri3, tet4, and hex8 shear wave examples which only
- contained a single simulation in a directory, in this example we consider
- several different simulations.
- Consequently, we separate the parameters into multiple
-\family typewriter
-.cfg
-\family default
- files.
- The parameters common parameters are placed in
-\family typewriter
-pylithapp.cfg
-\family default
- with the parameters specific to the kinematic fault example in
-\family typewriter
-kinematic.cfg
-\family default
-.
- To run the problem, simply run PyLith via:
-\end_layout
-
-\begin_layout LyX-Code
-pylith kinematic.cfg
-\end_layout
-
-\begin_layout Standard
-The VTK files will be written to the
-\family typewriter
-output
-\family default
- directory with the prefix
-\family typewriter
-kinematic
-\family default
-.
- The output includes the displacement field over the entire domain at every
- other time step (0.10 s), the slip and traction vectors on the fault surface
- in along-strike and normal directions at every other time step (0.10 s),
- and the strain and stress tensors for each cell at every 20th time step
- (1.0 s).
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:quad4:kinematic"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/quad4kinematic30.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Displacement field in the bar at 3.0 s.
- Deformation has been exaggerated by a factor of 800.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:quad4:kinematic"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Dynamic Fault
-\end_layout
-
-\begin_layout Standard
-In this set of examples we replace the kinematic fault interface with the
- dynamic fault interface, resulting in fault slip controlled by a fault-constitu
-tive model.
- See Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:fault:constitutive:models"
-
-\end_inset
-
- for detailed information about the fault constitutive models available
- in PyLith.
- Because this is a dynamic simulation we want the generated shear wave to
- continue to be absorbed at the ends of the bar, so we drive the fault by
- imposing initial tractions directly on the fault surface rather than through
- deformation within the bar.
- We employ a UniformDB object to specify 6.1 MPa of right-lateral shear and
- 10.0 MPa of normal compression for the initial fault tractions.
- The parameters common to the dynamic fault simulations are in
-\family typewriter
-dynamic.cfg
-\family default
-.
- We use the explicit time-stepping with a lumped Jacobian matrix.
- We also request that the fault output include slip, slip rate, and traction
- fields:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.interfaces.fault.output]
-\end_layout
-
-\begin_layout LyX-Code
-vertex_data_fields = [slip,slip_rate,traction]
-\end_layout
-
-\begin_layout Subsubsection
-Dynamic Fault with Static Friction
-\end_layout
-
-\begin_layout Standard
-The parameters specific to this example are related to the use of the static
- friction fault constitutive model.
- We set the fault constitutive model via
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.interfaces.fault]
-\end_layout
-
-\begin_layout LyX-Code
-friction = pylith.friction.StaticFriction
-\end_layout
-
-\begin_layout Standard
-and use a UniformDB to set the static friction parameters.
- We use a coefficient of friction of 0.6 and no cohesion (0 MPa).
- The parameters specific to this example are in
-\family typewriter
-dynamic_staticfriction.cfg
-\family default
-, so we run the problem via:
-\end_layout
-
-\begin_layout LyX-Code
-pylith dynamic.cfg dynamic_staticfriction.cfg
-\end_layout
-
-\begin_layout Standard
-The VTK files will be written to the
-\family typewriter
-output
-\family default
- directory with the prefix
-\family typewriter
-staticfriction
-\family default
-.
- The output includes the displacement and velocity fields over the entire
- domain at every other time step (0.10 s), the slip, slip rate, and traction
- vectors on the fault surface in along-strike and normal directions at every
- other time step (0.10 s), and the strain and stress tensors for each cell
- at every 20th time step (1.0 s).
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:quad4:staticfriction"
-
-\end_inset
-
-, which was generated using ParaView.
- The steady-state solution is a constant slip rate of 0.08 m/s, a shear traction
- of 6.0 MPa on the fault surface, and a uniform shear strain of 2e-5 in the
- bar with uniform, constant velocities in the y-direction of +0.04 m/s and
- -0.04 m/s on the -x and +x sides of the fault, respectively.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/quad4staticfriction30.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Velocity field in the bar at 3.0 s for the static friction fault constitutive
- model.
- Deformation has been exaggerated by a factor of 800.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:quad4:staticfriction"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Dynamic Fault with Slip-Weakening Friction
-\end_layout
-
-\begin_layout Standard
-The parameters specific to this example are related to the use of the slip-weake
-ning friction fault constitutive model (see Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:fault:constitutive:models"
-
-\end_inset
-
-).
- We set the fault constitutive model via
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.interfaces.fault]
-\end_layout
-
-\begin_layout LyX-Code
-friction = pylith.friction.SlipWeakening
-\end_layout
-
-\begin_layout Standard
-and use a UniformDB to set the slip-weakening friction parameters.
- We use a static coefficient of friction of 0.6, a dynamic coefficient of
- friction of 0.5, a slip-weakening parameter of 0.2 m, and no cohesion (0
- MPa).
- The fault constitutive model is associated with the fault, so we can append
- the fault constitutive model parameters to the vertex information fields
- and the fault constitutive model state variables to the vertex data fields:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.interfaces.fault.output]
-\end_layout
-
-\begin_layout LyX-Code
-vertex_info_fields = [strike_dir,normal_dir,initial_traction,static_coefficient,
-\begin_inset Newline newline
-\end_inset
-
-dynamic_coefficient,slip_weakening_parameter,cohesion]
-\end_layout
-
-\begin_layout LyX-Code
-vertex_data_fields = [slip,traction,cumulative_slip,previous_slip]
-\end_layout
-
-\begin_layout Standard
-The parameters specific to this example are in
-\family typewriter
-dynamic_slipweakening.cfg
-\family default
-, so we run the problem via:
-\end_layout
-
-\begin_layout LyX-Code
-pylith dynamic.cfg dynamic_slipweakening.cfg
-\end_layout
-
-\begin_layout Standard
-The VTK files will be written to the
-\family typewriter
-output
-\family default
- directory with the prefix
-\family typewriter
-slipweakening
-\family default
-.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:quad4:slipweakening"
-
-\end_inset
-
-, which was generated using ParaView.
- The steady-state solution is a constant slip rate of 0.88 m/s and shear
- traction of 5.0 MPa on the fault surface, a uniform shear strain of 2.2e-4
- in the bar with uniform, constant velocities in the y-direction of +0.44
- m/s and -0.44 m/s on the -x and +x sides of the fault, respectively.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/quad4slipweakening30.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Velocity field in the bar at 3.0 s for the slip-weakening friction fault
- constitutive model.
- Deformation has been exaggerated by a factor of 800.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:quad4:slipweakening"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsubsection
-Dynamic Fault with Rate-State Friction
-\end_layout
-
-\begin_layout Standard
-The parameters specific to this example are related to the use of the rate-
- and state-friction fault constitutive model (see Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:fault:constitutive:models"
-
-\end_inset
-
-).
- The evolution of the state variable uses the ageing law.
- We set the fault constitutive model via
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.interfaces.fault]
-\end_layout
-
-\begin_layout LyX-Code
-friction = pylith.friction.RateStateAgeing
-\end_layout
-
-\begin_layout Standard
-and use a UniformDB to set the static friction parameters.
- We use a reference coefficient of friction of 0.6, reference slip rate of
- 1.0e-6 m/s, characteristic slip distance of 0.037 m, coefficients a and b
- of 0.0125 and 0.0172, and no cohesion (0 MPa).
- The parameters specific to this example are in
-\family typewriter
-dynamic_ratestateageing.cfg
-\family default
-, so we run the problem via:
-\end_layout
-
-\begin_layout LyX-Code
-pylith dynamic.cfg dynamic_ratestateageing.cfg
-\end_layout
-
-\begin_layout Standard
-The VTK files will be written to the
-\family typewriter
-output
-\family default
- directory with the prefix
-\family typewriter
-ratestateageing
-\family default
-.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:quad4:ratestateageing"
-
-\end_inset
-
-, which was generated using ParaView.
- The steady-state solution is a constant slip rate of 0.572 m/s and shear
- traction of 5.385 MPa on the fault surface, a uniform shear strain of 1.43e-4
- in the bar with uniform, constant velocities in the y-direction of +0.286
- m/s and -0.286 m/s on the -x and +x sides of the fault, respectively.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/quad4ratestateageing30.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Velocity field in the bar at 3.0 s for the rate- and state-friction fault
- constitutive model.
- Deformation has been exaggerated by a factor of 800.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:quad4:ratestateageing"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 1in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:tutorial:shearwave:quad4"
+
+\end_inset
+
+3D Bar Discretized with Quadrilaterals
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Dynamic solution
+\end_layout
+
+\begin_layout Itemize
+CUBIT mesh format
+\end_layout
+
+\begin_layout Itemize
+Absorbing dampers boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Dynamic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Plane strain linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Linear quadrilateral cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Itemize
+UniformDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/bar_shearwave/quad4.
+\end_layout
+
+\begin_layout Subsection
+Mesh Generation
+\end_layout
+
+\begin_layout Standard
+The mesh is a simple rectangular prism 8 km by 400 m by 400 m (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:quad4:mesh"
+
+\end_inset
+
+).
+ We provide documented CUBIT journal files in
+\family typewriter
+examples/bar_shearwave/quad4.
+
+\family default
+ We first create the geometry, mesh the domain using quadrilateral cells,
+ and then create blocks and nodesets associated with the materials and boundary
+ conditions.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/quad4mesh.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of hexahedral cells generated by CUBIT used for the example
+ problem.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:quad4:mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Kinematic Fault
+\end_layout
+
+\begin_layout Standard
+The simulation parameters match those in the tri3, tet4, and hex8 examples.
+ Using four-point quadrature permits use of a time step of 1/20 s, which
+ is slightly larger than the time step of 1/30 s used in the tri3 and tet4
+ simulations.
+ In contrast to the tri3, tet4, and hex8 shear wave examples which only
+ contained a single simulation in a directory, in this example we consider
+ several different simulations.
+ Consequently, we separate the parameters into multiple
+\family typewriter
+.cfg
+\family default
+ files.
+ The common parameters are placed in
+\family typewriter
+pylithapp.cfg
+\family default
+ with the parameters specific to the kinematic fault example in
+\family typewriter
+kinematic.cfg
+\family default
+.
+ To run the problem, simply run PyLith via:
+\end_layout
+
+\begin_layout LyX-Code
+pylith kinematic.cfg
+\end_layout
+
+\begin_layout Standard
+The VTK files will be written to the
+\family typewriter
+output
+\family default
+ directory with the prefix
+\family typewriter
+kinematic
+\family default
+.
+ The output includes the displacement field over the entire domain at every
+ other time step (0.10 s), the slip and traction vectors on the fault surface
+ in along-strike and normal directions at every other time step (0.10 s),
+ and the strain and stress tensors for each cell at every 20th time step
+ (1.0 s).
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:quad4:kinematic"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/quad4kinematic30.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Displacement field in the bar at 3.0 s.
+ Deformation has been exaggerated by a factor of 800.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:quad4:kinematic"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Dynamic Fault
+\end_layout
+
+\begin_layout Standard
+In this set of examples we replace the kinematic fault interface with the
+ dynamic fault interface, resulting in fault slip controlled by a fault-constitu
+tive model.
+ See Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:fault:constitutive:models"
+
+\end_inset
+
+ for detailed information about the fault constitutive models available
+ in PyLith.
+ Because this is a dynamic simulation we want the generated shear wave to
+ continue to be absorbed at the ends of the bar, so we drive the fault by
+ imposing initial tractions directly on the fault surface rather than through
+ deformation within the bar.
+ We employ a UniformDB object to specify 6.1 MPa of right-lateral shear and
+ 10.0 MPa of normal compression for the initial fault tractions.
+ The parameters common to the dynamic fault simulations are in
+\family typewriter
+dynamic.cfg
+\family default
+.
+ We use the explicit time-stepping with a lumped Jacobian matrix.
+ We also request that the fault output include slip, slip rate, and traction
+ fields:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.interfaces.fault.output]
+\end_layout
+
+\begin_layout LyX-Code
+vertex_data_fields = [slip,slip_rate,traction]
+\end_layout
+
+\begin_layout Subsubsection
+Dynamic Fault with Static Friction
+\end_layout
+
+\begin_layout Standard
+The parameters specific to this example are related to the use of the static
+ friction fault constitutive model.
+ We set the fault constitutive model via
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.interfaces.fault]
+\end_layout
+
+\begin_layout LyX-Code
+friction = pylith.friction.StaticFriction
+\end_layout
+
+\begin_layout Standard
+and use a UniformDB to set the static friction parameters.
+ We use a coefficient of friction of 0.6 and no cohesion (0 MPa).
+ The parameters specific to this example are in
+\family typewriter
+dynamic_staticfriction.cfg
+\family default
+, so we run the problem via:
+\end_layout
+
+\begin_layout LyX-Code
+pylith dynamic.cfg dynamic_staticfriction.cfg
+\end_layout
+
+\begin_layout Standard
+The VTK files will be written to the
+\family typewriter
+output
+\family default
+ directory with the prefix
+\family typewriter
+staticfriction
+\family default
+.
+ The output includes the displacement and velocity fields over the entire
+ domain at every other time step (0.10 s), the slip, slip rate, and traction
+ vectors on the fault surface in along-strike and normal directions at every
+ other time step (0.10 s), and the strain and stress tensors for each cell
+ at every 20th time step (1.0 s).
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:quad4:staticfriction"
+
+\end_inset
+
+, which was generated using ParaView.
+ The steady-state solution is a constant slip rate of 0.08 m/s, a shear traction
+ of 6.0 MPa on the fault surface, and a uniform shear strain of 2e-5 in the
+ bar with uniform, constant velocities in the y-direction of +0.04 m/s and
+ -0.04 m/s on the -x and +x sides of the fault, respectively.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/quad4staticfriction30.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Velocity field in the bar at 3.0 s for the static friction fault constitutive
+ model.
+ Deformation has been exaggerated by a factor of 800.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:quad4:staticfriction"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Dynamic Fault with Slip-Weakening Friction
+\end_layout
+
+\begin_layout Standard
+The parameters specific to this example are related to the use of the slip-weake
+ning friction fault constitutive model (see Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:fault:constitutive:models"
+
+\end_inset
+
+).
+ We set the fault constitutive model via
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.interfaces.fault]
+\end_layout
+
+\begin_layout LyX-Code
+friction = pylith.friction.SlipWeakening
+\end_layout
+
+\begin_layout Standard
+and use a UniformDB to set the slip-weakening friction parameters.
+ We use a static coefficient of friction of 0.6, a dynamic coefficient of
+ friction of 0.5, a slip-weakening parameter of 0.2 m, and no cohesion (0
+ MPa).
+ The fault constitutive model is associated with the fault, so we can append
+ the fault constitutive model parameters to the vertex information fields
+ and the fault constitutive model state variables to the vertex data fields:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.interfaces.fault.output]
+\end_layout
+
+\begin_layout LyX-Code
+vertex_info_fields = [strike_dir,normal_dir,initial_traction,static_coefficient,
+\begin_inset Newline newline
+\end_inset
+
+dynamic_coefficient,slip_weakening_parameter,cohesion]
+\end_layout
+
+\begin_layout LyX-Code
+vertex_data_fields = [slip,traction,cumulative_slip,previous_slip]
+\end_layout
+
+\begin_layout Standard
+The parameters specific to this example are in
+\family typewriter
+dynamic_slipweakening.cfg
+\family default
+, so we run the problem via:
+\end_layout
+
+\begin_layout LyX-Code
+pylith dynamic.cfg dynamic_slipweakening.cfg
+\end_layout
+
+\begin_layout Standard
+The VTK files will be written to the
+\family typewriter
+output
+\family default
+ directory with the prefix
+\family typewriter
+slipweakening
+\family default
+.
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:quad4:slipweakening"
+
+\end_inset
+
+, which was generated using ParaView.
+ The steady-state solution is a constant slip rate of 0.88 m/s and shear
+ traction of 5.0 MPa on the fault surface, a uniform shear strain of 2.2e-4
+ in the bar with uniform, constant velocities in the y-direction of +0.44
+ m/s and -0.44 m/s on the -x and +x sides of the fault, respectively.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/quad4slipweakening30.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Velocity field in the bar at 3.0 s for the slip-weakening friction fault
+ constitutive model.
+ Deformation has been exaggerated by a factor of 800.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:quad4:slipweakening"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Dynamic Fault with Rate-State Friction
+\end_layout
+
+\begin_layout Standard
+The parameters specific to this example are related to the use of the rate-
+ and state-friction fault constitutive model (see Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:fault:constitutive:models"
+
+\end_inset
+
+).
+ The evolution of the state variable uses the aging law.
+ We set the fault constitutive model via
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.interfaces.fault]
+\end_layout
+
+\begin_layout LyX-Code
+friction = pylith.friction.RateStateAgeing
+\end_layout
+
+\begin_layout Standard
+and use a UniformDB to set the static friction parameters.
+ We use a reference coefficient of friction of 0.6, reference slip rate of
+ 1.0e-6 m/s, characteristic slip distance of 0.037 m, coefficients a and b
+ of 0.0125 and 0.0172, and no cohesion (0 MPa).
+ The parameters specific to this example are in
+\family typewriter
+dynamic_ratestateageing.cfg
+\family default
+, so we run the problem via:
+\end_layout
+
+\begin_layout LyX-Code
+pylith dynamic.cfg dynamic_ratestateageing.cfg
+\end_layout
+
+\begin_layout Standard
+The VTK files will be written to the
+\family typewriter
+output
+\family default
+ directory with the prefix
+\family typewriter
+ratestateageing
+\family default
+.
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:quad4:ratestateageing"
+
+\end_inset
+
+, which was generated using ParaView.
+ The steady-state solution is a constant slip rate of 0.572 m/s and shear
+ traction of 5.385 MPa on the fault surface, a uniform shear strain of 1.43e-4
+ in the bar with uniform, constant velocities in the y-direction of +0.286
+ m/s and -0.286 m/s on the -x and +x sides of the fault, respectively.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/quad4ratestateageing30.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Velocity field in the bar at 3.0 s for the rate- and state-friction fault
+ constitutive model.
+ Deformation has been exaggerated by a factor of 800.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:quad4:ratestateageing"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/shearwave.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/shearwave.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/shearwave.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,162 +1,180 @@
-#LyX 1.6.5 created this file. For more info see http://www.lyx.org/
-\lyxformat 345
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-
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-
-\begin_body
-
-\begin_layout Section
-Shear Wave in a Bar
-\end_layout
-
-\begin_layout Standard
-This suite of examples focuses on the dynamics of a shear wave propagating
- down an 8 km long bar with a 400 m wide cross-section.
- Motion is limited to shear deformation by fixing the longitudinal degree
- of freedom.
- For each cell type (tri3, quad4, tet4, and hex8) we generate a shear wave
- using a kinematic fault rupture with simultaneous slip over the fault surface,
- which we place at the center of the bar.
- The discretization size is 200 m in all cases.
- The slip time histories follow the integral of Brune's far-field time function
- with slip initiating at 0.1 s, a left-lateral final slip of 1.0 m, and a
- rise time of 2.0 s.
- The shear wave speed in the bar is 1.0 km/s, so the shear wave reaches each
- end of the bar at 4.1 s.
- Absorbing boundaries on the ends of the bar prevent significant reflections.
- The bar comes to a rest with a static offset.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status collapsed
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/bar.eps
- lyxscale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Domain for shear wave propagation in a 8.0 km bar with 400 m cross-section.
- We generate a shear wave via slip on a fault located in the middle of the
- bar while limiting deformation to the transverse direction.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:domain"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-For the bar discretized with quad4 cells we also consider the fault subjected
- to frictional sliding controlled by static friction, linear slip-weakening
- friction, and rate- and state-friction.
- We use initial tractions applied to the fault to drive the dislocation
- and generate the shear wave.
- Because the fault tractions are constant in time, they continue to drive
- the motion even after the shear wave reaches the absorbing boundary, leading
- to a steady state solution with uniform shear deformation in the bar and
- a constant slip rate on the fault.
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset CommandInset include
-LatexCommand input
-filename "tri3.lyx"
-
-\end_inset
-
-
-\begin_inset CommandInset include
-LatexCommand input
-filename "tet4.lyx"
-
-\end_inset
-
-
-\begin_inset CommandInset include
-LatexCommand input
-filename "hex8.lyx"
-
-\end_inset
-
-
-\begin_inset CommandInset include
-LatexCommand input
-filename "quad4.lyx"
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
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+\begin_header
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+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+Shear Wave in a Bar
+\end_layout
+
+\begin_layout Standard
+This suite of examples focuses on the dynamics of a shear wave propagating
+ down an 8 km-long bar with a 400 m-wide cross-section.
+ Motion is limited to shear deformation by fixing the longitudinal degree
+ of freedom.
+ For each cell type (tri3, quad4, tet4, and hex8) we generate a shear wave
+ using a kinematic fault rupture with simultaneous slip over the fault surface,
+ which we place at the center of the bar.
+ The discretization size is 200 m in all cases.
+ The slip-time histories follow the integral of Brune's far-field time function
+ with slip initiating at 0.1 s, a left-lateral final slip of 1.0 m, and a
+ rise time of 2.0 s.
+ The shear wave speed in the bar is 1.0 km/s, so the shear wave reaches each
+ end of the bar at 4.1 s.
+ Absorbing boundaries on the ends of the bar prevent significant reflections.
+ The bar comes to a rest with a static offset.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status collapsed
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/bar.eps
+ lyxscale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Domain for shear wave propagation in a 8.0 km bar with 400 m cross-section.
+ We generate a shear wave via slip on a fault located in the middle of the
+ bar while limiting deformation to the transverse direction.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:domain"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For the bar discretized with quad4 cells we also consider the fault subjected
+ to frictional sliding controlled by static friction, linear slip-weakening
+ friction, and rate- and state-friction.
+ We use initial tractions applied to the fault to drive the dislocation
+ and generate the shear wave.
+ Because the fault tractions are constant in time, they continue to drive
+ the motion even after the shear wave reaches the absorbing boundary, leading
+ to a steady state solution with uniform shear deformation in the bar and
+ a constant slip rate on the fault.
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand input
+filename "tri3.lyx"
+
+\end_inset
+
+
+\begin_inset CommandInset include
+LatexCommand input
+filename "tet4.lyx"
+
+\end_inset
+
+
+\begin_inset CommandInset include
+LatexCommand input
+filename "hex8.lyx"
+
+\end_inset
+
+
+\begin_inset CommandInset include
+LatexCommand input
+filename "quad4.lyx"
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/tet4.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/tet4.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/tet4.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,284 +1,288 @@
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-\shortcut idx
-\color #008000
-\end_index
-\leftmargin 1in
-\topmargin 1in
-\rightmargin 1in
-\bottommargin 1in
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-\paragraph_separation indent
-\paragraph_indentation default
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-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:tutorial:shearwave:tet4"
-
-\end_inset
-
-3-D Bar Discretized with Tetrahedra
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Dynamic solution
-\end_layout
-
-\begin_layout Itemize
-LaGriT mesh format
-\end_layout
-
-\begin_layout Itemize
-Absorbing dampers boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Elastic isotropic linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Linear tetrahedral cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/bar_shearwave/tet4.
-\end_layout
-
-\begin_layout Subsection
-Mesh Generation
-\end_layout
-
-\begin_layout Standard
-The mesh is a simple rectangular prism 8 km by 400 m by 400m (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:tet4:mesh"
-
-\end_inset
-
-).
- This mesh could be generated via a simple script, but it is even easier
- to generate this mesh using LaGriT.
- We provide documented LaGriT files in
-\family typewriter
-examples/bar_shearwave/tet4.
-
-\family default
- We first create the geometry, regions, mesh the domain using tetrahedral
- cells, and then create point sets associated with boundary conditions.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/tet4mesh.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of tetrahedral cells generated by LaGriT used for the example
- problem.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:tet4:mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Simulation Parameters
-\end_layout
-
-\begin_layout Standard
-The simulation parameters match those in the tri3 example with the exception
- of using the LaGriT mesh reader and switching the from a two-dimensional
- problem to a three-dimensional problem.
- In addition to fixing the longitudinal degree of freedom, we also fix the
- out-of-plane transverse degree of freedom.
- Because the fault separates two material regions in LaGriT, we use two
- materials in PyLith.
- All of the parameters are set in the pylithapp.cfg file.
- To run the problem, simply run PyLith without any command line arguments:
-\end_layout
-
-\begin_layout LyX-Code
-pylith
-\end_layout
-
-\begin_layout Standard
-The VTK files will be written to the
-\family typewriter
-output
-\family default
- directory.
- The output includes the displacement and velocity fields over the entire
- domain at every 3rd time step (0.10 s), the slip and change in traction
- vectors on the fault surface in along-strike and normal directions at every
- 3rd time step (0.10 s), and the strain and stress tensors for each cell
- at every 30th time step (1.0 s).
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:tet4:deform"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/tet4deform30.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Displacement field in the bar at 3.0 s.
- Deformation has been exaggerated by a factor of 800.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:tet4:deform"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
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+\shortcut idx
+\color #008000
+\end_index
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+\topmargin 1in
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+\tocdepth 3
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+\paragraph_indentation default
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+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:tutorial:shearwave:tet4"
+
+\end_inset
+
+3D Bar Discretized with Tetrahedra
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Dynamic solution
+\end_layout
+
+\begin_layout Itemize
+LaGriT mesh format
+\end_layout
+
+\begin_layout Itemize
+Absorbing dampers boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Elastic isotropic linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Linear tetrahedral cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/bar_shearwave/tet4.
+\end_layout
+
+\begin_layout Subsection
+Mesh Generation
+\end_layout
+
+\begin_layout Standard
+The mesh is a simple rectangular prism 8 km by 400 m by 400m (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:tet4:mesh"
+
+\end_inset
+
+).
+ This mesh could be generated via a simple script, but it is even easier
+ to generate this mesh using LaGriT.
+ We provide documented LaGriT files in
+\family typewriter
+examples/bar_shearwave/tet4.
+
+\family default
+ We first create the geometry and regions, mesh the domain using tetrahedral
+ cells, and then create point sets associated with boundary conditions.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/tet4mesh.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of tetrahedral cells generated by LaGriT used for the example
+ problem.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:tet4:mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Simulation Parameters
+\end_layout
+
+\begin_layout Standard
+The simulation parameters match those in the tri3 example with the exception
+ of using the LaGriT mesh reader and switching from a two-dimensional problem
+ to a three-dimensional problem.
+ In addition to fixing the longitudinal degree of freedom, we also fix the
+ out-of-plane transverse degree of freedom.
+ Because the fault separates two material regions in LaGriT, we use two
+ materials in PyLith.
+ All of the parameters are set in the
+\family typewriter
+pylithapp.cfg
+\family default
+ file.
+ To run the problem, simply run PyLith without any command line arguments:
+\end_layout
+
+\begin_layout LyX-Code
+pylith
+\end_layout
+
+\begin_layout Standard
+The VTK files will be written to the
+\family typewriter
+output
+\family default
+ directory.
+ The output includes the displacement and velocity fields over the entire
+ domain at every 3rd time step (0.10 s), the slip and change in traction
+ vectors on the fault surface in along-strike and normal directions at every
+ 3rd time step (0.10 s), and the strain and stress tensors for each cell
+ at every 30th time step (1.0 s).
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:tet4:deform"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/tet4deform30.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Displacement field in the bar at 3.0 s.
+ Deformation has been exaggerated by a factor of 800.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:tet4:deform"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/tri3.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/tri3.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/shearwave/tri3.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,348 +1,352 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
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-\font_sc false
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-
-\graphics default
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-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:tutorial:shearwave:tri3"
-
-\end_inset
-
-2-D Bar Discretized with Triangles
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Dynamic solution
-\end_layout
-
-\begin_layout Itemize
-CUBIT format
-\end_layout
-
-\begin_layout Itemize
-Absorbing dampers boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Plane strain linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Linear triangular cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/bar_shearwave/tri3.
-\end_layout
-
-\begin_layout Subsection
-Mesh Generation
-\end_layout
-
-\begin_layout Standard
-The mesh is a simple rectangle 8 km by 400 m (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:tet4:mesh"
-
-\end_inset
-
-).
- This mesh could be generated via a simple script, but it is even easier
- to generate this mesh using CUBIT.
- We provide documented journal files in
-\family typewriter
-examples/bar_shearwave/tri3.
-
-\family default
- We first create the geometry, mesh the domain using triangular cells, and
- then create blocks and nodesets to associated the cells and vertices with
- materials and boundary conditions.
- See Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Tutorial-3d-hex8"
-
-\end_inset
-
- for more information on using CUBIT to generate meshes.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/tri3mesh.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of triangular cells generated by CUBIT used for the example
- problem.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:tri3:mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Simulation Parameters
-\end_layout
-
-\begin_layout Standard
-All of the parameters are set in the pylithapp.cfg file.
- The structure of the file follows the same pattern as in all of the other
- examples.
- We set the parameters for the journal information followed by the mesh
- reader, problem, materials, boundary conditions, fault, and output.
- We change the time-stepping formulation from the default value of implicit
- time stepping to explicit time stepping by setting the formulation object
- via
-\end_layout
-
-\begin_layout LyX-Code
-formulation = pylith.problems.Explicit
-\end_layout
-
-\begin_layout Standard
-We can switch to explicit time stepping with a lumped Jacobian matrix (rather
- than the full Jacobian matrix) by changing Explicit to ExplicitLumped.
- Using the ExplicitLumped object automatically triggers lumping of the Jacobian
- cell matrices and assembly into a vector rather than a sparse matrix.
- Lumping the Jacobian decouples the equations, so we can use a very simple
- direct solver.
- Use of this simple solver is also triggered by the selection of the ExplicitLum
-ped object.
-
-\end_layout
-
-\begin_layout Standard
-For dynamic problems we use the NondimElasticDynamic object to nondimensionalize
- the equations.
- This object provides scales associated with wave propagation for nondimensional
-ization, including the minimum wave period, the shear wave speed, and mass
- density.
- In this example we use the default values of a minimum wave period of 1.0
- s, a shear wave speed of 3 km/s, and a mass density of 3000 kg/m
-\begin_inset Formula $^{3}$
-\end_inset
-
-.
- We simulate 12.0 s of motion with a time step of 1/30 s.
- This time step must follow the Courant–Friedrichs–Lewy condition; that
- is, the time step must be smaller than the time it takes the P wave to
- propagate across the shortest edge of a cell.
-
-\end_layout
-
-\begin_layout Standard
-The boundary conditions include the absorbing dampers at the ends of the
- bar and a Dirichlet boundary condition to prevent longitudinal motion.
- Because we cannot overlap the Dirichlet BC with the fault, we use the nodeset
- associated with all vertices except the fault.
- For the output over the entire domain, we request both displacement and
- velocity fields:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.output]
-\end_layout
-
-\begin_layout LyX-Code
-vertex_data_fields = [displacement,velocity]
-\end_layout
-
-\begin_layout Standard
-To run the problem, simply run PyLith without any command line arguments:
-\end_layout
-
-\begin_layout LyX-Code
-pylith
-\end_layout
-
-\begin_layout Standard
-The VTK files will be written to the
-\family typewriter
-output
-\family default
- directory.
- The output includes the displacement and velocity fields over the entire
- domain at every 3rd time step (0.10 s), the slip and change in traction
- vectors on the fault surface in along-strike and normal directions at every
- 3rd time step (0.10 s), and the strain and stress tensors for each cell
- at every 30th time step (1.0 s).
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:shearwave:tri3:deform"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/tri3deform30.jpg
- lyxscale 50
- scale 50
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Displacement field in the bar at 3.0 s.
- Deformation has been exaggerated by a factor of 800.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:shearwave:tri3:deform"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 1in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:tutorial:shearwave:tri3"
+
+\end_inset
+
+2D Bar Discretized with Triangles
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Dynamic solution
+\end_layout
+
+\begin_layout Itemize
+CUBIT format
+\end_layout
+
+\begin_layout Itemize
+Absorbing dampers boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Plane strain linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Linear triangular cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/bar_shearwave/tri3.
+\end_layout
+
+\begin_layout Subsection
+Mesh Generation
+\end_layout
+
+\begin_layout Standard
+The mesh is a simple rectangle 8 km by 400 m (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:tet4:mesh"
+
+\end_inset
+
+).
+ This mesh could be generated via a simple script, but it is even easier
+ to generate this mesh using CUBIT.
+ We provide documented journal files in
+\family typewriter
+examples/bar_shearwave/tri3.
+
+\family default
+ We first create the geometry, mesh the domain using triangular cells, and
+ then create blocks and nodesets to associate the cells and vertices with
+ materials and boundary conditions.
+ See Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Tutorial-3d-hex8"
+
+\end_inset
+
+ for more information on using CUBIT to generate meshes.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/tri3mesh.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of triangular cells generated by CUBIT used for the example
+ problem.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:tri3:mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Simulation Parameters
+\end_layout
+
+\begin_layout Standard
+All of the parameters are set in the
+\family typewriter
+pylithapp.cfg
+\family default
+ file.
+ The structure of the file follows the same pattern as in all of the other
+ examples.
+ We set the parameters for the journal information followed by the mesh
+ reader, problem, materials, boundary conditions, fault, and output.
+ We change the time-stepping formulation from the default value of implicit
+ time stepping to explicit time stepping by setting the formulation object
+ via
+\end_layout
+
+\begin_layout LyX-Code
+formulation = pylith.problems.Explicit
+\end_layout
+
+\begin_layout Standard
+We can switch to explicit time stepping with a lumped Jacobian matrix (rather
+ than the full Jacobian matrix) by changing Explicit to ExplicitLumped.
+ Using the ExplicitLumped object automatically triggers lumping of the Jacobian
+ cell matrices and assembly into a vector rather than a sparse matrix.
+ Lumping the Jacobian decouples the equations, so we can use a very simple
+ direct solver.
+ Use of this simple solver is also triggered by the selection of the ExplicitLum
+ped object.
+
+\end_layout
+
+\begin_layout Standard
+For dynamic problems we use the NondimElasticDynamic object to nondimensionalize
+ the equations.
+ This object provides scales associated with wave propagation for nondimensional
+ization, including the minimum wave period, the shear wave speed, and mass
+ density.
+ In this example we use the default values of a minimum wave period of 1.0
+ s, a shear wave speed of 3 km/s, and a mass density of 3000 kg/m
+\begin_inset Formula $^{3}$
+\end_inset
+
+.
+ We simulate 12.0 s of motion with a time step of 1/30 s.
+ This time step must follow the Courant–Friedrichs–Lewy condition; that
+ is, the time step must be smaller than the time it takes the P wave to
+ propagate across the shortest edge of a cell.
+
+\end_layout
+
+\begin_layout Standard
+The boundary conditions include the absorbing dampers at the ends of the
+ bar and a Dirichlet boundary condition to prevent longitudinal motion.
+ Because we cannot overlap the Dirichlet BC with the fault, we use the nodeset
+ associated with all vertices except the fault.
+ For the output over the entire domain, we request both displacement and
+ velocity fields:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.output]
+\end_layout
+
+\begin_layout LyX-Code
+vertex_data_fields = [displacement,velocity]
+\end_layout
+
+\begin_layout Standard
+To run the problem, simply run PyLith without any command line arguments:
+\end_layout
+
+\begin_layout LyX-Code
+pylith
+\end_layout
+
+\begin_layout Standard
+The VTK files will be written to the
+\family typewriter
+output
+\family default
+ directory.
+ The output includes the displacement and velocity fields over the entire
+ domain at every 3rd time step (0.10 s), the slip and change in traction
+ vectors on the fault surface in along-strike and normal directions at every
+ 3rd time step (0.10 s), and the strain and stress tensors for each cell
+ at every 30th time step (1.0 s).
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:shearwave:tri3:deform"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/tri3deform30.jpg
+ lyxscale 50
+ scale 50
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Displacement field in the bar at 3.0 s.
+ Deformation has been exaggerated by a factor of 800.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:shearwave:tri3:deform"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/subduction/subduction.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/subduction/subduction.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/subduction/subduction.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,1270 +1,1289 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
-\use_default_options false
-\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding latin1
-\fontencoding global
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\use_non_tex_fonts false
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
-\graphics default
-\default_output_format default
-\output_sync 0
-\bibtex_command default
-\index_command default
-\paperfontsize default
-\spacing single
-\use_hyperref false
-\papersize default
-\use_geometry true
-\use_amsmath 0
-\use_esint 0
-\use_mhchem 1
-\use_mathdots 1
-\cite_engine basic
-\use_bibtopic false
-\use_indices false
-\paperorientation portrait
-\suppress_date false
-\use_refstyle 0
-\index Index
-\shortcut idx
-\color #008000
-\end_index
-\leftmargin 1in
-\topmargin 1in
-\rightmargin 1in
-\bottommargin 1in
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\paragraph_indentation default
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-Subduction"
-
-\end_inset
-
-Tutorial for Slip on a Subduction Zone
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Static solution
-\end_layout
-
-\begin_layout Itemize
-Quasi-static solution
-\end_layout
-
-\begin_layout Itemize
-CUBIT mesh generation
-\end_layout
-
-\begin_deeper
-\begin_layout Itemize
-Nonplanar geometry
-\end_layout
-
-\begin_layout Itemize
-Variable mesh resolution
-\end_layout
-
-\begin_layout Itemize
-APREPRO programming language
-\end_layout
-
-\end_deeper
-\begin_layout Itemize
-Linear triangular cells
-\end_layout
-
-\begin_layout Itemize
-HDF5 output
-\end_layout
-
-\begin_layout Itemize
-Dirichlet displacement and velocity boundary conditions
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-UniformDB spatial database
-\end_layout
-
-\begin_layout Itemize
-Multiple materials
-\end_layout
-
-\begin_layout Itemize
-Nonlinear solver
-\end_layout
-
-\begin_layout Itemize
-Plane strain linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-Plane Maxwell linear viscoelastic material
-\end_layout
-
-\begin_layout Itemize
-Prescribed slip
-\end_layout
-
-\begin_deeper
-\begin_layout Itemize
-Static fault rupture
-\end_layout
-
-\begin_layout Itemize
-Multiple faults
-\end_layout
-
-\begin_layout Itemize
-Spatially variable coseismic slip
-\end_layout
-
-\begin_layout Itemize
-Spatially variable aseismic creep
-\end_layout
-
-\end_deeper
-\begin_layout Itemize
-Afterslip via fault friction
-\end_layout
-
-\begin_deeper
-\begin_layout Itemize
-Static fault rupture
-\end_layout
-
-\begin_layout Itemize
-Static friction
-\end_layout
-
-\end_deeper
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/2d/subduction.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial examines quasi-static interseismic and coseismic deformation
- in 2-D for a subduction zone (see Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:overview"
-
-\end_inset
-
-).
- It is based on the 2011 M9.0 Tohoku earthquake off the east coast of Japan.
- Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:steps"
-
-\end_inset
-
- shows the three steps of increasing complexity.
- Step 1 focuses on the coseismic slip, Step 2 focuses on interseismic deformatio
-n, and Step 3 combines the two into a pseudo-earthquake cycle deformation
- simulation.
- Step 4 focuses on using the change in tractions from Step 1 to construct
- a simulation with afterslip controlled by frictional sliding.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/cartoon_general.eps
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Cartoon of subduction zone example.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:overview"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="2" columns="3">
-<features tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
-<row>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Step 1
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Step 2
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Step 3
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Graphics
- filename figs/step01.eps
- lyxscale 66
- width 2in
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Graphics
- filename figs/step02.eps
- lyxscale 66
- width 2in
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Graphics
- filename figs/step03.eps
- lyxscale 66
- width 2in
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Diagram of fault slip and boundary conditions for each step in the subduction
- zone tutorial.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:steps"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Mesh Description
-\end_layout
-
-\begin_layout Standard
-We construct the mesh in CUBIT by constructing the geometry, prescribing
- the discretization, running the mesher, and then grouping cells and vertices
- for boundary conditions and materials.
- We use the APREPRO programming language within the journal files to enable
- use of units and to set variables for values used many times.
- An appendix in the CUBIT documentation discusses the features available
- with APREPRO in CUBIT.
- The CUBIT commands are in three separate journal files.
- The main driver is in the journal file mesh_tri3.jou.
- It calls the journal file geometry.jou to construct the geometry and createbc.jou
- to setup the groups associated with boundary conditions and materials.
- The journal files are documented and describe the various steps outlined
- below.
-\end_layout
-
-\begin_layout Enumerate
-Create the geometry defining the domain.
-\end_layout
-
-\begin_deeper
-\begin_layout Enumerate
-Create points.
-\end_layout
-
-\begin_layout Enumerate
-Connect points into spline curves.
-\end_layout
-
-\begin_layout Enumerate
-Split curves to separate them into sections bounding surfaces.
-
-\end_layout
-
-\begin_layout Enumerate
-Connect curves into surfaces.
-\end_layout
-
-\begin_layout Enumerate
-Stitch surfaces together.
-\end_layout
-
-\end_deeper
-\begin_layout Enumerate
-Define meshing scheme and cell size variation.
-\end_layout
-
-\begin_deeper
-\begin_layout Enumerate
-Define cell size along curves near fault.
-\end_layout
-
-\begin_layout Enumerate
-Increase cell size away from fault at a geometric rate (bias).
-\end_layout
-
-\end_deeper
-\begin_layout Enumerate
-Generate mesh.
-\end_layout
-
-\begin_layout Enumerate
-Create blocks for materials and nodesets for boundary conditions.
-\end_layout
-
-\begin_layout Enumerate
-Export mesh.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/subduction_tri3.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Variable resolution finite-element mesh with triangular cells.
- The nominal cell size increases at a geometric rate of 1.2 away from the
- region of coseismic slip.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Common Information
-\end_layout
-
-\begin_layout Standard
-As in the examples discussed in previous sections of these tutorials, we
- place parameters common to the three steps in the
-\family typewriter
-pylithapp.cfg
-\family default
- file so that we do not have to duplicate them for each step.
- The settings contained in
-\family typewriter
-pylithapp.cfg
-\family default
- for this problem consist of:
-\end_layout
-
-\begin_layout Description
-pylithapp.journal.info Settings that control the verbosity of the output written
- to stdout for the different components.
-\end_layout
-
-\begin_layout Description
-pylithapp.mesh_generator Settings that control mesh importing, such as the
- importer type, the filename, and the spatial dimension of the mesh.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Settings that control the problem, such as the total
- time, time step size, and spatial dimension.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials Settings that control the material type,
- specify which material IDs are to be associated with a particular material
- type, and give the name of the spatial database containing the physical
- properties for the material.
- The quadrature information is also given.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output Settings related output of the solution
- over the domain and subdomain (ground surface).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.
-\shape italic
-MATERIAL
-\shape default
-.output Settings related to output of the state variables for material
-\shape italic
-MATERIAL
-\shape default
-.
-\end_layout
-
-\begin_layout Description
-pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
- type.
-\end_layout
-
-\begin_layout Standard
-The physical properties for each material are specified in spatial database
- files.
- For example, the elastic properties for the continental crust are in mat_concru
-st.spatialdb.
- The provided spatial database files all use just a single point to specify
- uniform physical properties within each material.
- A good exercise is to alter the spatial database files with the physical
- properties to match PREM.
-\end_layout
-
-\begin_layout Subsection
-Step 1: Coseismic Slip Simulation
-\end_layout
-
-\begin_layout Standard
-The first example problem is earthquake rupture involving coseismic slip
- along the interface between the subducting slab and the continental crust
- and upper most portion of the mantle below the continental crust.
- The spatial variation of slip comes from a cross-section of Gavin Hayes'
- finite-source model
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/finite_fault.php
-\end_layout
-
-\end_inset
-
-.
- On the lateral and bottom boundaries of the domain, we fix the degrees
- of freedom perpendicular to the boundary as shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:steps"
-
-\end_inset
-
-.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step01.cfg
-\family default
-.
- These settings are:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.formulation.time_step Adjust the total simulation time
- to 0 years (static simulation).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies the array of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.
-\shape italic
-BOUNDARY
-\shape default
- Defines the settings for boundary
-\shape italic
-BOUNDARY
-\shape default
-, including which degrees of freedom are being constrained (x or y), the
- label (defined in
-\family typewriter
- mesh_tri3.exo
-\family default
-) corresponding to the nodeset in CUBIT, and a label to the boundary condition
- used in any error messages.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces.fault Specify the coseismic slip along the
- interface between the oceanic crust and continental crust with a small
- amount of slip penetrating into the upper mantle.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain Gives the base filenames for HDF5
- output (
-\family typewriter
-for example, step01.h5
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-We run this example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step01.cfg
-\end_layout
-
-\begin_layout Standard
-The problem will produce twelve pairs of HDF5/Xdmf files.
- The HDF5 files contain the data and the Xdmf files contain the metadata
- required by ParaView and Visit (and possibly other visualization tools
- that use Xdmf files) to access the mesh and data sets in the HDF5 files.
- The files include the solution over the domain and ground surface (two
- pairs of files), physical properties, stress, and strain within each material
- (eight pairs of files), and fault parameters, slip, and traction (two pairs
- of files).
-
-\end_layout
-
-\begin_layout Standard
-Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:step01"
-
-\end_inset
-
-, which was created using ParaView, displays the magnitude of the displacement
- field with the deformation exaggerated by a factor of 1000.
- We construct a three-dimensional displacement vector from the two-dimensional
- displacement components using the Calculator with the expression
-\end_layout
-
-\begin_layout LyX-Code
-displacement_x*iHat + displacement_y*jHat
-\end_layout
-
-\begin_layout Standard
-where we select the displacement components from the Scalars drop-down menu
- and the iHat, jHat, and kHat values from the Calculator buttons.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step01_soln.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Solution for Step 1.
- The colors indicate the magnitude of the displacement and the deformation
- is exaggerated by a factor of 1000.
-
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:step01"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Step 2: Interseismic Deformation Simulation
-\end_layout
-
-\begin_layout Standard
-In this example we simulate the interseismic deformation associated with
- the oceanic crust subducting beneath the continental crust and into the
- mantle.
- We prescribe steady aseismic slip of 8 cm/yr along the interfaces between
- the oceanic crust and mantle with the interface between the oceanic crust
- and continental crust locked as shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:steps"
-
-\end_inset
-
-.
- We adjust the Dirichlet boundary conditions on the lateral edges and bottom
- of the domain by pinning only the portions of the boundaries in the mantle
- and continental crust (i.e., not part of the oceanic crust).
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step02.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.formulation.time_step Adjust the total simulation time
- to 100 years.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies the array of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.
-\shape italic
-BOUNDARY
-\shape default
- Defines the settings for boundary
-\shape italic
-BOUNDARY
-\shape default
-, including which degrees of freedom are being constrained (x or y), the
- label (defined in
-\family typewriter
- mesh_tri3.exo
-\family default
-) corresponding to the nodeset in CUBIT, and a label to the boundary condition
- used in any error messages.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces Specify the steady aseismic slip as a constant
- slip rate on the fault surfaces.
-
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain Gives the base filename for HDF5
- output (
-\family typewriter
-for example, step02.h5
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-We run this example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step02.cfg
-\end_layout
-
-\begin_layout Standard
-The simulation will produce pairs of HDF5/Xdmf files with separate files
- for each material and fault interface.
- Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:step02"
-
-\end_inset
-
-, which was created using ParaView, displays the magnitude of the displacement
- field with the deformation exaggerated by a factor of 1000.
- Using the animation features within ParaView or Visit you can illustrate
- how the continental crust near the trench subsides during the interseismic
- deformation.
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step02_soln.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Solution for Step 2 at 100 years.
- The colors indicate the magnitude of the displacement and the deformation
- is exaggerated by a factor of 1000.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:step02"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Step 3: Pseudo-earthquake Cycle Model
-\end_layout
-
-\begin_layout Standard
-This simulation combines 300 years of interseismic deformation from Step
- 2 with the coseismic deformation from Step 1 applied at 150 years to create
- a simple model of the earthquake cycle.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step03.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.formulation.time_step Adjust the total simulation time
- to 300 years.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies the array of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.
-\shape italic
-BOUNDARY
-\shape default
- The Dirichlet boundary conditions match those in Step 2.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces On the interface between the subducting
- oceanic crust and the mantle, we prescribe the same steady, aseismic slip
- as that in Step 2.
- On the interface along the top of the subducting oceanic crust and the
- continental crust and mantle we create two earthquake ruptures, The first
- rupture applies the coseismic slip form Step 1 at 150 years, while the
- second rupture prescribes the same steady, aseismic slip as in Step 2.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain Gives the base filename for HDF5
- output (
-\family typewriter
-for example, step03.h5
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-We run this example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step03.cfg
-\end_layout
-
-\begin_layout Standard
-The simulation will produce pairs of HDF5/Xdmf files with separate files
- for each material and fault interface.
- Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:step03"
-
-\end_inset
-
-, which was created using ParaView, displays the magnitude of the displacement
- field with the deformation exaggerated by a factor of 1000.
- Using the animation features within ParaView or Visit you can illustrate
- how the continental crust near the trench rebounds during the earthquake
- after subsiding during the interseismic deformation.
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step03_soln.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Solution for Step 3 at 150 years (immediately following the earthquake rupture).
- The colors indicate the magnitude of the displacement and the deformation
- is exaggerated by a factor of 1000.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:step03"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Step 4: Frictional Afterslip Simulation
-\end_layout
-
-\begin_layout Standard
-This simulation demonstrates how to combine the change in tractions associated
- with coseismic slip with a background stress field to compute afterslip
- controlled by static friction.
- The Python script
-\family typewriter
-afterslip_tractions.py
-\family default
- will create a spatial database file with initial tractions based on the
- change in tractions from Step 1 and a background stress field.
- The background stress field is simply normal tractions consistent with
- the overburden (lithostatic load) for a uniform half-space and shear tractions
- consistent with a coefficient of friction of 0.6.
- The
-\family typewriter
-afterslip_tractions.spatialdb
-\family default
- file is provided, so you do not need to run the Python script
-\family typewriter
-afterslip_tractions.py
-\family default
-; however, you can do so by typing
-\end_layout
-
-\begin_layout LyX-Code
-python afterslip_tractions.py
-\end_layout
-
-\begin_layout Standard
-We provide 2.0 MPa of strength excess associated with the background stress
- field by using a cohesion of 2.0 MPa in the static friction model.
- Slip will occur in regions where the coseismic slip increased the shear
- tractions by more than 2.0 MPa.
- On the lateral and bottom boundaries of the domain, we fix the degrees
- of freedom perpendicular to the boundary as shown in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:steps"
-
-\end_inset
-
-.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-step04.cfg
-\family default
-.
- These settings are:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.formulation.time_step Adjust the total simulation time
- to 0 years (static simulation).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Selects the nonlinear solver and specifies the array
- of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.
-\shape italic
-BOUNDARY
-\shape default
- Defines the settings for boundary
-\shape italic
-BOUNDARY
-\shape default
-, including which degrees of freedom are being constrained (x or y), the
- label (defined in
-\family typewriter
- mesh_tri3.exo
-\family default
-) corresponding to the nodeset in CUBIT, and a label to the boundary condition
- used in any error messages.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces.fault Specify a fault with a fault constitutive
- model (static friction) and initial fault tractions.
-
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.domain Gives the base filenames for HDF5
- output (
-\family typewriter
-for example, step04.h5
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-We run this example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith step04.cfg
-\end_layout
-
-\begin_layout Standard
-The problem will produce twelve pairs of HDF5/Xdmf files.
- The HDF5 files contain the data and the Xdmf files contain the metadata
- required by ParaView and Visit (and possibly other visualization tools
- that use Xdmf files) to access the mesh and data sets in the HDF5 files.
- The files include the solution over the domain and ground surface (two
- pairs of files), physical properties, stress, and strain within each material
- (eight pairs of files), and fault parameters, slip, and traction (two pairs
- of files).
-
-\end_layout
-
-\begin_layout Standard
-Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:tutorial:subduction:step04"
-
-\end_inset
-
-, which was created using ParaView, displays the magnitude of the displacement
- field with the original configuration.
- Slip occurs down-dip from the coseismic slip as well as three areas with
- sharp gradients in slip, including the trench.
- The location of the afterslip can be shifted by changing the spatial variation
- of the coseismic slip and background stress field.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/step01_soln.png
- lyxscale 50
- width 4.5in
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Solution for Step 4.
- The colors indicate the magnitude of the displacement
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:tutorial:subduction:step04"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Suggested Variations
-\end_layout
-
-\begin_layout Standard
-The list below includes some suggested modifications to the problem that
- will allow you to become more familiar with PyLith while examining some
- interesting physics.
-\end_layout
-
-\begin_layout Itemize
-Change the resolution of the mesh by editing the mesh_tri3.jou journal file.
- Change the resolution and bias factor.
-\end_layout
-
-\begin_layout Itemize
-Add depth dependent viscosity to the mantle and crust.
- This requires using the linear Maxwell plane strain bulk constitutive model
- in the crust as well and creating spatial databases that include viscosity
- for the crust.
- Specifying a depth dependent variation in the parameters will require adding
- points, updating num-locs accordingly, and changing data-dim to 1.
-\end_layout
-
-\begin_layout Itemize
-Modify the spatial database files for the material properties to use depth-depen
-dent elastic properties based on PREM (Dziewonski and Anderson, 1981, 10.1016/003
-1-9201(81)90046-7).
- See
-\begin_inset Flex URL
-status open
-
-\begin_layout Plain Layout
-
-geophysics.ou.edu/solid_earth/prem.html
-\end_layout
-
-\end_inset
-
- for a simple table of values.
- Add points, update num-locs accordingly, and change data-dim to be 1.
-\end_layout
-
-\begin_layout Itemize
-Modify the CUBIT journal files to use quad4 cells rather than tri3 cells.
- This requires using the pave mesh scheme.
-\end_layout
-
-\begin_layout Itemize
-Create a simulation with multiple earthquake cycles by lengthening the duration
- of the simulation and adding additional earthquake ruptures.
- See
-\family typewriter
-examples/3d/hex8/step06.cfg
-\family default
- for an example with multiple earthquake ruptures.
- Examine spinup towards a steady-state solution.
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 1in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-Subduction"
+
+\end_inset
+
+Tutorial for Slip on a Subduction Zone
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Static solution
+\end_layout
+
+\begin_layout Itemize
+Quasi-static solution
+\end_layout
+
+\begin_layout Itemize
+CUBIT mesh generation
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Nonplanar geometry
+\end_layout
+
+\begin_layout Itemize
+Variable mesh resolution
+\end_layout
+
+\begin_layout Itemize
+APREPRO programming language
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Linear triangular cells
+\end_layout
+
+\begin_layout Itemize
+HDF5 output
+\end_layout
+
+\begin_layout Itemize
+Dirichlet displacement and velocity boundary conditions
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+UniformDB spatial database
+\end_layout
+
+\begin_layout Itemize
+Multiple materials
+\end_layout
+
+\begin_layout Itemize
+Nonlinear solver
+\end_layout
+
+\begin_layout Itemize
+Plane strain linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+Plane Maxwell linear viscoelastic material
+\end_layout
+
+\begin_layout Itemize
+Prescribed slip
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Static fault rupture
+\end_layout
+
+\begin_layout Itemize
+Multiple faults
+\end_layout
+
+\begin_layout Itemize
+Spatially variable coseismic slip
+\end_layout
+
+\begin_layout Itemize
+Spatially variable aseismic creep
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Afterslip via fault friction
+\end_layout
+
+\begin_deeper
+\begin_layout Itemize
+Static fault rupture
+\end_layout
+
+\begin_layout Itemize
+Static friction
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/2d/subduction.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial examines quasi-static interseismic and coseismic deformation
+ in 2D for a subduction zone (see Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:overview"
+
+\end_inset
+
+).
+ It is based on the 2011 M9.0 Tohoku earthquake off the east coast of Japan.
+ Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:steps"
+
+\end_inset
+
+ shows the three steps of increasing complexity.
+ Step 1 focuses on the coseismic slip, Step 2 focuses on interseismic deformatio
+n, and Step 3 combines the two into a pseudo-earthquake cycle deformation
+ simulation.
+ Step 4 focuses on using the change in tractions from Step 1 to construct
+ a simulation with afterslip controlled by frictional sliding.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/cartoon_general.eps
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Cartoon of subduction zone example.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:overview"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="3">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Step 1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Step 2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Step 3
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+ filename figs/step01.eps
+ lyxscale 66
+ width 2in
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+ filename figs/step02.eps
+ lyxscale 66
+ width 2in
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+ filename figs/step03.eps
+ lyxscale 66
+ width 2in
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Diagram of fault slip and boundary conditions for each step in the subduction
+ zone tutorial.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:steps"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Mesh Description
+\end_layout
+
+\begin_layout Standard
+We construct the mesh in CUBIT by constructing the geometry, prescribing
+ the discretization, running the mesher, and then grouping cells and vertices
+ for boundary conditions and materials.
+ We use the APREPRO programming language within the journal files to enable
+ use of units and to set variables for values used many times.
+ An appendix in the CUBIT documentation discusses the features available
+ with APREPRO in CUBIT.
+ The CUBIT commands are in three separate journal files.
+ The main driver is in the journal file
+\family typewriter
+mesh_tri3.jou
+\family default
+.
+ It calls the journal file
+\family typewriter
+geometry.jou
+\family default
+ to construct the geometry and
+\family typewriter
+createbc.jou
+\family default
+ to set up the groups associated with boundary conditions and materials.
+ The journal files are documented and describe the various steps outlined
+ below.
+\end_layout
+
+\begin_layout Enumerate
+Create the geometry defining the domain.
+\end_layout
+
+\begin_deeper
+\begin_layout Enumerate
+Create points.
+\end_layout
+
+\begin_layout Enumerate
+Connect points into spline curves.
+\end_layout
+
+\begin_layout Enumerate
+Split curves to separate them into sections bounding surfaces.
+
+\end_layout
+
+\begin_layout Enumerate
+Connect curves into surfaces.
+\end_layout
+
+\begin_layout Enumerate
+Stitch surfaces together.
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Define meshing scheme and cell size variation.
+\end_layout
+
+\begin_deeper
+\begin_layout Enumerate
+Define cell size along curves near fault.
+\end_layout
+
+\begin_layout Enumerate
+Increase cell size away from fault at a geometric rate (bias).
+\end_layout
+
+\end_deeper
+\begin_layout Enumerate
+Generate mesh.
+\end_layout
+
+\begin_layout Enumerate
+Create blocks for materials and nodesets for boundary conditions.
+\end_layout
+
+\begin_layout Enumerate
+Export mesh.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/subduction_tri3.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Variable resolution finite-element mesh with triangular cells.
+ The nominal cell size increases at a geometric rate of 1.2 away from the
+ region of coseismic slip.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Common Information
+\end_layout
+
+\begin_layout Standard
+As in the examples discussed in previous sections of these tutorials, we
+ place parameters common to the three steps in the
+\family typewriter
+pylithapp.cfg
+\family default
+ file so that we do not have to duplicate them for each step.
+ The settings contained in
+\family typewriter
+pylithapp.cfg
+\family default
+ for this problem consist of:
+\end_layout
+
+\begin_layout Description
+pylithapp.journal.info Settings that control the verbosity of the output written
+ to stdout for the different components.
+\end_layout
+
+\begin_layout Description
+pylithapp.mesh_generator Settings that control mesh importing, such as the
+ importer type, the filename, and the spatial dimension of the mesh.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Settings that control the problem, such as the total
+ time, time-step size, and spatial dimension.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials Settings that control the material type,
+ specify which material IDs are to be associated with a particular material
+ type, and give the name of the spatial database containing the physical
+ properties for the material.
+ The quadrature information is also given.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output Settings related output of the solution
+ over the domain and subdomain (ground surface).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials.
+\shape italic
+MATERIAL
+\shape default
+.output Settings related to output of the state variables for material
+\shape italic
+MATERIAL
+\shape default
+.
+\end_layout
+
+\begin_layout Description
+pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
+ type.
+\end_layout
+
+\begin_layout Standard
+The physical properties for each material are specified in spatial database
+ files.
+ For example, the elastic properties for the continental crust are in
+\family typewriter
+mat_concrust.spatialdb
+\family default
+.
+ The provided spatial database files all use just a single point to specify
+ uniform physical properties within each material.
+ A good exercise is to alter the spatial database files with the physical
+ properties to match PREM.
+\end_layout
+
+\begin_layout Subsection
+Step 1: Coseismic Slip Simulation
+\end_layout
+
+\begin_layout Standard
+The first example problem is earthquake rupture involving coseismic slip
+ along the interface between the subducting slab and the continental crust
+ and uppermost portion of the mantle below the continental crust.
+ The spatial variation of slip comes from a cross-section of Gavin Hayes'
+ finite-source model
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/finite_fault.php
+\end_layout
+
+\end_inset
+
+.
+ On the lateral and bottom boundaries of the domain, we fix the degrees
+ of freedom perpendicular to the boundary as shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:steps"
+
+\end_inset
+
+.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step01.cfg
+\family default
+.
+ These settings are:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.formulation.time_step Adjust the total simulation time
+ to 0 years (static simulation).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies the array of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.
+\shape italic
+BOUNDARY
+\shape default
+ Defines the settings for boundary
+\shape italic
+BOUNDARY
+\shape default
+, including which degrees of freedom are being constrained (x or y), the
+ label (defined in
+\family typewriter
+ mesh_tri3.exo
+\family default
+) corresponding to the nodeset in CUBIT, and a label to the boundary condition
+ used in any error messages.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces.fault Specify the coseismic slip along the
+ interface between the oceanic crust and continental crust with a small
+ amount of slip penetrating into the upper mantle.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain Gives the base filenames for HDF5
+ output (for example,
+\family typewriter
+step01.h5
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+We run this example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step01.cfg
+\end_layout
+
+\begin_layout Standard
+The problem will produce twelve pairs of HDF5/Xdmf files.
+ The HDF5 files contain the data and the Xdmf files contain the metadata
+ required by ParaView and Visit (and possibly other visualization tools
+ that use Xdmf files) to access the mesh and data sets in the HDF5 files.
+ The files include the solution over the domain and ground surface (two
+ pairs of files), physical properties, stress, and strain within each material
+ (eight pairs of files), and fault parameters, slip, and traction (two pairs
+ of files).
+
+\end_layout
+
+\begin_layout Standard
+Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:step01"
+
+\end_inset
+
+, which was created using ParaView, displays the magnitude of the displacement
+ field with the deformation exaggerated by a factor of 1000.
+ We construct a three-dimensional displacement vector from the two-dimensional
+ displacement components using the Calculator with the expression
+\end_layout
+
+\begin_layout LyX-Code
+displacement_x*iHat + displacement_y*jHat
+\end_layout
+
+\begin_layout Standard
+where we select the displacement components from the Scalars drop-down menu
+ and the iHat, jHat, and kHat values from the Calculator buttons.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step01_soln.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Solution for Step 1.
+ The colors indicate the magnitude of the displacement, and the deformation
+ is exaggerated by a factor of 1000.
+
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:step01"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Step 2: Interseismic Deformation Simulation
+\end_layout
+
+\begin_layout Standard
+In this example we simulate the interseismic deformation associated with
+ the oceanic crust subducting beneath the continental crust and into the
+ mantle.
+ We prescribe steady aseismic slip of 8 cm/yr along the interfaces between
+ the oceanic crust and mantle with the interface between the oceanic crust
+ and continental crust locked as shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:steps"
+
+\end_inset
+
+.
+ We adjust the Dirichlet boundary conditions on the lateral edges and bottom
+ of the domain by pinning only the portions of the boundaries in the mantle
+ and continental crust (i.e., not part of the oceanic crust).
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step02.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.formulation.time_step Adjust the total simulation time
+ to 100 years.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies the array of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.
+\shape italic
+BOUNDARY
+\shape default
+ Defines the settings for boundary
+\shape italic
+BOUNDARY
+\shape default
+, including which degrees of freedom are being constrained (x or y), the
+ label (defined in
+\family typewriter
+ mesh_tri3.exo
+\family default
+) corresponding to the nodeset in CUBIT, and a label to the boundary condition
+ used in any error messages.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces Specify the steady aseismic slip as a constant
+ slip rate on the fault surfaces.
+
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain Gives the base filename for HDF5
+ output (for example,
+\family typewriter
+step02.h5
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+We run this example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step02.cfg
+\end_layout
+
+\begin_layout Standard
+The simulation will produce pairs of HDF5/Xdmf files with separate files
+ for each material and fault interface.
+ Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:step02"
+
+\end_inset
+
+, which was created using ParaView, displays the magnitude of the displacement
+ field with the deformation exaggerated by a factor of 1000.
+ Using the animation features within ParaView or Visit you can illustrate
+ how the continental crust near the trench subsides during the interseismic
+ deformation.
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step02_soln.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Solution for Step 2 at 100 years.
+ The colors indicate the magnitude of the displacement, and the deformation
+ is exaggerated by a factor of 1000.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:step02"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Step 3: Pseudo-Earthquake Cycle Model
+\end_layout
+
+\begin_layout Standard
+This simulation combines 300 years of interseismic deformation from Step
+ 2 with the coseismic deformation from Step 1 applied at 150 years to create
+ a simple model of the earthquake cycle.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step03.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.formulation.time_step Adjust the total simulation time
+ to 300 years.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies the array of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.
+\shape italic
+BOUNDARY
+\shape default
+ The Dirichlet boundary conditions match those in Step 2.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces On the interface between the subducting
+ oceanic crust and the mantle, we prescribe the same steady, aseismic slip
+ as that in Step 2.
+ On the interface along the top of the subducting oceanic crust and the
+ continental crust and mantle we create two earthquake ruptures, The first
+ rupture applies the coseismic slip form Step 1 at 150 years, while the
+ second rupture prescribes the same steady, aseismic slip as in Step 2.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain Gives the base filename for HDF5
+ output (for example,
+\family typewriter
+step03.h5
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+We run this example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step03.cfg
+\end_layout
+
+\begin_layout Standard
+The simulation will produce pairs of HDF5/Xdmf files with separate files
+ for each material and fault interface.
+ Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:step03"
+
+\end_inset
+
+, which was created using ParaView, displays the magnitude of the displacement
+ field with the deformation exaggerated by a factor of 1000.
+ Using the animation features within ParaView or Visit you can illustrate
+ how the continental crust near the trench rebounds during the earthquake
+ after subsiding during the interseismic deformation.
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step03_soln.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Solution for Step 3 at 150 years (immediately following the earthquake rupture).
+ The colors indicate the magnitude of the displacement, and the deformation
+ is exaggerated by a factor of 1000.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:step03"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Step 4: Frictional Afterslip Simulation
+\end_layout
+
+\begin_layout Standard
+This simulation demonstrates how to combine the change in tractions associated
+ with coseismic slip with a background stress field to compute afterslip
+ controlled by static friction.
+ The Python script
+\family typewriter
+afterslip_tractions.py
+\family default
+ will create a spatial database file with initial tractions based on the
+ change in tractions from Step 1 and a background stress field.
+ The background stress field is simply normal tractions consistent with
+ the overburden (lithostatic load) for a uniform half-space and shear tractions
+ consistent with a coefficient of friction of 0.6.
+ The
+\family typewriter
+afterslip_tractions.spatialdb
+\family default
+ file is provided, so you do not need to run the Python script
+\family typewriter
+afterslip_tractions.py
+\family default
+; however, you can do so by typing
+\end_layout
+
+\begin_layout LyX-Code
+python afterslip_tractions.py
+\end_layout
+
+\begin_layout Standard
+We provide 2.0 MPa of strength excess associated with the background stress
+ field by using a cohesion of 2.0 MPa in the static friction model.
+ Slip will occur in regions where the coseismic slip increased the shear
+ tractions by more than 2.0 MPa.
+ On the lateral and bottom boundaries of the domain, we fix the degrees
+ of freedom perpendicular to the boundary as shown in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:steps"
+
+\end_inset
+
+.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+step04.cfg
+\family default
+.
+ These settings are:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.formulation.time_step Adjust the total simulation time
+ to 0 years (static simulation).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Selects the nonlinear solver and specifies the array
+ of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.
+\shape italic
+BOUNDARY
+\shape default
+ Defines the settings for boundary
+\shape italic
+BOUNDARY
+\shape default
+, including which degrees of freedom are being constrained (x or y), the
+ label (defined in
+\family typewriter
+ mesh_tri3.exo
+\family default
+) corresponding to the nodeset in CUBIT, and a label to the boundary condition
+ used in any error messages.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces.fault Specify a fault with a fault constitutive
+ model (static friction) and initial fault tractions.
+
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.domain Gives the base filenames for HDF5
+ output (for example,
+\family typewriter
+step04.h5
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+We run this example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith step04.cfg
+\end_layout
+
+\begin_layout Standard
+The problem will produce twelve pairs of HDF5/Xdmf files.
+ The HDF5 files contain the data and the Xdmf files contain the metadata
+ required by ParaView and Visit (and possibly other visualization tools
+ that use Xdmf files) to access the mesh and data sets in the HDF5 files.
+ The files include the solution over the domain and ground surface (two
+ pairs of files), physical properties, stress, and strain within each material
+ (eight pairs of files), and fault parameters, slip, and traction (two pairs
+ of files).
+
+\end_layout
+
+\begin_layout Standard
+Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:tutorial:subduction:step04"
+
+\end_inset
+
+, which was created using ParaView, displays the magnitude of the displacement
+ field with the original configuration.
+ Slip occurs down-dip from the coseismic slip as well as three areas with
+ sharp gradients in slip, including the trench.
+ The location of the afterslip can be shifted by changing the spatial variation
+ of the coseismic slip and background stress field.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/step01_soln.png
+ lyxscale 50
+ width 4.5in
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Solution for Step 4.
+ The colors indicate the magnitude of the displacement.
+
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:tutorial:subduction:step04"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Suggested Variations
+\end_layout
+
+\begin_layout Standard
+The list below includes some suggested modifications to the problem that
+ will allow you to become more familiar with PyLith while examining some
+ interesting physics.
+\end_layout
+
+\begin_layout Itemize
+Change the resolution of the mesh by editing the
+\family typewriter
+mesh_tri3.jou
+\family default
+ journal file.
+ Change the resolution and bias factor.
+\end_layout
+
+\begin_layout Itemize
+Add depth dependent viscosity to the mantle and crust.
+ This requires using the linear Maxwell plane strain bulk constitutive model
+ in the crust as well and creating spatial databases that include viscosity
+ for the crust.
+ Specifying a depth dependent variation in the parameters will require adding
+ points, updating num-locs accordingly, and changing data-dim to 1.
+\end_layout
+
+\begin_layout Itemize
+Modify the spatial database files for the material properties to use depth-depen
+dent elastic properties based on PREM (Dziewonski and Anderson, 1981, 10.1016/003
+1-9201(81)90046-7).
+ See
+\begin_inset Flex URL
+status open
+
+\begin_layout Plain Layout
+
+geophysics.ou.edu/solid_earth/prem.html
+\end_layout
+
+\end_inset
+
+ for a simple table of values.
+ Add points, update num-locs accordingly, and change data-dim to 1.
+\end_layout
+
+\begin_layout Itemize
+Modify the CUBIT journal files to use quad4 cells rather than tri3 cells.
+ This requires using the pave mesh scheme.
+\end_layout
+
+\begin_layout Itemize
+Create a simulation with multiple earthquake cycles by lengthening the duration
+ of the simulation and adding additional earthquake ruptures.
+ See
+\family typewriter
+examples/3d/hex8/step06.cfg
+\family default
+ for an example with multiple earthquake ruptures.
+ Examine spinup towards a steady-state solution.
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twohex8/twohex8.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twohex8/twohex8.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twohex8/twohex8.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,855 +1,855 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
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-
-\end_preamble
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-\language english
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-\use_hyperref false
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-\shortcut idx
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-\end_index
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-\topmargin 1in
-\rightmargin 1in
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-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
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-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-Two-hexahedra"
-
-\end_inset
-
-Tutorial Using Two Hexahedra
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Quasi-static solution
-\end_layout
-
-\begin_layout Itemize
-Mesh ASCII format
-\end_layout
-
-\begin_layout Itemize
-Dirichlet boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Maxwell viscoelastic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Trilinear hexahedral cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Itemize
-UniformDB spatial database
-\end_layout
-
-\begin_layout Itemize
-Filtering of cell output fields
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/twocells/twohex8.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial is a simple 3D example of a quasi-static finite element problem.
- It is a mesh composed of two trilinear hexahedra subject to displacement
- boundary conditions.
- One primary difference between this example and the example with two tetrahedra
- is that we use a Maxwell viscoelastic material model, and run the model
- for 10 time steps of 0.1 year each.
- Due to the simple geometry of the problem, the mesh may be constructed
- by hand, using PyLith mesh ASCII format to describe the mesh.
- In this tutorial, we will walk through the steps necessary to construct,
- run, and view three problems that use the same mesh.
- In addition to this manual, each of the files for the example problems
- includes extensive comments.
-\end_layout
-
-\begin_layout Subsection
-Mesh Description
-\end_layout
-
-\begin_layout Standard
-The mesh consists of two hexahedra forming a rectangular prism (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twohex8-mesh"
-
-\end_inset
-
-).
- The mesh geometry and topology are described in the file
-\family typewriter
-twohex8.mesh
-\family default
-, which is in PyLith mesh ASCII format.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/twohex8-mesh.eps
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of two trilinear hexahedral cells used for the example problems.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twohex8-mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Additional Common Information
-\end_layout
-
-\begin_layout Standard
-In addition to the mesh, the three example problems share additional information
-, which we place in
-\family typewriter
-pylithapp.cfg
-\family default
-.
- Note that in this example we make use of the UniformDB spatial database,
- rather than the SimpleDB implementation used to specify the physical properties
- in the other example problems.
- For simple distributions of material properties (or boundary conditions),
- this implementation is often easier to use.
- Examining
-\family typewriter
-pylithapp.cfg
-\family default
-, we specify the material information with the following set of parameters:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.materials]
-\end_layout
-
-\begin_layout LyX-Code
-material = pylith.materials.MaxwellIsotropic3D
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.materials.material]
-\end_layout
-
-\begin_layout LyX-Code
-label = viscoelastic material
-\end_layout
-
-\begin_layout LyX-Code
-id = 1
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-db = spatialdata.spatialdb.UniformDB
-\end_layout
-
-\begin_layout LyX-Code
-db.values = [vp,vs,density,viscosity]
-\end_layout
-
-\begin_layout LyX-Code
-db.data = [5773.502691896258*m/s, 3333.333333333333*m/s, 2700.0*kg/m**3, 1.0e18*Pa*s]
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-quadrature.cell = pylith.feassemble.FIATLagrange
-\end_layout
-
-\begin_layout LyX-Code
-quadrature.cell.dimension = 3
-\end_layout
-
-\begin_layout Subsection
-Axial Displacement Example
-\end_layout
-
-\begin_layout Standard
-The first example problem is extension of the mesh along the long axis of
- the prism.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-axialdisp.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Defines which degrees of freedom are being
- constrained (x, y, and z), gives the label (
-\family typewriter
-x_neg
-\family default
-, defined in
-\family typewriter
-twohex8.mesh
-\family default
-) defining the points desired, assigns a label to the boundary condition
- set, and gives the name of the spatial database with the values for the
- Dirichlet boundary conditions (
-\family typewriter
-axialdisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Defines which degrees of freedom are being
- constrained (x, y, and z), gives the label (
-\family typewriter
-x_
-\family default
-pos, defined in
-\family typewriter
-twohex8.mesh
-\family default
-) defining the points desired, assigns a label to the boundary condition
- set, and gives the name of the spatial database with the values for the
- Dirichlet boundary conditions (
-\family typewriter
-axialdisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.material.output Defines the filter to be used
- when writing cell state variables (average over the quadrature points of
- the cell), specifies which state variables and properties to output, gives
- the base filename for state variable output files, and defines the format
- to use when defining the output filenames for each time step.
-\end_layout
-
-\begin_layout Standard
-The values for the Dirichlet boundary conditions are given in the file
-\family typewriter
-axialdisp.spatialdb
-\family default
-, as specified in
-\family typewriter
-axialdisp.cfg
-\family default
-.
- Since data are being specified using two control points (rather than being
- uniform over the mesh, for example), the data dimension is one.
- Note that since we are using a Maxwell viscoelastic model, we request that
- additional state variables and properties be output:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.materials.material.output]
-\end_layout
-
-\begin_layout LyX-Code
-cell_data_fields = [total_strain,viscous_strain,stress]
-\end_layout
-
-\begin_layout LyX-Code
-cell_info_fields = [mu,lambda,density,maxwell_time]
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twohex8.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-) along with the problem-specific files (
-\family typewriter
-axialdisp.cfg
-\family default
-,
-\family typewriter
-axialdisp.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith axialdisp.cfg
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, two sets of files will be produced, along with
- one additional file.
- The first set will have filenames such as
-\family typewriter
-axialdisp_txxxx.vtk
-\family default
-, where
-\family typewriter
-xxxx
-\family default
- is the time for which output has been produced.
- In
-\family typewriter
-axialdisp.cfg
-\family default
- we specify that the time stamp should be normalized by a value of 1.0 years
- and the time stamp should be of the form
-\family typewriter
-xxx.x
-\family default
- (recall that the decimal point is removed in the filename).
- As a result, the filenames contain the time in tenths of a year.
- These files will contain mesh information as well as displacement values
- for the mesh vertices at the given time.
- The second set of files will have names such as
-\family typewriter
-axialdisp-statevars_txxxx.vtk
-\family default
-, where
-\family typewriter
-xxxx
-\family default
- is the time in tenths of a year (as above) for which output has been produced.
- These files contain the state variables for each cell at the given time.
- The default fields are the total strain and stress fields; however, we
- have also requested the viscous strains.
- As specified in
-\family typewriter
-axialdisp.cfg
-\family default
-, these values are averaged over each cell.
- The final file (
-\family typewriter
-axialdisp-statevars_info.vtk
-\family default
-) gives the material properties used for the problem.
- We have requested all of the properties available for this material model
- (
-\family typewriter
-mu
-\family default
-,
-\family typewriter
-lambda
-\family default
-,
-\family typewriter
-density
-\family default
-,
-\family typewriter
-maxwell_time
-\family default
-).
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twohex8-axial"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/axialdisp.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the axial displacement example
- using a mesh composed of two trilinear hexahedral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twohex8-axial"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Shear Displacement Example
-\end_layout
-
-\begin_layout Standard
-The second example problem is shearing of the mesh in the y direction.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-sheardisp.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Defines which degrees of freedom are being
- constrained (x, y, and z), gives the label (
-\family typewriter
-x_neg
-\family default
-, defined in
-\family typewriter
-twohex8.mesh
-\family default
-) defining the points desired, assigns a label to the boundary condition
- set, and gives the name of the spatial database with the values for the
- Dirichlet boundary conditions (
-\family typewriter
-sheardisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Defines which degrees of freedom are being
- constrained (x, y, and z), gives the label (
-\family typewriter
-x_
-\family default
-pos, defined in
-\family typewriter
-twohex8.mesh
-\family default
-) defining the points desired, assigns a label to the boundary condition
- set, and gives the name of the spatial database with the values for the
- Dirichlet boundary conditions (
-\family typewriter
-sheardisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-The values for the Dirichlet boundary conditions are given in the file
-\family typewriter
-sheardisp.spatialdb
-\family default
-, as specified in
-\family typewriter
-sheardisp.cfg
-\family default
-.
- Data are being specified at two control points (rather than being uniform
- over the mesh, for example), so the data dimension is one.
- The files containing common information (
-\family typewriter
-twohex8.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-) along with the problem-specific files (
-\family typewriter
-sheardisp.cfg
-\family default
-,
-\family typewriter
-sheardisp.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith sheardisp.cfg
-\end_layout
-
-\begin_layout Standard
-If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twohex8-shear"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/sheardisp.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the shear displacement example
- using a mesh composed of two trilinear hexahedral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twohex8-shear"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Kinematic Fault Slip Example
-\end_layout
-
-\begin_layout Standard
-The next example problem is left-lateral fault slip applied between the
- two hexahedral cells using kinematic cohesive cells.
- The vertices away from the fault are held fixed in the x, y, and z directions.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-dislocation.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Defines which degrees of freedom are being
- constrained (x, y, and z), gives the label (
-\family typewriter
-x_neg
-\family default
-, defined in
-\family typewriter
-twohex8.mesh
-\family default
-) defining the points desired, and assigns a label to the boundary condition
- set.
- In this case, we use the default spatial database (ZeroDispDB) for the
- Dirichlet boundary condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Defines which degrees of freedom are being
- constrained (x, y, and z), gives the label (
-\family typewriter
-x_
-\family default
-pos, defined in
-\family typewriter
-twohex8.mesh
-\family default
-) defining the points desired, and assigns a label to the boundary condition
- set.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces Gives the label (defined in
-\family typewriter
-twohex8.mesh
-\family default
-) defining the points on the fault, provides quadrature information, and
- then gives database names for material properties (needed for conditioning),
- fault slip, peak fault slip rate, and fault slip time.
-\end_layout
-
-\begin_layout Standard
-The fault example requires three additional database files that were not
- needed for the simple displacement examples.
- The first file (
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-) specifies 0.01 m of left-lateral fault slip for the entire fault.
- The data dimension is zero since the same data are applied to all points
- in the set.
- The default slip time function is a step-function, so we also must provide
- the time at which slip begins.
- The elastic solution is associated with advancing from
-\begin_inset Formula $t=-dt$
-\end_inset
-
- to
-\begin_inset Formula $t=0$
-\end_inset
-
-, so we set the slip initiation time for the step-function to 0 in
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-.
- The files containing common information (
-\family typewriter
-\size small
-twohex8.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-\size default
-) along with the problem-specific files (
-\family typewriter
-\size small
-dislocation.cfg
-\family default
-,
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-,
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith dislocation.cfg
-\end_layout
-
-\begin_layout Standard
-If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twohex8-disloc"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\noindent
-\align center
-\begin_inset Graphics
- filename figs/dislocation.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the kinematic fault example
- using a mesh composed of two trilinear hexahedral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twohex8-disloc"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 2in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-Two-hexahedra"
+
+\end_inset
+
+Tutorial Using Two Hexahedra
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Quasi-static solution
+\end_layout
+
+\begin_layout Itemize
+Mesh ASCII format
+\end_layout
+
+\begin_layout Itemize
+Dirichlet boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Maxwell viscoelastic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Trilinear hexahedral cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Itemize
+UniformDB spatial database
+\end_layout
+
+\begin_layout Itemize
+Filtering of cell output fields
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/twocells/twohex8.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial is a simple 3D example of a quasi-static finite element problem.
+ It is a mesh composed of two trilinear hexahedra subject to displacement
+ boundary conditions.
+ One primary difference between this example and the example with two tetrahedra
+ is that we use a Maxwell viscoelastic material model, and run the model
+ for 10 time steps of 0.1 year each.
+ Due to the simple geometry of the problem, the mesh may be constructed
+ by hand, using PyLith mesh ASCII format to describe the mesh.
+ In this tutorial, we will walk through the steps necessary to construct,
+ run, and view three problems that use the same mesh.
+ In addition to this manual, each of the files for the example problems
+ includes extensive comments.
+\end_layout
+
+\begin_layout Subsection
+Mesh Description
+\end_layout
+
+\begin_layout Standard
+The mesh consists of two hexahedra forming a rectangular prism (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twohex8-mesh"
+
+\end_inset
+
+).
+ The mesh geometry and topology are described in the file
+\family typewriter
+twohex8.mesh
+\family default
+, which is in PyLith mesh ASCII format.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/twohex8-mesh.eps
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of two trilinear hexahedral cells used for the example problems.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twohex8-mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Additional Common Information
+\end_layout
+
+\begin_layout Standard
+In addition to the mesh, the three example problems share additional information
+, which we place in
+\family typewriter
+pylithapp.cfg
+\family default
+.
+ Note that in this example we make use of the UniformDB spatial database,
+ rather than the SimpleDB implementation used to specify the physical properties
+ in the other example problems.
+ For simple distributions of material properties (or boundary conditions),
+ this implementation is often easier to use.
+ Examining
+\family typewriter
+pylithapp.cfg
+\family default
+, we specify the material information with the following set of parameters:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials]
+\end_layout
+
+\begin_layout LyX-Code
+material = pylith.materials.MaxwellIsotropic3D
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials.material]
+\end_layout
+
+\begin_layout LyX-Code
+label = viscoelastic material
+\end_layout
+
+\begin_layout LyX-Code
+id = 1
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+db = spatialdata.spatialdb.UniformDB
+\end_layout
+
+\begin_layout LyX-Code
+db.values = [vp,vs,density,viscosity]
+\end_layout
+
+\begin_layout LyX-Code
+db.data = [5773.502691896258*m/s, 3333.333333333333*m/s, 2700.0*kg/m**3, 1.0e18*Pa*s]
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+quadrature.cell = pylith.feassemble.FIATLagrange
+\end_layout
+
+\begin_layout LyX-Code
+quadrature.cell.dimension = 3
+\end_layout
+
+\begin_layout Subsection
+Axial Displacement Example
+\end_layout
+
+\begin_layout Standard
+The first example problem is extension of the mesh along the long axis of
+ the prism.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+axialdisp.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Defines which degrees of freedom are being
+ constrained (x, y, and z), gives the label (
+\family typewriter
+x_neg
+\family default
+, defined in
+\family typewriter
+twohex8.mesh
+\family default
+) defining the points desired, assigns a label to the boundary condition
+ set, and gives the name of the spatial database with the values for the
+ Dirichlet boundary conditions (
+\family typewriter
+axialdisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Defines which degrees of freedom are being
+ constrained (x, y, and z), gives the label (
+\family typewriter
+x_pos
+\family default
+, defined in
+\family typewriter
+twohex8.mesh
+\family default
+) defining the points desired, assigns a label to the boundary condition
+ set, and gives the name of the spatial database with the values for the
+ Dirichlet boundary conditions (
+\family typewriter
+axialdisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials.material.output Defines the filter to be used
+ when writing cell state variables (average over the quadrature points of
+ the cell), specifies which state variables and properties to output, gives
+ the base filename for state variable output files, and defines the format
+ to use when defining the output filenames for each time step.
+\end_layout
+
+\begin_layout Standard
+The values for the Dirichlet boundary conditions are given in the file
+\family typewriter
+axialdisp.spatialdb
+\family default
+, as specified in
+\family typewriter
+axialdisp.cfg
+\family default
+.
+ Since data are being specified using two control points (rather than being
+ uniform over the mesh, for example), the data dimension is one.
+ Note that since we are using a Maxwell viscoelastic model, we request that
+ additional state variables and properties be output:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials.material.output]
+\end_layout
+
+\begin_layout LyX-Code
+cell_data_fields = [total_strain,viscous_strain,stress]
+\end_layout
+
+\begin_layout LyX-Code
+cell_info_fields = [mu,lambda,density,maxwell_time]
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twohex8.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+) along with the problem-specific files (
+\family typewriter
+axialdisp.cfg
+\family default
+,
+\family typewriter
+axialdisp.spatialdb
+\family default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith axialdisp.cfg
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, two sets of files will be produced, along with
+ one additional file.
+ The first set will have filenames such as
+\family typewriter
+axialdisp_txxxx.vtk
+\family default
+, where
+\family typewriter
+xxxx
+\family default
+ is the time for which output has been produced.
+ In
+\family typewriter
+axialdisp.cfg
+\family default
+ we specify that the time stamp should be normalized by a value of 1.0 years
+ and the time stamp should be of the form
+\family typewriter
+xxx.x
+\family default
+ (recall that the decimal point is removed in the filename).
+ As a result, the filenames contain the time in tenths of a year.
+ These files will contain mesh information as well as displacement values
+ for the mesh vertices at the given time.
+ The second set of files will have names such as
+\family typewriter
+axialdisp-statevars_txxxx.vtk
+\family default
+, where
+\family typewriter
+xxxx
+\family default
+ is the time in tenths of a year (as above) for which output has been produced.
+ These files contain the state variables for each cell at the given time.
+ The default fields are the total strain and stress fields; however, we
+ have also requested the viscous strains.
+ As specified in
+\family typewriter
+axialdisp.cfg
+\family default
+, these values are averaged over each cell.
+ The final file (
+\family typewriter
+axialdisp-statevars_info.vtk
+\family default
+) gives the material properties used for the problem.
+ We have requested all of the properties available for this material model
+ (
+\family typewriter
+mu
+\family default
+,
+\family typewriter
+lambda
+\family default
+,
+\family typewriter
+density
+\family default
+,
+\family typewriter
+maxwell_time
+\family default
+).
+ If the problem ran correctly, you should be able to produce a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twohex8-axial"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/axialdisp.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the axial displacement example
+ using a mesh composed of two trilinear hexahedral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twohex8-axial"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Shear Displacement Example
+\end_layout
+
+\begin_layout Standard
+The second example problem is shearing of the mesh in the y direction.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+sheardisp.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Defines which degrees of freedom are being
+ constrained (x, y, and z), gives the label (
+\family typewriter
+x_neg
+\family default
+, defined in
+\family typewriter
+twohex8.mesh
+\family default
+) defining the points desired, assigns a label to the boundary condition
+ set, and gives the name of the spatial database with the values for the
+ Dirichlet boundary conditions (
+\family typewriter
+sheardisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Defines which degrees of freedom are being
+ constrained (x, y, and z), gives the label (
+\family typewriter
+x_pos
+\family default
+, defined in
+\family typewriter
+twohex8.mesh
+\family default
+) defining the points desired, assigns a label to the boundary condition
+ set, and gives the name of the spatial database with the values for the
+ Dirichlet boundary conditions (
+\family typewriter
+sheardisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+The values for the Dirichlet boundary conditions are given in the file
+\family typewriter
+sheardisp.spatialdb
+\family default
+, as specified in
+\family typewriter
+sheardisp.cfg
+\family default
+.
+ Data are being specified at two control points (rather than being uniform
+ over the mesh, for example), so the data dimension is one.
+ The files containing common information (
+\family typewriter
+twohex8.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+) along with the problem-specific files (
+\family typewriter
+sheardisp.cfg
+\family default
+,
+\family typewriter
+sheardisp.spatialdb
+\family default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith sheardisp.cfg
+\end_layout
+
+\begin_layout Standard
+If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twohex8-shear"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/sheardisp.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the shear displacement example
+ using a mesh composed of two trilinear hexahedral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twohex8-shear"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Kinematic Fault Slip Example
+\end_layout
+
+\begin_layout Standard
+The next example problem is left-lateral fault slip applied between the
+ two hexahedral cells using kinematic cohesive cells.
+ The vertices away from the fault are held fixed in the x, y, and z directions.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+dislocation.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Defines which degrees of freedom are being
+ constrained (x, y, and z), gives the label (
+\family typewriter
+x_neg
+\family default
+, defined in
+\family typewriter
+twohex8.mesh
+\family default
+) defining the points desired, and assigns a label to the boundary condition
+ set.
+ In this case, we use the default spatial database (ZeroDispDB) for the
+ Dirichlet boundary condition, which sets the displacements to zero.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Defines which degrees of freedom are being
+ constrained (x, y, and z), gives the label (
+\family typewriter
+x_pos
+\family default
+, defined in
+\family typewriter
+twohex8.mesh
+\family default
+) defining the points desired, and assigns a label to the boundary condition
+ set.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces Gives the label (defined in
+\family typewriter
+twohex8.mesh
+\family default
+) defining the points on the fault, provides quadrature information, and
+ then gives database names for material properties (needed for conditioning),
+ fault slip, peak fault slip rate, and fault slip time.
+\end_layout
+
+\begin_layout Standard
+The fault example requires three additional database files that were not
+ needed for the simple displacement examples.
+ The first file (
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+) specifies 0.01 m of left-lateral fault slip for the entire fault.
+ The data dimension is zero since the same data are applied to all points
+ in the set.
+ The default slip time function is a step-function, so we also must provide
+ the time at which slip begins.
+ The elastic solution is associated with advancing from
+\begin_inset Formula $t=-dt$
+\end_inset
+
+ to
+\begin_inset Formula $t=0$
+\end_inset
+
+, so we set the slip initiation time for the step-function to 0 in
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+.
+ The files containing common information (
+\family typewriter
+\size small
+twohex8.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+\size default
+) along with the problem-specific files (
+\family typewriter
+\size small
+dislocation.cfg
+\family default
+,
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+,
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+\size default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith dislocation.cfg
+\end_layout
+
+\begin_layout Standard
+If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twohex8-disloc"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align center
+\begin_inset Graphics
+ filename figs/dislocation.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the kinematic fault example
+ using a mesh composed of two trilinear hexahedral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twohex8-disloc"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twoquad4/twoquad4.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twoquad4/twoquad4.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twoquad4/twoquad4.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,1001 +1,1001 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
-\use_default_options false
-\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding latin1
-\fontencoding global
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\use_non_tex_fonts false
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
-\graphics default
-\default_output_format default
-\output_sync 0
-\bibtex_command default
-\index_command default
-\paperfontsize default
-\spacing single
-\use_hyperref false
-\papersize default
-\use_geometry true
-\use_amsmath 0
-\use_esint 0
-\use_mhchem 1
-\use_mathdots 1
-\cite_engine basic
-\use_bibtopic false
-\use_indices false
-\paperorientation portrait
-\suppress_date false
-\use_refstyle 0
-\index Index
-\shortcut idx
-\color #008000
-\end_index
-\leftmargin 1in
-\topmargin 1in
-\rightmargin 1in
-\bottommargin 1in
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\paragraph_indentation default
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-Two-quad4"
-
-\end_inset
-
-Tutorial Using Two Quadrilaterals
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Quasi-static solution
-\end_layout
-
-\begin_layout Itemize
-Mesh ASCII format
-\end_layout
-
-\begin_layout Itemize
-Dirichlet boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Neumann boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Plane strain linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Bilinear quadrilateral cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/twocells/twoquad4.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial is another simple 2D example of a quasi-static finite element
- problem.
- It is a mesh composed of two bilinear quadrilaterals subject to displacement
- or traction boundary conditions, assuming plane-strain linear elastic behavior.
- Due to the simple geometry of the problem, the mesh may be constructed
- by hand, using PyLith mesh ASCII format to describe the mesh.
- In this tutorial, we will walk through the steps necessary to construct,
- run, and view four problems that use the same mesh.
- In addition to this manual, each of the files for the example problem includes
- extensive comments.
-\end_layout
-
-\begin_layout Subsection
-Mesh Description
-\end_layout
-
-\begin_layout Standard
-The mesh consists of two square cells with edge lengths of one unit forming
- a regular region (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twoquad4-mesh"
-
-\end_inset
-
-).
- The mesh geometry and topology are described in the file
-\family typewriter
-twoquad4.mesh
-\family default
-, which is in PyLith mesh ASCII format.
- This file describes the dimensionality of the problem (in this case 2D),
- the coordinates of the vertices (nodes), the vertices composing each cell
- (element), the material ID to be associated with each cell, and then provides
- groups of vertices that may be used to define faults or surfaces to which
- boundary conditions may be applied.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/twoquad4-mesh.eps
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of two bilinear quadrilateral cells used for the example problems.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twoquad4-mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Additional Common Information
-\end_layout
-
-\begin_layout Standard
-In addition to the mesh, the four example problems share additional information.
- As in the previous examples, we place this information in
-\family typewriter
-pylithapp.cfg
-\family default
-, since this file is read automatically every time PyLith is run.
- Settings specific to a particular problem may be placed in other
-\family typewriter
-.cfg
-\family default
- files, as described later, and then those files are placed on the command
- line.
-\end_layout
-
-\begin_layout Subsection
-Axial Displacement Example
-\end_layout
-
-\begin_layout Standard
-The first example problem is extension of the mesh along the x axis.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-axialdisp.cfg
-\family default
-.
- These include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (x), giving the label (defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database with the values for the
- Dirichlet boundary condition (
-\family typewriter
-axialdisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- right side of the mesh, defining which degrees of freedom are being constrained
- (x), giving the label (defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database defining the boundary
- conditions (
-\family typewriter
-axialdisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.y_neg Specifies the boundary conditions for the
- bottom two corners of the mesh, defining which degrees of freedom are being
- constrained (y), giving the label (defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database with the values for the
- Dirichlet boundary condition (
-\family typewriter
-axialdisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-The values for the Dirichlet boundary condition are given in the file
-\family typewriter
-axialdisp.spatialdb
-\family default
-, as specified in
-\family typewriter
-axialdisp.cfg
-\family default
-.
- Because the data are being specified using two control points with a linear
- variation in the values between the two (rather than being uniform over
- the mesh, for example), the data dimension is one.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twoquad4.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-axialdisp.cfg
-\family default
-,
-\family typewriter
-axialdisp.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith axialdisp.cfg
-\end_layout
-
-\begin_layout Standard
-As in the two triangle axial displacement example, three files will be produced.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:twoquad4-axial"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-placement t
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/axialdisp.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the axial displacement example
- using a mesh composed of two bilinear quadrilateral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twoquad4-axial"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Shear Displacement Example
-\end_layout
-
-\begin_layout Standard
-The next example problem is shearing of the mesh in the y direction using
- displacements applied along the positive and negative x boundaries.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-sheardisp.cfg
-\family default
-.
- These include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (x and y), giving the label (
-\family typewriter
-x_neg
-\family default
-, defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database with the values for the
- Dirichlet boundary condition (
-\family typewriter
-sheardisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (y only), giving the label (
-\family typewriter
-x_
-\family default
-pos, defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database with the values for the
- Dirichlet boundary condition (
-\family typewriter
-sheardisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-The values for the Dirichlet boundary conditions are described in the file
-
-\family typewriter
-sheardisp.spatialdb
-\family default
-, as specified in
-\family typewriter
-sheardisp.cfg
-\family default
-.
- In this case, the desired displacement values are given at two control
- points, corresponding to the two edges we want to constrain.
- Since data are being specified at two points with a linear variations in
- the values between the points (rather than being uniform over the mesh,
- for example), the data dimension is one.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twoquad4.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-sheardisp.cfg
-\family default
-,
-\family typewriter
-sheardisp.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith sheardisp.cfg
-\end_layout
-
-\begin_layout Standard
-As in the previous example, three files will be produced.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:twoquad4-shear"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/sheardispl.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the shear displacement example
- using a mesh composed of two bilinear quadrilateral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twoquad4-shear"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Kinematic Fault Slip Example
-\end_layout
-
-\begin_layout Standard
-The next example problem is a left-lateral fault slip applied between the
- two square cells using kinematic cohesive cells.
- The left and right boundaries are held fixed in the x and y directions.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-dislocation.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (x and y), giving the label (
-\family typewriter
-x_neg
-\family default
-, defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Instead of specifying a spatial database file for the values of the Dirichlet
- boundary condition, we use the default spatial database (ZeroDispDB) for
- the Dirichlet boundary condition, which sets the displacements to zero
- for all time.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- right side of the mesh, defining which degrees of freedom are being constrained
- (x and y), giving the label (
-\family typewriter
-x_neg
-\family default
-, defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- We use the ZeroDispDB for this boundary condition as well, which sets the
- displacements to zero for all time.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces Gives the label (defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points on the fault, provides quadrature information, and
- then gives database names for material properties (needed for conditioning),
- fault slip, peak fault slip rate, and fault slip time.
-\end_layout
-
-\begin_layout Standard
-The fault example requires three additional database files that were not
- needed for the simple displacement examples.
- The first file (
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-) specifies 0.01 m of left-lateral fault slip for the entire fault.
- The data dimension is zero since the same data are applied to all points
- in the set.
- The default slip time function is a step-function, so we also must provide
- the time at which slip begins.
- The elastic solution is associated with advancing from
-\begin_inset Formula $t=-dt$
-\end_inset
-
- to
-\begin_inset Formula $t=0$
-\end_inset
-
-, so we set the slip initiation time for the step-function to 0 in
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twoquad4.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-\size small
-dislocation.cfg
-\family default
-,
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-,
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith dislocation.cfg
-\end_layout
-
-\begin_layout Standard
-The additional of a fault results in two additional output files (as in
- the two triangle fault example),
-\family typewriter
-dislocation-fault_t0000000.vtk
-\family default
- and
-\family typewriter
-dislocation-fault_info.vtk
-\family default
-.
- These files provide output of fault slip, change in tractions, and diagnostic
- information such as the normal direction, final slip, and slip time for
- each vertex on the fault.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twoquad4-disloc"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/dislocation.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the kinematic fault example
- using a mesh composed of two bilinear quadrilateral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twoquad4-disloc"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Tutorial-twoquad4-traction"
-
-\end_inset
-
-Axial Traction Example
-\end_layout
-
-\begin_layout Standard
-The fourth example demonstrates the use of Neumann (traction) boundary condition
-s.
- Constant tractions are applied to the right edge of the mesh, while displacemen
-ts normal to the boundaries are held fixed along the left and bottom edges
- of the mesh.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-axialtract.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies an implicit formulation for the problem
- and specifies the array of boundary conditions.
- The boundary condition type for
-\family typewriter
-x_pos
-\family default
- is explicitly set to
-\family typewriter
-Neumann
-\family default
-, since the default boundary condition type is
-\family typewriter
-Dirichlet
-\family default
-.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (x) and giving the label (defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired.
- In this case, rather than specifying a spatial database file with values
- for the Dirichlet boundary conditions, we use the default spatial database
- (ZeroDispDB) for the Dirichlet boundary condition, which sets the displacements
- to zero for all time.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the Neumann boundary conditions
- for the right side of the mesh, giving the label (defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database with the traction vectors
- for the Neumann boundary condition (
-\family typewriter
-axialtract.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.y_neg Specifies the boundary conditions for the
- bottom two corners of the mesh, defining which degrees of freedom are being
- constrained (y) and giving the label (defined in
-\family typewriter
-twoquad4.mesh
-\family default
-) defining the points desired.
- In this case, we again use the ZeroDispDB, which sets the displacements
- to zero for all time.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.output.writer Gives the base filename for
- VTK output
-\begin_inset Newline newline
-\end_inset
-
-(
-\family typewriter
-axialtract.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos.output Gives the field to be output for the
-
-\family typewriter
-x_pos
-\family default
- boundary (
-\family typewriter
-tractions
-\family default
-), and gives the base filename for
-\family typewriter
-x_pos
-\family default
- boundary output (
-\family typewriter
-axialtract-tractions.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-The traction vectors for the Neumann boundary conditions are given in the
- file
-\family typewriter
-axialtract.spatialdb
-\family default
-, as specified in
-\family typewriter
-axialtract.cfg
-\family default
-.
- The files containing common information (
-\family typewriter
-twoquad4.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-axialtract.cfg
-\family default
-,
-\family typewriter
-axialtract.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith axialtract.cfg
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, six files will be produced.
- This includes the five files as in the previous example plus
-\family typewriter
-axialtract-tractions_info.vtk
-\family default
-, which gives the
-\family typewriter
-x
-\family default
- and
-\family typewriter
-y
-\family default
- components of traction applied at each integration point.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:twoquad4-axialtract"
-
-\end_inset
-
-, which was generated using ParaView.
- The results may be compared against the analytical solution derived in
- Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Analytical-Constant-Traction"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/axialtract.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the axial traction example
- using a mesh composed of two bilinear quadrilateral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twoquad4-axialtract"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 1in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-Two-quad4"
+
+\end_inset
+
+Tutorial Using Two Quadrilaterals
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Quasi-static solution
+\end_layout
+
+\begin_layout Itemize
+Mesh ASCII format
+\end_layout
+
+\begin_layout Itemize
+Dirichlet boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Neumann boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Plane strain linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Bilinear quadrilateral cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/twocells/twoquad4.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial is another simple 2D example of a quasi-static finite element
+ problem.
+ It is a mesh composed of two bilinear quadrilaterals subject to displacement
+ or traction boundary conditions, assuming plane-strain linear elastic behavior.
+ Due to the simple geometry of the problem, the mesh may be constructed
+ by hand, using PyLith mesh ASCII format to describe the mesh.
+ In this tutorial, we will walk through the steps necessary to construct,
+ run, and view four problems that use the same mesh.
+ In addition to this manual, each of the files for the example problem includes
+ extensive comments.
+\end_layout
+
+\begin_layout Subsection
+Mesh Description
+\end_layout
+
+\begin_layout Standard
+The mesh consists of two square cells with edge lengths of one unit forming
+ a regular region (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twoquad4-mesh"
+
+\end_inset
+
+).
+ The mesh geometry and topology are described in the file
+\family typewriter
+twoquad4.mesh
+\family default
+, which is in PyLith mesh ASCII format.
+ This file describes the dimensionality of the problem (in this case 2D),
+ the coordinates of the vertices (nodes), the vertices composing each cell
+ (element), the material ID to be associated with each cell, and then provides
+ groups of vertices that may be used to define faults or surfaces to which
+ boundary conditions may be applied.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/twoquad4-mesh.eps
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of two bilinear quadrilateral cells used for the example problems.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twoquad4-mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Additional Common Information
+\end_layout
+
+\begin_layout Standard
+In addition to the mesh, the four example problems share additional information.
+ As in the previous examples, we place this information in
+\family typewriter
+pylithapp.cfg
+\family default
+, since this file is read automatically every time PyLith is run.
+ Settings specific to a particular problem may be placed in other
+\family typewriter
+.cfg
+\family default
+ files, as described later, and then those files are placed on the command
+ line.
+\end_layout
+
+\begin_layout Subsection
+Axial Displacement Example
+\end_layout
+
+\begin_layout Standard
+The first example problem is extension of the mesh along the x axis.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+axialdisp.cfg
+\family default
+.
+ These include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (x), giving the label (defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database with the values for the
+ Dirichlet boundary condition (
+\family typewriter
+axialdisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
+ right side of the mesh, defining which degrees of freedom are being constrained
+ (x), giving the label (defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database defining the boundary
+ conditions (
+\family typewriter
+axialdisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.y_neg Specifies the boundary conditions for the
+ bottom two corners of the mesh, defining which degrees of freedom are being
+ constrained (y), giving the label (defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database with the values for the
+ Dirichlet boundary condition (
+\family typewriter
+axialdisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+The values for the Dirichlet boundary condition are given in the file
+\family typewriter
+axialdisp.spatialdb
+\family default
+, as specified in
+\family typewriter
+axialdisp.cfg
+\family default
+.
+ Because the data are being specified using two control points with a linear
+ variation in the values between the two (rather than being uniform over
+ the mesh, for example), the data dimension is one.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twoquad4.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+axialdisp.cfg
+\family default
+,
+\family typewriter
+axialdisp.spatialdb
+\family default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith axialdisp.cfg
+\end_layout
+
+\begin_layout Standard
+As in the two triangle axial displacement example, three files will be produced.
+ If the problem ran correctly, you should be able to produce a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:twoquad4-axial"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+placement t
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/axialdisp.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the axial displacement example
+ using a mesh composed of two bilinear quadrilateral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twoquad4-axial"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Shear Displacement Example
+\end_layout
+
+\begin_layout Standard
+The next example problem is shearing of the mesh in the y direction using
+ displacements applied along the positive and negative x boundaries.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+sheardisp.cfg
+\family default
+.
+ These include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (x and y), giving the label (
+\family typewriter
+x_neg
+\family default
+, defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database with the values for the
+ Dirichlet boundary condition (
+\family typewriter
+sheardisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (y only), giving the label (
+\family typewriter
+x_
+\family default
+pos, defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database with the values for the
+ Dirichlet boundary condition (
+\family typewriter
+sheardisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+The values for the Dirichlet boundary conditions are described in the file
+
+\family typewriter
+sheardisp.spatialdb
+\family default
+, as specified in
+\family typewriter
+sheardisp.cfg
+\family default
+.
+ In this case, the desired displacement values are given at two control
+ points, corresponding to the two edges we want to constrain.
+ Since data are being specified at two points with a linear variations in
+ the values between the points (rather than being uniform over the mesh,
+ for example), the data dimension is one.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twoquad4.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+sheardisp.cfg
+\family default
+,
+\family typewriter
+sheardisp.spatialdb
+\family default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith sheardisp.cfg
+\end_layout
+
+\begin_layout Standard
+As in the previous example, three files will be produced.
+ If the problem ran correctly, you should be able to produce a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:twoquad4-shear"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/sheardispl.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the shear displacement example
+ using a mesh composed of two bilinear quadrilateral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twoquad4-shear"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Kinematic Fault Slip Example
+\end_layout
+
+\begin_layout Standard
+The next example problem is a left-lateral fault slip applied between the
+ two square cells using kinematic cohesive cells.
+ The left and right boundaries are held fixed in the x and y directions.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+dislocation.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (x and y), giving the label (
+\family typewriter
+x_neg
+\family default
+, defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired, and assigning a label to the boundary condition
+ set.
+ Instead of specifying a spatial database file for the values of the Dirichlet
+ boundary condition, we use the default spatial database (ZeroDispDB) for
+ the Dirichlet boundary condition, which sets the displacements to zero
+ for all time.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
+ right side of the mesh, defining which degrees of freedom are being constrained
+ (x and y), giving the label (
+\family typewriter
+x_neg
+\family default
+, defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired, and assigning a label to the boundary condition
+ set.
+ We use the ZeroDispDB for this boundary condition as well, which sets the
+ displacements to zero for all time.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces Gives the label (defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points on the fault, provides quadrature information, and
+ then gives database names for material properties (needed for conditioning),
+ fault slip, peak fault slip rate, and fault slip time.
+\end_layout
+
+\begin_layout Standard
+The fault example requires three additional database files that were not
+ needed for the simple displacement examples.
+ The first file (
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+) specifies 0.01 m of left-lateral fault slip for the entire fault.
+ The data dimension is zero since the same data are applied to all points
+ in the set.
+ The default slip time function is a step-function, so we also must provide
+ the time at which slip begins.
+ The elastic solution is associated with advancing from
+\begin_inset Formula $t=-dt$
+\end_inset
+
+ to
+\begin_inset Formula $t=0$
+\end_inset
+
+, so we set the slip initiation time for the step-function to 0 in
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twoquad4.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+\size small
+dislocation.cfg
+\family default
+,
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+,
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+\size default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith dislocation.cfg
+\end_layout
+
+\begin_layout Standard
+The addition of a fault results in two additional output files (as in the
+ two triangle fault example),
+\family typewriter
+dislocation-fault_t0000000.vtk
+\family default
+ and
+\family typewriter
+dislocation-fault_info.vtk
+\family default
+.
+ These files provide output of fault slip, change in tractions, and diagnostic
+ information such as the normal direction, final slip, and slip time for
+ each vertex on the fault.
+ If the problem ran correctly, you should be able to produce a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twoquad4-disloc"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/dislocation.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the kinematic fault example
+ using a mesh composed of two bilinear quadrilateral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twoquad4-disloc"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Tutorial-twoquad4-traction"
+
+\end_inset
+
+Axial Traction Example
+\end_layout
+
+\begin_layout Standard
+The fourth example demonstrates the use of Neumann (traction) boundary condition
+s.
+ Constant tractions are applied to the right edge of the mesh, while displacemen
+ts normal to the boundaries are held fixed along the left and bottom edges
+ of the mesh.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+axialtract.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies an implicit formulation for the problem
+ and specifies the array of boundary conditions.
+ The boundary condition type for
+\family typewriter
+x_pos
+\family default
+ is explicitly set to
+\family typewriter
+Neumann
+\family default
+, since the default boundary condition type is
+\family typewriter
+Dirichlet
+\family default
+.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (x) and giving the label (defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired.
+ In this case, rather than specifying a spatial database file with values
+ for the Dirichlet boundary conditions, we use the default spatial database
+ (ZeroDispDB) for the Dirichlet boundary condition, which sets the displacements
+ to zero for all time.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Specifies the Neumann boundary conditions
+ for the right side of the mesh, giving the label (defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database with the traction vectors
+ for the Neumann boundary condition (
+\family typewriter
+axialtract.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.y_neg Specifies the boundary conditions for the
+ bottom two corners of the mesh, defining which degrees of freedom are being
+ constrained (y) and giving the label (defined in
+\family typewriter
+twoquad4.mesh
+\family default
+) defining the points desired.
+ In this case, we again use the ZeroDispDB, which sets the displacements
+ to zero for all time.
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.output.writer Gives the base filename for
+ VTK output
+\begin_inset Newline newline
+\end_inset
+
+(
+\family typewriter
+axialtract.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos.output Gives the field to be output for the
+
+\family typewriter
+x_pos
+\family default
+ boundary (
+\family typewriter
+tractions
+\family default
+), and gives the base filename for
+\family typewriter
+x_pos
+\family default
+ boundary output (
+\family typewriter
+axialtract-tractions.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+The traction vectors for the Neumann boundary conditions are given in the
+ file
+\family typewriter
+axialtract.spatialdb
+\family default
+, as specified in
+\family typewriter
+axialtract.cfg
+\family default
+.
+ The files containing common information (
+\family typewriter
+twoquad4.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+axialtract.cfg
+\family default
+,
+\family typewriter
+axialtract.spatialdb
+\family default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith axialtract.cfg
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, six files will be produced.
+ This includes the five files as in the previous example plus
+\family typewriter
+axialtract-tractions_info.vtk
+\family default
+, which gives the
+\family typewriter
+x
+\family default
+ and
+\family typewriter
+y
+\family default
+ components of traction applied at each integration point.
+ If the problem ran correctly, you should be able to produce a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:twoquad4-axialtract"
+
+\end_inset
+
+, which was generated using ParaView.
+ The results may be compared against the analytical solution derived in
+ Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Analytical-Constant-Traction"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/axialtract.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the axial traction example
+ using a mesh composed of two bilinear quadrilateral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twoquad4-axialtract"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotet4/twotet4.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotet4/twotet4.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotet4/twotet4.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,549 +1,549 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
-\use_default_options false
-\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding latin1
-\fontencoding global
-\font_roman default
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-\use_non_tex_fonts false
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
-\graphics default
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-\output_sync 0
-\bibtex_command default
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-\spacing single
-\use_hyperref false
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-\use_geometry true
-\use_amsmath 0
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-\cite_engine basic
-\use_bibtopic false
-\use_indices false
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-\use_refstyle 0
-\index Index
-\shortcut idx
-\color #008000
-\end_index
-\leftmargin 1in
-\topmargin 1in
-\rightmargin 1in
-\bottommargin 2in
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\paragraph_indentation default
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-Two-tet4"
-
-\end_inset
-
-Tutorial Using Two Tetrahedra
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Quasi-static solution
-\end_layout
-
-\begin_layout Itemize
-Mesh ASCII format
-\end_layout
-
-\begin_layout Itemize
-Dirichlet boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Linearly elastic isotropic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Linear tetrahedral cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/twocells/twotet4.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial is a simple 3D example of a quasi-static finite element problem.
- It is a mesh composed of two linear tetrahedra subject to displacement
- boundary conditions, and is probably the simplest example of a 3D elastic
- problem.
- Due to the simple geometry of the problem, the mesh may be constructed
- by hand, using PyLith mesh ASCII format.
- In this tutorial, we will walk through the steps necessary to construct,
- run, and view two problems that use the same mesh.
- In addition to this manual, each of the files for the example problem includes
- extensive comments.
-\end_layout
-
-\begin_layout Subsection
-Mesh Description
-\end_layout
-
-\begin_layout Standard
-The mesh consists of two tetrahedra forming a pyramid shape (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twotet4-mesh"
-
-\end_inset
-
-).
- The mesh geometry and topology is described in the file
-\family typewriter
-twotet4.mesh
-\family default
-, which is in PyLith mesh ASCII format.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/twotet4-mesh.eps
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of two linear tetrahedral cells used for example problems.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotet4-mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Additional Common Information
-\end_layout
-
-\begin_layout Standard
-In addition to the mesh, the two example problems share additional information,
- which we place in
-\family typewriter
-pylithapp.cfg
-\family default
-.
-\end_layout
-
-\begin_layout Subsection
-Axial Displacement Example
-\end_layout
-
-\begin_layout Standard
-The first example problem is extension of the mesh along the diagonal, extending
- along the base of the pyramid between two opposing vertices.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-axialdisp.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.bc Defines which degrees of freedom are being constraine
-d (
-\family typewriter
-x
-\family default
-,
-\family typewriter
-y
-\family default
-, and
-\family typewriter
-z
-\family default
-), gives the label (defined in
-\family typewriter
-twotet4.mesh
-\family default
-) defining the points desired, assigns a label to the boundary condition
- set, and gives the name of the spatial database defining the boundary condition
-s (
-\family typewriter
-axialdisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-The values for the Dirichlet boundary conditions are described in the file
-
-\family typewriter
-axialdisp.spatialdb
-\family default
-, as specified in
-\family typewriter
-axialdisp.cfg
-\family default
-.
- Because data are being specified using two control points (rather than
- being uniform over the mesh), the data dimension is one.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twotet4.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-axialdisp.cfg
-\family default
-,
-\family typewriter
-axialdisp.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith axialdisp.cfg
-\end_layout
-
-\begin_layout Standard
-If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twotet4-axial"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/axialdisp.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the axial displacement example
- using a mesh composed of two linear tetrahedral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotet4-axial"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Kinematic Fault Slip Example
-\end_layout
-
-\begin_layout Standard
-The next example problem is a left-lateral fault slip applied between the
- two tetrahedral cells using kinematic cohesive cells.
- The vertices away from the fault are held fixed in the
-\family typewriter
-x
-\family default
-,
-\family typewriter
-y
-\family default
-, and
-\family typewriter
-z
-\family default
- directions.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-dislocation.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.bc Defines which degrees of freedom are being constraine
-d (
-\family typewriter
-x
-\family default
-,
-\family typewriter
-y
-\family default
-, and
-\family typewriter
-z
-\family default
-), gives the label (defined in
-\family typewriter
-twotet4.mesh
-\family default
-) defining the points desired, and assigns a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces Gives the label (defined in
-\family typewriter
-twotet4.mesh
-\family default
-) defining the points on the fault, provides quadrature information, and
- then gives database names for material properties (needed for conditioning),
- fault slip, peak fault slip rate, and fault slip time.
-\end_layout
-
-\begin_layout Standard
-The fault example requires three additional database files that were not
- needed for the simple displacement examples.
- The first file (
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-) specifies 0.01 m of left-lateral fault slip for the entire fault.
- The data dimension is zero since the same data are applied to all points
- in the set.
- The default slip time function is a step-function, so we also must provide
- the time at which slip begins.
- The elastic solution is associated with advancing from
-\begin_inset Formula $t=-dt$
-\end_inset
-
- to
-\begin_inset Formula $t=0$
-\end_inset
-
-, so we set the slip initiation time for the step-function to 0 in
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twotet4.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-\size small
-dislocation.cfg
-\family default
-,
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-,
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith dislocation.cfg
-\end_layout
-
-\begin_layout Standard
-If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:twotet4-disloc"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/dislocation.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the kinematic fault example
- using a mesh composed of two linear tetrahedral cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotet4-disloc"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 2in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-Two-tet4"
+
+\end_inset
+
+Tutorial Using Two Tetrahedra
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Quasi-static solution
+\end_layout
+
+\begin_layout Itemize
+Mesh ASCII format
+\end_layout
+
+\begin_layout Itemize
+Dirichlet boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Linearly elastic isotropic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Linear tetrahedral cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/twocells/twotet4.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial is a simple 3D example of a quasi-static finite element problem.
+ It is a mesh composed of two linear tetrahedra subject to displacement
+ boundary conditions, and is probably the simplest example of a 3D elastic
+ problem.
+ Due to the simple geometry of the problem, the mesh may be constructed
+ by hand, using PyLith mesh ASCII format.
+ In this tutorial, we will walk through the steps necessary to construct,
+ run, and view two problems that use the same mesh.
+ In addition to this manual, each of the files for the example problem includes
+ extensive comments.
+\end_layout
+
+\begin_layout Subsection
+Mesh Description
+\end_layout
+
+\begin_layout Standard
+The mesh consists of two tetrahedra forming a pyramid shape (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twotet4-mesh"
+
+\end_inset
+
+).
+ The mesh geometry and topology is described in the file
+\family typewriter
+twotet4.mesh
+\family default
+, which is in PyLith mesh ASCII format.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/twotet4-mesh.eps
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of two linear tetrahedral cells used for example problems.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotet4-mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Additional Common Information
+\end_layout
+
+\begin_layout Standard
+In addition to the mesh, the two example problems share additional information,
+ which we place in
+\family typewriter
+pylithapp.cfg
+\family default
+.
+\end_layout
+
+\begin_layout Subsection
+Axial Displacement Example
+\end_layout
+
+\begin_layout Standard
+The first example problem is extension of the mesh along the diagonal, extending
+ along the base of the pyramid between two opposing vertices.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+axialdisp.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.bc Defines which degrees of freedom are being constraine
+d (
+\family typewriter
+x
+\family default
+,
+\family typewriter
+y
+\family default
+, and
+\family typewriter
+z
+\family default
+), gives the label (defined in
+\family typewriter
+twotet4.mesh
+\family default
+) defining the points desired, assigns a label to the boundary condition
+ set, and gives the name of the spatial database defining the boundary condition
+s (
+\family typewriter
+axialdisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+The values for the Dirichlet boundary conditions are described in the file
+
+\family typewriter
+axialdisp.spatialdb
+\family default
+, as specified in
+\family typewriter
+axialdisp.cfg
+\family default
+.
+ Because data are being specified using two control points (rather than
+ being uniform over the mesh), the data dimension is one.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twotet4.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+axialdisp.cfg
+\family default
+,
+\family typewriter
+axialdisp.spatialdb
+\family default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith axialdisp.cfg
+\end_layout
+
+\begin_layout Standard
+If the problem ran correctly, you should be able to produce a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twotet4-axial"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/axialdisp.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the axial displacement example
+ using a mesh composed of two linear tetrahedral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotet4-axial"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Kinematic Fault Slip Example
+\end_layout
+
+\begin_layout Standard
+The next example problem is a left-lateral fault slip applied between the
+ two tetrahedral cells using kinematic cohesive cells.
+ The vertices away from the fault are held fixed in the
+\family typewriter
+x
+\family default
+,
+\family typewriter
+y
+\family default
+, and
+\family typewriter
+z
+\family default
+ directions.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+dislocation.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.bc Defines which degrees of freedom are being constraine
+d (
+\family typewriter
+x
+\family default
+,
+\family typewriter
+y
+\family default
+, and
+\family typewriter
+z
+\family default
+), gives the label (defined in
+\family typewriter
+twotet4.mesh
+\family default
+) defining the points desired, and assigns a label to the boundary condition
+ set.
+ Rather than specifying a spatial database file to define the boundary condition
+s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
+ condition, which sets the displacements to zero.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces Gives the label (defined in
+\family typewriter
+twotet4.mesh
+\family default
+) defining the points on the fault, provides quadrature information, and
+ then gives database names for material properties (needed for conditioning),
+ fault slip, peak fault slip rate, and fault slip time.
+\end_layout
+
+\begin_layout Standard
+The fault example requires three additional database files that were not
+ needed for the simple displacement examples.
+ The first file (
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+) specifies 0.01 m of left-lateral fault slip for the entire fault.
+ The data dimension is zero since the same data are applied to all points
+ in the set.
+ The default slip time function is a step-function, so we also must provide
+ the time at which slip begins.
+ The elastic solution is associated with advancing from
+\begin_inset Formula $t=-dt$
+\end_inset
+
+ to
+\begin_inset Formula $t=0$
+\end_inset
+
+, so we set the slip initiation time for the step-function to 0 in
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twotet4.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+\size small
+dislocation.cfg
+\family default
+,
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+,
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+\size default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith dislocation.cfg
+\end_layout
+
+\begin_layout Standard
+If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:twotet4-disloc"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/dislocation.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the kinematic fault example
+ using a mesh composed of two linear tetrahedral cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotet4-disloc"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotet4-geoproj/twotet4-geoproj.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotet4-geoproj/twotet4-geoproj.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotet4-geoproj/twotet4-geoproj.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,577 +1,577 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
-\use_default_options false
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-\language english
-\language_package default
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-
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-\spacing single
-\use_hyperref false
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-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-Two-tet4-geoproj"
-
-\end_inset
-
-Tutorial Using Two Tetrahedra with Georeferenced Coordinate System Mesh
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Quasi-static solution
-\end_layout
-
-\begin_layout Itemize
-Mesh ASCII format
-\end_layout
-
-\begin_layout Itemize
-Dirichlet boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Linearly elastic isotropic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Linear tetrahedral cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database with geographic coordinates
-\end_layout
-
-\begin_layout Itemize
-SCEC CVM-H spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/twocells/twotet4-geoproj.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial is virtually identical to the other tutorial using two linear
- tetrahedra (See Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Tutorial-Two-tet4"
-
-\end_inset
-
-).
- The primary difference is in how the material properties are assigned.
- For this tutorial, the physical properties come from the SCEC CVM-H database
- (described in Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:SCECCVMH-Impl"
-
-\end_inset
-
-).
- Using the SCEC CVM-H database is straightforward, requiring only a few
- modifications to
-\family typewriter
-pylithapp.cfg
-\family default
-.
- Because the SCEC CVM-H database uses geographic coordinates, we must also
- use geographic coordinates in the PyLith mesh ASCII file and other spatial
- databases.
- Note that all of these geographic coordinate systems do not need to be
- the same.
- PyLith will automatically transform from one geographic coordinate system
- to another using the spatialdata package.
- The spatial databases should all use a georeferenced Cartesian coordinate
- system, such as a geographic projection to insure interpolation is performed
- properly.
- Since all aspects of this problem other than the material database and
- the coordinate system are identical to the examples in Section
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Tutorial-Two-tet4"
-
-\end_inset
-
-, we only describe the kinematic fault problem in this tutorial.
-\end_layout
-
-\begin_layout Subsection
-Mesh Description
-\end_layout
-
-\begin_layout Standard
-The mesh consists of two tetrahedra forming a pyramid shape (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twotet4-geoproj-mesh"
-
-\end_inset
-
-).
- The mesh geometry and topology are described in the file
-\family typewriter
-twotet4.mesh
-\family default
-, which is in PyLith mesh ASCII format.
- If you compare this mesh against the one used in
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Tutorial-Two-tet4"
-
-\end_inset
-
-, you will notice that, although the mesh topology is the same, the vertex
- coordinates are significantly different.
- We use zone 11 UTM coordinates with the NAD27 datum for the mesh.
- Although we used the same coordinate system as the SCEC CVM-H, we could
- have also used any another geographic projection supported by spatialdata
- and Proj.4.
- See Appendix
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sec:Spatialdata:SimpleIOAscii"
-
-\end_inset
-
- for other examples of using geographic coordinates.
-
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/twotet4-mesh.eps
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of two linear tetrahedral cells in a georeferenced coordinate
- system used for the example problems.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotet4-geoproj-mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Additional Common Information
-\end_layout
-
-\begin_layout Standard
-This problem has some unique aspects compared to the other tutorials.
- First, all of the other tutorials use a Cartesian coordinate system, while
- this one uses a geographic coordinate system.
- In addition to using different vertex coordinates, we also define the coordinat
-e system for the mesh in
-\family typewriter
-pylithapp.cfg
-\family default
-:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.mesh_generator.importer]
-\end_layout
-
-\begin_layout LyX-Code
-coordsys = spatialdata.geocoords.CSGeoProj
-\end_layout
-
-\begin_layout LyX-Code
-filename = twotet4.mesh
-\end_layout
-
-\begin_layout LyX-Code
-coordsys.space_dim = 3
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.mesh_generator.importer.coordsys]
-\end_layout
-
-\begin_layout LyX-Code
-datum_horiz = NAD27
-\end_layout
-
-\begin_layout LyX-Code
-datum_vert = mean sea level
-\end_layout
-
-\begin_layout LyX-Code
-ellipsoid = clrk66
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.mesh_generator.importer.coordsys.projector]
-\end_layout
-
-\begin_layout LyX-Code
-projection = utm
-\end_layout
-
-\begin_layout LyX-Code
-proj-options = +zone=11
-\end_layout
-
-\begin_layout Standard
-At the top level, we define the type of coordinate system, give the file
- describing the mesh, and give the number of spatial dimensions for the
- coordinate system.
- We then provide the horizontal datum and vertical datum for the coordinate
- system, along with the ellipsoid to be used.
- Finally, we specify a UTM projection, and specify zone 11 as the zone to
- be used.
-\end_layout
-
-\begin_layout Standard
-In addition to the usual material information, we must specify that we want
- to use the
-\family typewriter
-SCECCVMH
-\family default
- database implementation:
-\end_layout
-
-\begin_layout LyX-Code
-[pylithapp.timedependent.materials.material]
-\end_layout
-
-\begin_layout LyX-Code
-db = spatialdata.spatialdb.SCECCVMH
-\end_layout
-
-\begin_layout LyX-Code
-db.data_dir = /home/brad/data/sceccvm-h/vx53/bin
-\end_layout
-
-\begin_layout Standard
-The first
-\family typewriter
-db
-\family default
- option defines
-\family typewriter
-SCECCVMH
-\family default
- as the spatial database to be used.
- The next line defines the location of the
-\family typewriter
-vx53
-\family default
- data files, and must be changed to the location specified by the user when
- the package is installed.
- The package may be obtained from Harvard's Structural Geology and Tectonics
-
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-structure.harvard.edu/cvm-h
-\end_layout
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-The final difference with the other examples is in the description of the
- spatial databases.
- They must also use geographic coordinates.
- Examining
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-, we find:
-\end_layout
-
-\begin_layout LyX-Code
-// We are specifying the data in a projected geographic coordinate system.
-\end_layout
-
-\begin_layout LyX-Code
-cs-data = geo-projected {
-\end_layout
-
-\begin_layout LyX-Code
- to-meters = 1.0
-\end_layout
-
-\begin_layout LyX-Code
- ellipsoid = clrk66
-\end_layout
-
-\begin_layout LyX-Code
- datum-horiz = NAD27
-\end_layout
-
-\begin_layout LyX-Code
- datum-vert = mean sea level
-\end_layout
-
-\begin_layout LyX-Code
- projector = projection {
-\end_layout
-
-\begin_layout LyX-Code
- projection = utm
-\end_layout
-
-\begin_layout LyX-Code
- units = m
-\end_layout
-
-\begin_layout LyX-Code
- proj-options = +zone=11
-\end_layout
-
-\begin_layout LyX-Code
- }
-\end_layout
-
-\begin_layout LyX-Code
-}
-\end_layout
-
-\begin_layout Subsection
-Kinematic Fault Slip Example
-\end_layout
-
-\begin_layout Standard
-This example problem is a left-lateral fault slip applied between the two
- tetrahedral cells using kinematic cohesive cells.
- Note that we vary the amount of fault slip for each vertex with this example,
- as described in
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-.
- The vertices away from the fault are held fixed in the x, y, and z directions.
- Parameter settings that override or augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-dislocation.cfg
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-Recall that we condition problems with the kinematic fault interface using
- the material properties.
- Since the material properties are being defined using the SCEC CVM-H database,
- this same database should be used as the material database for the faults.
- This also applies to the AbsorbingDampers boundary condition.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twotet4.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-) along with the problem-specific files (
-\family typewriter
-\size small
-dislocation.cfg
-\family default
-,
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-,
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith dislocation.cfg
-\end_layout
-
-\begin_layout Standard
-If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:twotet4-geoproj-disloc"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/dislocation.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the kinematic fault example
- using a mesh composed of two linear tetrahedral cells in a georeferenced
- coordinate system.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotet4-geoproj-disloc"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 2in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-Two-tet4-geoproj"
+
+\end_inset
+
+Tutorial Using Two Tetrahedra with Georeferenced Coordinate System Mesh
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Quasi-static solution
+\end_layout
+
+\begin_layout Itemize
+Mesh ASCII format
+\end_layout
+
+\begin_layout Itemize
+Dirichlet boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Linearly elastic isotropic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Linear tetrahedral cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database with geographic coordinates
+\end_layout
+
+\begin_layout Itemize
+SCEC CVM-H spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/twocells/twotet4-geoproj.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial is virtually identical to the other tutorial using two linear
+ tetrahedra (See Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Tutorial-Two-tet4"
+
+\end_inset
+
+).
+ The primary difference is in how the material properties are assigned.
+ For this tutorial, the physical properties come from the SCEC CVM-H database
+ (described in Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:SCECCVMH-Impl"
+
+\end_inset
+
+).
+ Using the SCEC CVM-H database is straightforward, requiring only a few
+ modifications to
+\family typewriter
+pylithapp.cfg
+\family default
+.
+ Because the SCEC CVM-H database uses geographic coordinates, we must also
+ use geographic coordinates in the PyLith mesh ASCII file and other spatial
+ databases.
+ Note that all of these geographic coordinate systems do not need to be
+ the same.
+ PyLith will automatically transform from one geographic coordinate system
+ to another using the spatialdata package.
+ The spatial databases should all use a georeferenced Cartesian coordinate
+ system, such as a geographic projection to insure interpolation is performed
+ properly.
+ Since all aspects of this problem other than the material database and
+ the coordinate system are identical to the examples in Section
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Tutorial-Two-tet4"
+
+\end_inset
+
+, we only describe the kinematic fault problem in this tutorial.
+\end_layout
+
+\begin_layout Subsection
+Mesh Description
+\end_layout
+
+\begin_layout Standard
+The mesh consists of two tetrahedra forming a pyramid shape (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twotet4-geoproj-mesh"
+
+\end_inset
+
+).
+ The mesh geometry and topology are described in the file
+\family typewriter
+twotet4.mesh
+\family default
+, which is in PyLith mesh ASCII format.
+ If you compare this mesh against the one used in
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Tutorial-Two-tet4"
+
+\end_inset
+
+, you will notice that, although the mesh topology is the same, the vertex
+ coordinates are significantly different.
+ We use zone 11 UTM coordinates with the NAD27 datum for the mesh.
+ Although we used the same coordinate system as the SCEC CVM-H, we could
+ have also used any other geographic projection supported by spatialdata
+ and Proj.4.
+ See Appendix
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Spatialdata:SimpleIOAscii"
+
+\end_inset
+
+ for other examples of using geographic coordinates.
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/twotet4-mesh.eps
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of two linear tetrahedral cells in a georeferenced coordinate
+ system used for the example problems.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotet4-geoproj-mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Additional Common Information
+\end_layout
+
+\begin_layout Standard
+This problem has some unique aspects compared to the other tutorials.
+ First, all of the other tutorials use a Cartesian coordinate system, while
+ this one uses a geographic coordinate system.
+ In addition to using different vertex coordinates, we also define the coordinat
+e system for the mesh in
+\family typewriter
+pylithapp.cfg
+\family default
+:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.mesh_generator.importer]
+\end_layout
+
+\begin_layout LyX-Code
+coordsys = spatialdata.geocoords.CSGeoProj
+\end_layout
+
+\begin_layout LyX-Code
+filename = twotet4.mesh
+\end_layout
+
+\begin_layout LyX-Code
+coordsys.space_dim = 3
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.mesh_generator.importer.coordsys]
+\end_layout
+
+\begin_layout LyX-Code
+datum_horiz = NAD27
+\end_layout
+
+\begin_layout LyX-Code
+datum_vert = mean sea level
+\end_layout
+
+\begin_layout LyX-Code
+ellipsoid = clrk66
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.mesh_generator.importer.coordsys.projector]
+\end_layout
+
+\begin_layout LyX-Code
+projection = utm
+\end_layout
+
+\begin_layout LyX-Code
+proj-options = +zone=11
+\end_layout
+
+\begin_layout Standard
+At the top level, we define the type of coordinate system, give the file
+ describing the mesh, and give the number of spatial dimensions for the
+ coordinate system.
+ We then provide the horizontal datum and vertical datum for the coordinate
+ system, along with the ellipsoid to be used.
+ Finally, we specify a UTM projection, and specify zone 11 as the zone to
+ be used.
+\end_layout
+
+\begin_layout Standard
+In addition to the usual material information, we must specify that we want
+ to use the
+\family typewriter
+SCECCVMH
+\family default
+ database implementation:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials.material]
+\end_layout
+
+\begin_layout LyX-Code
+db = spatialdata.spatialdb.SCECCVMH
+\end_layout
+
+\begin_layout LyX-Code
+db.data_dir = /home/brad/data/sceccvm-h/vx53/bin
+\end_layout
+
+\begin_layout Standard
+The first
+\family typewriter
+db
+\family default
+ option defines
+\family typewriter
+SCECCVMH
+\family default
+ as the spatial database to be used.
+ The next line defines the location of the
+\family typewriter
+vx53
+\family default
+ data files, and must be changed to the location specified by the user when
+ the package is installed.
+ The package may be obtained from Harvard's Structural Geology and Tectonics
+
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+structure.harvard.edu/cvm-h
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The final difference with the other examples is in the description of the
+ spatial databases.
+ They must also use geographic coordinates.
+ Examining
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+, we find:
+\end_layout
+
+\begin_layout LyX-Code
+// We are specifying the data in a projected geographic coordinate system.
+\end_layout
+
+\begin_layout LyX-Code
+cs-data = geo-projected {
+\end_layout
+
+\begin_layout LyX-Code
+ to-meters = 1.0
+\end_layout
+
+\begin_layout LyX-Code
+ ellipsoid = clrk66
+\end_layout
+
+\begin_layout LyX-Code
+ datum-horiz = NAD27
+\end_layout
+
+\begin_layout LyX-Code
+ datum-vert = mean sea level
+\end_layout
+
+\begin_layout LyX-Code
+ projector = projection {
+\end_layout
+
+\begin_layout LyX-Code
+ projection = utm
+\end_layout
+
+\begin_layout LyX-Code
+ units = m
+\end_layout
+
+\begin_layout LyX-Code
+ proj-options = +zone=11
+\end_layout
+
+\begin_layout LyX-Code
+ }
+\end_layout
+
+\begin_layout LyX-Code
+}
+\end_layout
+
+\begin_layout Subsection
+Kinematic Fault Slip Example
+\end_layout
+
+\begin_layout Standard
+This example problem is a left-lateral fault slip applied between the two
+ tetrahedral cells using kinematic cohesive cells.
+ Note that we vary the amount of fault slip for each vertex with this example,
+ as described in
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+.
+ The vertices away from the fault are held fixed in the x, y, and z directions.
+ Parameter settings that override or augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+dislocation.cfg
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+Recall that we condition problems with the kinematic fault interface using
+ the material properties.
+ Since the material properties are being defined using the SCEC CVM-H database,
+ this same database should be used as the material database for the faults.
+ This also applies to the AbsorbingDampers boundary condition.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twotet4.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+) along with the problem-specific files (
+\family typewriter
+\size small
+dislocation.cfg
+\family default
+,
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+,
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+\size default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith dislocation.cfg
+\end_layout
+
+\begin_layout Standard
+If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:twotet4-geoproj-disloc"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/dislocation.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the kinematic fault example
+ using a mesh composed of two linear tetrahedral cells in a georeferenced
+ coordinate system.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotet4-geoproj-disloc"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
Modified: short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotri3/twotri3.lyx
===================================================================
--- short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotri3/twotri3.lyx 2012-06-24 18:07:08 UTC (rev 20401)
+++ short/3D/PyLith/branches/v1.7-stable/doc/userguide/tutorials/twotri3/twotri3.lyx 2012-06-25 04:33:44 UTC (rev 20402)
@@ -1,870 +1,870 @@
-#LyX 2.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 413
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-
-\end_preamble
-\use_default_options false
-\maintain_unincluded_children false
-\language english
-\language_package default
-\inputencoding latin1
-\fontencoding global
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\use_non_tex_fonts false
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-
-\graphics default
-\default_output_format default
-\output_sync 0
-\bibtex_command default
-\index_command default
-\paperfontsize default
-\spacing single
-\use_hyperref false
-\papersize default
-\use_geometry true
-\use_amsmath 0
-\use_esint 0
-\use_mhchem 1
-\use_mathdots 1
-\cite_engine basic
-\use_bibtopic false
-\use_indices false
-\paperorientation portrait
-\suppress_date false
-\use_refstyle 0
-\index Index
-\shortcut idx
-\color #008000
-\end_index
-\leftmargin 1in
-\topmargin 1in
-\rightmargin 1in
-\bottommargin 1in
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\paragraph_indentation default
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\html_math_output 0
-\html_css_as_file 0
-\html_be_strict false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Tutorial-Two-triangle"
-
-\end_inset
-
-Tutorial Using Two Triangles
-\end_layout
-
-\begin_layout Standard
-PyLith features discussed in this tutorial:
-\end_layout
-
-\begin_layout Itemize
-Quasi-static solution
-\end_layout
-
-\begin_layout Itemize
-Mesh ASCII format
-\end_layout
-
-\begin_layout Itemize
-Dirichlet boundary conditions
-\end_layout
-
-\begin_layout Itemize
-Kinematic fault interface conditions
-\end_layout
-
-\begin_layout Itemize
-Plane strain linearly elastic material
-\end_layout
-
-\begin_layout Itemize
-VTK output
-\end_layout
-
-\begin_layout Itemize
-Linear triangular cells
-\end_layout
-
-\begin_layout Itemize
-SimpleDB spatial database
-\end_layout
-
-\begin_layout Itemize
-ZeroDispDB spatial database
-\end_layout
-
-\begin_layout Standard
-All of the files necessary to run the examples are contained in the directory
-
-\family typewriter
-examples/twocells/twotri3.
-\end_layout
-
-\begin_layout Subsection
-Overview
-\end_layout
-
-\begin_layout Standard
-This tutorial is the simplest 2D example of a quasi-static finite element
- problem (a simpler problem would consist of a 1D bar).
- It is a mesh composed of two linear triangles subject to displacement boundary
- conditions, assuming plane-strain linear elastic behavior.
- Due to the simple geometry of the problem, the mesh may be constructed
- by hand, using PyLith mesh ASCII format.
- In this tutorial, we will walk through the steps necessary to construct,
- run, and view three problems that use the same mesh.
- In addition to this manual, each of the files for the example problem includes
- extensive comments.
-\end_layout
-
-\begin_layout Subsection
-Mesh Description
-\end_layout
-
-\begin_layout Standard
-The mesh consists of two triangles forming a square with edge lengths of
- one unit (Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:twotri3-mesh"
-
-\end_inset
-
-).
- The mesh geometry and topology are described in the file
-\family typewriter
-twotri3.mesh
-\family default
-, which is in PyLith mesh ASCII format.
- This file format is described in Appendix
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "cha:File-Formats"
-
-\end_inset
-
-.
- This file describes the dimensionality of the problem (1D, 2D, or 3D),
- the coordinates of the vertices (nodes), the vertices composing each cell
- (element), the material ID to be associated with each cell, and groups
- of vertices that may be used to define faults or surfaces to which boundary
- conditions may be applied.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/twotri3-mesh.eps
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Mesh composed of two linear triangular cells used in the example problems.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotri3-mesh"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Additional Common Information
-\end_layout
-
-\begin_layout Standard
-In addition to the mesh, the three example problems share additional information.
- For problems of this type, it is generally useful to create a file named
-
-\family typewriter
-pylithapp.cfg
-\family default
- in the working directory, since this file is read automatically every time
- PyLith is run.
- Settings specific to a particular problem may be placed in other
-\family typewriter
-.cfg
-\family default
- files, as described later, and then those files are placed on the command
- line.
- The settings contained in
-\family typewriter
-pylithapp.cfg
-\family default
- for this problem consist of:
-\end_layout
-
-\begin_layout Description
-pylithapp.journal.info Settings that control the verbosity of the output for
- the different components.
-\end_layout
-
-\begin_layout Description
-pylithapp.mesh_generator Settings that control mesh importing, such as the
- importer type, the filename, and the spatial dimension of the mesh.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Settings that control the problem, such as the total
- time, time step size, and spatial dimension.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials Settings that control the material type,
- specify which material IDs are to be associated with a particular material
- type, and give the name of the spatial database containing the physical
- properties for the material.
- The quadrature information is also given.
-\end_layout
-
-\begin_layout Description
-pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
- type.
-\end_layout
-
-\begin_layout Standard
-All of the problems in this directory use the same material database, as
- specified under
-\end_layout
-
-\begin_layout LyX-Code
-
-\family typewriter
-pylithapp.timedependent.materials
-\family default
-
-\end_layout
-
-\begin_layout Standard
-in
-\family typewriter
-pylithapp.cfg
-\family default
-.
- This information is contained in the file
-\family typewriter
-matprops.spatialdb
-\family default
-.
- Although the material model is specified in
-\family typewriter
-pylithapp.cfg
-\family default
-, the values for the physical properties of the material are given in
-\family typewriter
-matprops.spatialdb
-\family default
-.
- For this example, values describing elastic plane strain material properties
- are given at a single point, resulting in uniform material properties.
-\end_layout
-
-\begin_layout Subsection
-Axial Displacement Example
-\end_layout
-
-\begin_layout Standard
-The first example problem is extension of the mesh along the diagonal extending
- from the lower left to the upper right of the square mesh.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-axialdisp.cfg
-\family default
-.
- These settings are:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies an implicit formulation for the problem
- and specifies the array of boundary conditions.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.bc Defines which degrees of freedom are being constraine
-d (x and y), gives the label (defined in
-\family typewriter
-twotri3.mesh
-\family default
-) defining the points desired, assigns a label to the boundary condition
- set, and gives the name of the spatial database with the values for the
- Dirichlet boundary condition (
-\family typewriter
-axialdisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.output.writer Gives the base filename for
- VTK output
-\begin_inset Newline newline
-\end_inset
-
-(
-\family typewriter
-axialdisp.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.material.output Gives the base filename for
- state variable output files (
-\family typewriter
-axialdisp-statevars.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-The values for the Dirichlet boundary condition are given in the file
-\family typewriter
-axialdisp.spatialdb
-\family default
-, as specified in
-\family typewriter
-axialdisp.cfg
-\family default
-.
- The format of all spatial database files is similar.
- In this case, the desired displacement values are given at two points (lower
- left and upper right).
- Since data are being specified at points (rather than being uniform over
- the mesh, for example), the data dimension is one.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twotri3.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-axialdisp.cfg
-\family default
-,
-\family typewriter
-axialdisp.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith axialdisp.cfg
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, three files will be produced.
- The first file is named
-\family typewriter
-axialdisp_t0000000.vtk
-\family default
-.
- The
-\family typewriter
-t0000000
-\family default
- indicates that the output is for the first (and only) time step, corresponding
- to an elastic solution.
- This file contains mesh information as well as displacement values at the
- mesh vertices.
- The second file is named
-\family typewriter
-axialdisp-statevars_t0000000.vtk
-\family default
-.
- This file contains the state variables for each cell.
- The default fields are the total strain and stress fields.
- Since the cells are linear triangles, there is a single quadrature point
- for each cell and thus a single set of stress and strain values for each
- cell.
- The final file (
-\family typewriter
-axialdisp-statevars_info.vtk
-\family default
-) gives the material properties used for the problem.
- Since we have not specified which properties to write, the default properties
- (
-\family typewriter
-mu
-\family default
-,
-\family typewriter
-lambda
-\family default
-,
-\family typewriter
-density
-\family default
-) are written.
- All of the
-\family typewriter
-.vtk
-\family default
- files may be used with a number of visualization packages.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:twotri3-axial"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/axialdisp.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the axial displacement example
- using a mesh composed of two linear triangular cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotri3-axial"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Shear Displacement Example
-\end_layout
-
-\begin_layout Standard
-The next example problem is shearing of the mesh in the y direction using
- displacements applied along the positive and negative x boundaries.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-sheardisp.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (x and y), giving the label (
-\family typewriter
-x_neg
-\family default
-, defined in
-\family typewriter
-twotri3.mesh
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database with the values for the
- Dirichlet boundary condition (
-\family typewriter
-sheardisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (y only), giving the label (
-\family typewriter
-x_
-\family default
-pos, defined in
-\family typewriter
-twotri3.mesh
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database with the values for the
- Dirichlet boundary condition (
-\family typewriter
-sheardisp.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twotri3.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-sheardisp.cfg
-\family default
-,
-\family typewriter
-sheardisp.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith sheardisp.cfg
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, three files will be produced as in the previous
- example.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:twotri-shear"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/sheardisp.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the shear displacement example
- using a mesh composed of two linear triangular cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotri-shear"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Kinematic Fault Slip Example
-\end_layout
-
-\begin_layout Standard
-The next example problem is left-lateral fault slip applied between the
- two triangular cells using kinematic cohesive cells.
- The lower left and upper right boundaries are held fixed in the x and y
- directions.
- Parameter settings that augment those in
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file
-\family typewriter
-dislocation.cfg
-\family default
-.
- The solution corresponds to rigid body rotation of each triangular cell.
- As a result, the tractions on the fault are zero.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.journal.info Turns on journaling for 1D quadrature (used for 2D
- faults) and for cohesive kinematic faults.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.bc Defines which degrees of freedom are being constraine
-d (x and y), gives the label (defined in
-\family typewriter
-twotri3.mesh
-\family default
-) defining the points desired, and assigns a label to the boundary condition
- set.
- In this case, rather than specifying a spatial database file with the values
- for the Dirichlet boundary condition.
- The default database (ZeroDispDB) for Dirichlet boundary conditions is
- used, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces Gives the label (defined in
-\family typewriter
-twotri3.mesh
-\family default
-) defining the points on the fault, provides quadrature information, and
- then gives database names for material properties (needed for conditioning),
- fault slip, peak fault slip rate, and fault slip time.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces.fault.output.writer Gives the base filename
- for cohesive cell output files (
-\family typewriter
-dislocation-fault.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Standard
-Rather than specifying the displacement boundary conditions in a spatial
- database file, we use the default behavior for Dirichlet boundary conditions,
- which is a uniform, constant displacement of zero.
-\end_layout
-
-\begin_layout Standard
-The fault example requires three additional database files that were not
- needed for the simple displacement examples.
- The first file (
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-) specifies 0.01 m of left-lateral fault slip for the entire fault.
- The data dimension is zero since the same data are applied to all points
- in the set.
- The default slip time function is a step-function, so we also must provide
- the time at which slip begins.
- The elastic solution is associated with advancing from
-\begin_inset Formula $t=-dt$
-\end_inset
-
- to
-\begin_inset Formula $t=0$
-\end_inset
-
-, so we set the slip initiation time for the step-function to 0 in
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-twotri3.mesh
-\family default
-,
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-matprops.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-\size small
-dislocation.cfg
-\family default
-,
-\family typewriter
-dislocation_slip.spatialdb
-\family default
-,
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith dislocation.cfg
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, five files are produced.
- In addition to the files produced in the previous two examples, this example
- produces two files associated with the fault interface.
- The file
-\family typewriter
-dislocation-fault_t0000000.vtk
-\family default
- gives the fault slip for each vertex on the fault along with the computed
- traction change for the cohesive cell.
- The file
-\family typewriter
-dislocation-fault_info.vtk
-\family default
- provides information such as the normal direction, final slip, and slip
- time for each vertex on the fault.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:twotri-disloc"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/dislocation.jpg
- lyxscale 50
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the kinematic fault example
- using a mesh composed of two linear triangular cells.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:twotri-disloc"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding latin1
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 1in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Section
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-Two-triangle"
+
+\end_inset
+
+Tutorial Using Two Triangles
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Quasi-static solution
+\end_layout
+
+\begin_layout Itemize
+Mesh ASCII format
+\end_layout
+
+\begin_layout Itemize
+Dirichlet boundary conditions
+\end_layout
+
+\begin_layout Itemize
+Kinematic fault interface conditions
+\end_layout
+
+\begin_layout Itemize
+Plane strain linearly elastic material
+\end_layout
+
+\begin_layout Itemize
+VTK output
+\end_layout
+
+\begin_layout Itemize
+Linear triangular cells
+\end_layout
+
+\begin_layout Itemize
+SimpleDB spatial database
+\end_layout
+
+\begin_layout Itemize
+ZeroDispDB spatial database
+\end_layout
+
+\begin_layout Standard
+All of the files necessary to run the examples are contained in the directory
+
+\family typewriter
+examples/twocells/twotri3.
+\end_layout
+
+\begin_layout Subsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This tutorial is the simplest 2D example of a quasi-static finite element
+ problem (a simpler problem would consist of a 1D bar).
+ It is a mesh composed of two linear triangles subject to displacement boundary
+ conditions, assuming plane-strain linear elastic behavior.
+ Due to the simple geometry of the problem, the mesh may be constructed
+ by hand, using PyLith mesh ASCII format.
+ In this tutorial, we will walk through the steps necessary to construct,
+ run, and view three problems that use the same mesh.
+ In addition to this manual, each of the files for the example problem includes
+ extensive comments.
+\end_layout
+
+\begin_layout Subsection
+Mesh Description
+\end_layout
+
+\begin_layout Standard
+The mesh consists of two triangles forming a square with edge lengths of
+ one unit (Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:twotri3-mesh"
+
+\end_inset
+
+).
+ The mesh geometry and topology are described in the file
+\family typewriter
+twotri3.mesh
+\family default
+, which is in PyLith mesh ASCII format.
+ This file format is described in Appendix
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "cha:File-Formats"
+
+\end_inset
+
+.
+ This file describes the dimensionality of the problem (1D, 2D, or 3D),
+ the coordinates of the vertices (nodes), the vertices composing each cell
+ (element), the material ID to be associated with each cell, and groups
+ of vertices that may be used to define faults or surfaces to which boundary
+ conditions may be applied.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/twotri3-mesh.eps
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Mesh composed of two linear triangular cells used in the example problems.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotri3-mesh"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Additional Common Information
+\end_layout
+
+\begin_layout Standard
+In addition to the mesh, the three example problems share additional information.
+ For problems of this type, it is generally useful to create a file named
+
+\family typewriter
+pylithapp.cfg
+\family default
+ in the working directory, since this file is read automatically every time
+ PyLith is run.
+ Settings specific to a particular problem may be placed in other
+\family typewriter
+.cfg
+\family default
+ files, as described later, and then those files are placed on the command
+ line.
+ The settings contained in
+\family typewriter
+pylithapp.cfg
+\family default
+ for this problem consist of:
+\end_layout
+
+\begin_layout Description
+pylithapp.journal.info Settings that control the verbosity of the output for
+ the different components.
+\end_layout
+
+\begin_layout Description
+pylithapp.mesh_generator Settings that control mesh importing, such as the
+ importer type, the filename, and the spatial dimension of the mesh.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Settings that control the problem, such as the total
+ time, time step size, and spatial dimension.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials Settings that control the material type,
+ specify which material IDs are to be associated with a particular material
+ type, and give the name of the spatial database containing the physical
+ properties for the material.
+ The quadrature information is also given.
+\end_layout
+
+\begin_layout Description
+pylithapp.petsc PETSc settings to use for the problem, such as the preconditioner
+ type.
+\end_layout
+
+\begin_layout Standard
+All of the problems in this directory use the same material database, as
+ specified under
+\end_layout
+
+\begin_layout LyX-Code
+
+\family typewriter
+pylithapp.timedependent.materials
+\family default
+
+\end_layout
+
+\begin_layout Standard
+in
+\family typewriter
+pylithapp.cfg
+\family default
+.
+ This information is contained in the file
+\family typewriter
+matprops.spatialdb
+\family default
+.
+ Although the material model is specified in
+\family typewriter
+pylithapp.cfg
+\family default
+, the values for the physical properties of the material are given in
+\family typewriter
+matprops.spatialdb
+\family default
+.
+ For this example, values describing elastic plane strain material properties
+ are given at a single point, resulting in uniform material properties.
+\end_layout
+
+\begin_layout Subsection
+Axial Displacement Example
+\end_layout
+
+\begin_layout Standard
+The first example problem is extension of the mesh along the diagonal extending
+ from the lower left to the upper right of the square mesh.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+axialdisp.cfg
+\family default
+.
+ These settings are:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent Specifies an implicit formulation for the problem
+ and specifies the array of boundary conditions.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.bc Defines which degrees of freedom are being constraine
+d (x and y), gives the label (defined in
+\family typewriter
+twotri3.mesh
+\family default
+) defining the points desired, assigns a label to the boundary condition
+ set, and gives the name of the spatial database with the values for the
+ Dirichlet boundary condition (
+\family typewriter
+axialdisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.problem.formulation.output.output.writer Gives the base filename for
+ VTK output
+\begin_inset Newline newline
+\end_inset
+
+(
+\family typewriter
+axialdisp.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.materials.material.output Gives the base filename for
+ state variable output files (
+\family typewriter
+axialdisp-statevars.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+The values for the Dirichlet boundary condition are given in the file
+\family typewriter
+axialdisp.spatialdb
+\family default
+, as specified in
+\family typewriter
+axialdisp.cfg
+\family default
+.
+ The format of all spatial database files is similar.
+ In this case, the desired displacement values are given at two points (lower
+ left and upper right).
+ Since data are being specified at points (rather than being uniform over
+ the mesh, for example), the data dimension is one.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twotri3.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+axialdisp.cfg
+\family default
+,
+\family typewriter
+axialdisp.spatialdb
+\family default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith axialdisp.cfg
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, three files will be produced.
+ The first file is named
+\family typewriter
+axialdisp_t0000000.vtk
+\family default
+.
+ The
+\family typewriter
+t0000000
+\family default
+ indicates that the output is for the first (and only) time step, corresponding
+ to an elastic solution.
+ This file contains mesh information as well as displacement values at the
+ mesh vertices.
+ The second file is named
+\family typewriter
+axialdisp-statevars_t0000000.vtk
+\family default
+.
+ This file contains the state variables for each cell.
+ The default fields are the total strain and stress fields.
+ Since the cells are linear triangles, there is a single quadrature point
+ for each cell and thus a single set of stress and strain values for each
+ cell.
+ The final file (
+\family typewriter
+axialdisp-statevars_info.vtk
+\family default
+) gives the material properties used for the problem.
+ Since we have not specified which properties to write, the default properties
+ (
+\family typewriter
+mu
+\family default
+,
+\family typewriter
+lambda
+\family default
+,
+\family typewriter
+density
+\family default
+) are written.
+ All of the
+\family typewriter
+.vtk
+\family default
+ files may be used with a number of visualization packages.
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:twotri3-axial"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/axialdisp.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the axial displacement example
+ using a mesh composed of two linear triangular cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotri3-axial"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Shear Displacement Example
+\end_layout
+
+\begin_layout Standard
+The next example problem is shearing of the mesh in the y direction using
+ displacements applied along the positive and negative x boundaries.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+sheardisp.cfg
+\family default
+.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (x and y), giving the label (
+\family typewriter
+x_neg
+\family default
+, defined in
+\family typewriter
+twotri3.mesh
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database with the values for the
+ Dirichlet boundary condition (
+\family typewriter
+sheardisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
+ left side of the mesh, defining which degrees of freedom are being constrained
+ (y only), giving the label (
+\family typewriter
+x_
+\family default
+pos, defined in
+\family typewriter
+twotri3.mesh
+\family default
+) defining the points desired, assigning a label to the boundary condition
+ set, and giving the name of the spatial database with the values for the
+ Dirichlet boundary condition (
+\family typewriter
+sheardisp.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twotri3.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+sheardisp.cfg
+\family default
+,
+\family typewriter
+sheardisp.spatialdb
+\family default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith sheardisp.cfg
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, three files will be produced as in the previous
+ example.
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:twotri-shear"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/sheardisp.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the shear displacement example
+ using a mesh composed of two linear triangular cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotri-shear"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Kinematic Fault Slip Example
+\end_layout
+
+\begin_layout Standard
+The next example problem is left-lateral fault slip applied between the
+ two triangular cells using kinematic cohesive cells.
+ The lower left and upper right boundaries are held fixed in the x and y
+ directions.
+ Parameter settings that augment those in
+\family typewriter
+pylithapp.cfg
+\family default
+ are contained in the file
+\family typewriter
+dislocation.cfg
+\family default
+.
+ The solution corresponds to rigid body rotation of each triangular cell.
+ As a result, the tractions on the fault are zero.
+ These settings include:
+\end_layout
+
+\begin_layout Description
+pylithapp.journal.info Turns on journaling for 1D quadrature (used for 2D
+ faults) and for cohesive kinematic faults.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.bc.bc Defines which degrees of freedom are being constraine
+d (x and y), gives the label (defined in
+\family typewriter
+twotri3.mesh
+\family default
+) defining the points desired, and assigns a label to the boundary condition
+ set.
+ In this case, rather than specifying a spatial database file with the values
+ for the Dirichlet boundary condition, the default database (ZeroDispDB)
+ for Dirichlet boundary conditions is used, which sets the displacements
+ to zero.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces Gives the label (defined in
+\family typewriter
+twotri3.mesh
+\family default
+) defining the points on the fault, provides quadrature information, and
+ then gives database names for material properties (needed for conditioning),
+ fault slip, peak fault slip rate, and fault slip time.
+\end_layout
+
+\begin_layout Description
+pylithapp.timedependent.interfaces.fault.output.writer Gives the base filename
+ for cohesive cell output files (
+\family typewriter
+dislocation-fault.vtk
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+Rather than specifying the displacement boundary conditions in a spatial
+ database file, we use the default behavior for Dirichlet boundary conditions,
+ which is a uniform, constant displacement of zero.
+\end_layout
+
+\begin_layout Standard
+The fault example requires three additional database files that were not
+ needed for the simple displacement examples.
+ The first file (
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+) specifies 0.01 m of left-lateral fault slip for the entire fault.
+ The data dimension is zero since the same data are applied to all points
+ in the set.
+ The default slip time function is a step-function, so we also must provide
+ the time at which slip begins.
+ The elastic solution is associated with advancing from
+\begin_inset Formula $t=-dt$
+\end_inset
+
+ to
+\begin_inset Formula $t=0$
+\end_inset
+
+, so we set the slip initiation time for the step-function to 0 in
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+The files containing common information (
+\family typewriter
+twotri3.mesh
+\family default
+,
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+matprops.spatialdb
+\family default
+) along with the problem-specific files (
+\family typewriter
+\size small
+dislocation.cfg
+\family default
+,
+\family typewriter
+dislocation_slip.spatialdb
+\family default
+,
+\family typewriter
+dislocation_sliptime.spatialdb
+\family default
+\size default
+) provide a complete description of the problem, and we can then run this
+ example by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith dislocation.cfg
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, five files are produced.
+ In addition to the files produced in the previous two examples, this example
+ produces two files associated with the fault interface.
+ The file
+\family typewriter
+dislocation-fault_t0000000.vtk
+\family default
+ gives the fault slip for each vertex on the fault along with the computed
+ traction change for the cohesive cell.
+ The file
+\family typewriter
+dislocation-fault_info.vtk
+\family default
+ provides information such as the normal direction, final slip, and slip
+ time for each vertex on the fault.
+ If the problem ran correctly, you should be able to generate a figure such
+ as Figure
+\begin_inset CommandInset ref
+LatexCommand vref
+reference "fig:twotri-disloc"
+
+\end_inset
+
+, which was generated using ParaView.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/dislocation.jpg
+ lyxscale 50
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Color contours and vectors of displacement for the kinematic fault example
+ using a mesh composed of two linear triangular cells.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:twotri-disloc"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
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