[cig-commits] r22096 - in short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott: . figs
brad at geodynamics.org
brad at geodynamics.org
Fri May 17 13:32:33 PDT 2013
Author: brad
Date: 2013-05-17 13:32:33 -0700 (Fri, 17 May 2013)
New Revision: 22096
Added:
short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/model_descript.pdf
short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/soln_profiles.pdf
Removed:
short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/geometry.png
short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/model-3d.png
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short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/model_3d.eps
short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/model_descript.eps
short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/soln_profiles.eps
Modified:
short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/savageprescott.lyx
Log:
Cleaned up benchmark figures.
Deleted: short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/geometry.png
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--- short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/model-3d.svg 2013-05-17 20:25:28 UTC (rev 22095)
+++ short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/model-3d.svg 2013-05-17 20:32:33 UTC (rev 22096)
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===================================================================
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Property changes on: short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/figs/soln_profiles.pdf
___________________________________________________________________
Added: svn:mime-type
+ application/octet-stream
Modified: short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/savageprescott.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/savageprescott.lyx 2013-05-17 20:25:28 UTC (rev 22095)
+++ short/3D/PyLith/trunk/doc/userguide/benchmarks/savageprescott/savageprescott.lyx 2013-05-17 20:32:33 UTC (rev 22096)
@@ -1,530 +1,530 @@
-#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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-\use_bibtopic false
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-\index Index
-\shortcut idx
-\color #008000
-\end_index
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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:benchmarks:savageprescott"
-
-\end_inset
-
-Savage and Prescott Benchmark
-\end_layout
-
-\begin_layout Standard
-This benchmark problem computes the viscoelastic (Maxwell) relaxation of
- stresses from repeated infinite, strike-slip earthquakes in 3D without
- gravity.
- The files needed to run the benchmark may be found at
-\begin_inset Flex URL
-status collapsed
-
-\begin_layout Plain Layout
-
-geodynamics.org/svn/cig/short/2.5D/benchmarks/savageprescott
-\end_layout
-
-\end_inset
-
-.
- An analytical solution to this problem is described by Savage and Prescott
-
-\begin_inset CommandInset citation
-LatexCommand cite
-key "Savage:Prescott:1978"
-
-\end_inset
-
-, which provides a simple way to check our numerical solution.
- A python utility code is provided in the utils directory to compute the
- analytical solution.
- Although this problem is actually 2.5D (infinite along-strike), we solve
- it using a 3D finite element model.
-\end_layout
-
-\begin_layout Subsection
-Problem Description
-\end_layout
-
-\begin_layout Standard
-Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:benchmark:savageprescott:geometry"
-
-\end_inset
-
- shows the geometry of the problem, as described by
-\begin_inset CommandInset citation
-LatexCommand cite
-key "Savage:Prescott:1978"
-
-\end_inset
-
-.
- The analytical solution describes the surface deformation due to repeated
- earthquakes on an infinite strike-slip fault embedded in an elastic layer
- overlying a Maxwell viscoelastic half-space.
- The upper portion of the fault (red in the figure) is locked between earthquake
-s, while the lower portion (blue in the figure) creeps at plate velocity.
- At regular recurrence intervals, the upper portion of the fault abruptly
- slips by an amount equal to the plate velocity multiplied by the recurrence
- interval, thus 'catching up' with the lower part of the fault.
-\end_layout
-
-\begin_layout Standard
-There are some differences between the analytical solution and our numerical
- representation.
- First, the analytical solution represents the earthquake cycle as the superposi
-tion of uniform fault creep and an elementary earthquake cycle.
- Uniform fault creep is simply the uniform movement of the two plates past
- each other at plate velocity.
- For the elementary earthquake cycle, no slip occurs below the locked portion
- of the fault (blue portion in the figure).
- On the locked (red) portion of the fault, backslip equal to plate velocity
- occurs until the earthquake recurrence interval, at which point abrupt
- forward slip occurs.
- In the finite element solution, we perform the simulation as described
- in the figure.
- Velocity boundary conditions are applied at the extreme edges of the model
- to simulate block motion, steady creep is applied along the blue portion
- of the fault, and regular earthquakes are applied along the upper portion
- of the fault.
- It takes several earthquake cycles for the velocity boundary conditions
- to approximate the steady flow due to steady block motion, so we would
- not expect the analytical and numerical solutions to match until several
- earthquakes have occurred.
- Another difference lies in the dimensions of the domain.
- The analytical solution assumes an infinite strike-slip fault in an elastic
- layer overlying a Maxwell viscoelastic half-space.
- In our finite element model we are restricted to finite dimensions.
- We therefore extend the outer boundaries far enough from the region of
- interest to approximate boundaries at infinity.
-\end_layout
-
-\begin_layout Standard
-Due to the difficulties in representing solutions in an infinite domain,
- there are several meshes that have been tested for this problem.
- The simplest meshes have uniform resolution (all cells have equal dimensions);
- however, such meshes typically do not provide accurate solutions since
- the resolution is too coarse in the region of interest.
- For that reason, we also tested meshes where the mesh resolution decreases
- away from the center.
- In the problem description that follows, we will focus on the hexahedral
- mesh with finer discretization near the fault
-\begin_inset Newline linebreak
-\end_inset
-
-(
-\family typewriter
-meshes/hex8_6.7km.exo.gz
-\family default
-), which provides a good match with the analytical solution.
- It will first be necessary to gunzip this mesh so that it may be used by
- PyLith.
-\end_layout
-
-\begin_layout Description
-Domain The domain for this mesh spans the region
-\begin_inset Formula
-\begin{gather*}
--1000\leq x\leq1000\ km,\\
--500\leq y\leq500\ km,\\
--400\ km\leq z\leq0.
-\end{gather*}
-
-\end_inset
-
-The top (elastic) layer occupies the region
-\begin_inset Formula $-40\ km\ \leq z\leq0$
-\end_inset
-
- and the bottom (viscoelastic) layer occupies the region
-\begin_inset Formula $-400\ km\ \leq z\leq-40\ km$
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Description
-Material
-\begin_inset space ~
-\end_inset
-
-properties The material is a Poisson solid with a shear modulus (
-\begin_inset Formula $\mu$
-\end_inset
-
-) of 30 GPa.
- The domain is modeled using an elastic isotropic material for the top layer
- and a Maxwell viscoelastic material for the bottom layer.
- The bottom layer has a viscosity (
-\begin_inset Formula $\eta$
-\end_inset
-
-) of 2.36682e+19 Pa-s, yielding a relaxation time (
-\begin_inset Formula $2\eta/\mu$
-\end_inset
-
-) of 50 years.
-\end_layout
-
-\begin_layout Description
-Fault The fault is a vertical, left-lateral strike-slip fault.
- The strike is parallel to the y-direction at the center of the model:
-\begin_inset Formula
-\begin{gather*}
-x=0\ km,\\
--500\leq y\leq500\ km,\\
--40\ km\leq z\leq0.
-\end{gather*}
-
-\end_inset
-
-The locked portion of the fault (red section in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:benchmark:savageprescott:geometry"
-
-\end_inset
-
-) extends from
-\begin_inset Formula $-20\: km\leq z\leq0$
-\end_inset
-
-, while the creeping section (blue) extends from
-\begin_inset Formula $-40\: km\leq z\leq0$
-\end_inset
-
-.
- Along the line where the two sections coincide (
-\begin_inset Formula $z=-20\: km$
-\end_inset
-
-), half of the coseismic displacement and half of the steady creep is applied
- (see
-\family typewriter
-finalslip.spatialdb
-\family default
- and
-\family typewriter
-creeprate.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-Boundary
-\begin_inset space ~
-\end_inset
-
-conditions On the bottom boundary, vertical displacements are set to zero,
- while on the y-boundaries the x-displacements are set to zero.
- On the x-boundaries, the x-displacements are set to zero, while constant
- velocities of +/- 1 cm/yr are applied in the y-direction, giving a relative
- plate motion of 2 cm/year.
-\end_layout
-
-\begin_layout Description
-Discretization For the nonuniform hexahedral mesh, the resolution at the
- outer boundaries is 20 km.
- An inner region is then put through one level of refinement, so that near
- the center of the mesh the resolution is 6.7 km.
- All meshes were generated with CUBIT.
-\end_layout
-
-\begin_layout Description
-Basis
-\begin_inset space ~
-\end_inset
-
-functions We use trilinear hexahedral cells.
-\end_layout
-
-\begin_layout Description
-Solution We compute the surface displacements and compare these to the analytica
-l solution in Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:benchmark:savageprescott:solution"
-
-\end_inset
-
-.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
- filename figs/model_descript.eps
- scale 33
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Problem description for the Savage and Prescott strike-slip benchmark problem.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:benchmark:savageprescott:geometry"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Running the Benchmark
-\end_layout
-
-\begin_layout Standard
-After checking out the benchmark files from the CIG SVN repository, change
- to the
-\family typewriter
-meshes
-\family default
- directory.
- Decompress the gzipped files in the
-\family typewriter
-mesh
-\family default
- directory,
-\end_layout
-
-\begin_layout LyX-Code
-gunzip *.gz
-\end_layout
-
-\begin_layout Standard
-Alternatively, simply gunzip the mesh you want to use.
- There are a number of
-\family typewriter
-.cfg
-\family default
- files corresponding to the different meshes, as well as a
-\family typewriter
-pylithapp.cfg
-\family default
- file defining parameters common to all problems.
- Each problem uses four
-\family typewriter
-.cfg
-\family default
- files:
-\family typewriter
-pylithapp.cfg
-\family default
-,
-\family typewriter
-fieldsplit.cfg
-\family default
- (algrebraic multigrid preconditioner), a cell-specific file (e.g.,
-\family typewriter
-hex8.cfg
-\family default
-), and a resolution specific file (e.g., hex8_6.7km.cfg).
- You can then run the problem by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith hex8.cfg hex8_6.7km.cfg fieldsplit.cfg
-\end_layout
-
-\begin_layout Standard
-This will run the problem for 10 earthquake cycles of 200 years each, using
- a time-step size of 10 years, for a total simulation time of 2000 years.
- Ground surface output occurs every 10 years, while all other outputs occur
- every 50 years.
-\end_layout
-
-\begin_layout Standard
-Once the problem has run, results will be placed in the
-\family typewriter
-output
-\family default
- directory.
- These results may be viewed directly with a package such as ParaView; however,
- to compare results to the analytical solution, some postprocessing is required.
- First, generate the analytical results by running the
-\family typewriter
-calc_analytic.py
-\family default
- script.
- This will produce files with displacements and velocities (
-\family typewriter
-analytic_disp.txt
-\family default
- and
-\family typewriter
-analytic_vel.txt
-\family default
-) in the
-\family typewriter
-output
-\family default
- directory that are easy to use with a plotting package, such as matplotlib
- or Matlab.
-\end_layout
-
-\begin_layout Subsection
-Benchmark Results
-\end_layout
-
-\begin_layout Standard
-Figure
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:benchmark:savageprescott:solution"
-
-\end_inset
-
- shows the computed surface displacements for the 10th earthquake cycle
- compared with the analytical solution.
- The profile results were obtained as described above, and then all results
- (analytical and numerical) were referenced to the displacements immediately
- following the last earthquake.
- We find very good agreement between the analytical and numerical solutions,
- even for meshes with uniform refinement.
- We have not yet explored quantitative fits as a function of mesh resolution.
- For this benchmark, it is also important to consider the distance of the
- boundary from the region of interest.
- Also note that the agreement between analytical and numerical solutions
- is poor for early earthquake cycles, due to the differences in simulating
- the problem, as noted above.
-\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/soln_profiles.eps
- scale 66
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Displacement profiles perpendicular to the fault for a PyLith simulation
- with hex8 cells and the analytical solution for earthquake cycle 10.
-
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:benchmark:savageprescott:solution"
-
-\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:benchmarks:savageprescott"
+
+\end_inset
+
+Savage and Prescott Benchmark
+\end_layout
+
+\begin_layout Standard
+This benchmark problem computes the viscoelastic (Maxwell) relaxation of
+ stresses from repeated infinite, strike-slip earthquakes in 3D without
+ gravity.
+ The files needed to run the benchmark may be found at
+\begin_inset Flex URL
+status collapsed
+
+\begin_layout Plain Layout
+
+geodynamics.org/svn/cig/short/2.5D/benchmarks/savageprescott
+\end_layout
+
+\end_inset
+
+.
+ An analytical solution to this problem is described by Savage and Prescott
+
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Savage:Prescott:1978"
+
+\end_inset
+
+, which provides a simple way to check our numerical solution.
+ A python utility code is provided in the utils directory to compute the
+ analytical solution.
+ Although this problem is actually 2.5D (infinite along-strike), we solve
+ it using a 3D finite element model.
+\end_layout
+
+\begin_layout Subsection
+Problem Description
+\end_layout
+
+\begin_layout Standard
+Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:benchmark:savageprescott:geometry"
+
+\end_inset
+
+ shows the geometry of the problem, as described by
+\begin_inset CommandInset citation
+LatexCommand cite
+key "Savage:Prescott:1978"
+
+\end_inset
+
+.
+ The analytical solution describes the surface deformation due to repeated
+ earthquakes on an infinite strike-slip fault embedded in an elastic layer
+ overlying a Maxwell viscoelastic half-space.
+ The upper portion of the fault (red in the figure) is locked between earthquake
+s, while the lower portion (blue in the figure) creeps at plate velocity.
+ At regular recurrence intervals, the upper portion of the fault abruptly
+ slips by an amount equal to the plate velocity multiplied by the recurrence
+ interval, thus 'catching up' with the lower part of the fault.
+\end_layout
+
+\begin_layout Standard
+There are some differences between the analytical solution and our numerical
+ representation.
+ First, the analytical solution represents the earthquake cycle as the superposi
+tion of uniform fault creep and an elementary earthquake cycle.
+ Uniform fault creep is simply the uniform movement of the two plates past
+ each other at plate velocity.
+ For the elementary earthquake cycle, no slip occurs below the locked portion
+ of the fault (blue portion in the figure).
+ On the locked (red) portion of the fault, backslip equal to plate velocity
+ occurs until the earthquake recurrence interval, at which point abrupt
+ forward slip occurs.
+ In the finite element solution, we perform the simulation as described
+ in the figure.
+ Velocity boundary conditions are applied at the extreme edges of the model
+ to simulate block motion, steady creep is applied along the blue portion
+ of the fault, and regular earthquakes are applied along the upper portion
+ of the fault.
+ It takes several earthquake cycles for the velocity boundary conditions
+ to approximate the steady flow due to steady block motion, so we would
+ not expect the analytical and numerical solutions to match until several
+ earthquakes have occurred.
+ Another difference lies in the dimensions of the domain.
+ The analytical solution assumes an infinite strike-slip fault in an elastic
+ layer overlying a Maxwell viscoelastic half-space.
+ In our finite element model we are restricted to finite dimensions.
+ We therefore extend the outer boundaries far enough from the region of
+ interest to approximate boundaries at infinity.
+\end_layout
+
+\begin_layout Standard
+Due to the difficulties in representing solutions in an infinite domain,
+ there are several meshes that have been tested for this problem.
+ The simplest meshes have uniform resolution (all cells have equal dimensions);
+ however, such meshes typically do not provide accurate solutions since
+ the resolution is too coarse in the region of interest.
+ For that reason, we also tested meshes where the mesh resolution decreases
+ away from the center.
+ In the problem description that follows, we will focus on the hexahedral
+ mesh with finer discretization near the fault
+\begin_inset Newline linebreak
+\end_inset
+
+(
+\family typewriter
+meshes/hex8_6.7km.exo.gz
+\family default
+), which provides a good match with the analytical solution.
+ It will first be necessary to gunzip this mesh so that it may be used by
+ PyLith.
+\end_layout
+
+\begin_layout Description
+Domain The domain for this mesh spans the region
+\begin_inset Formula
+\begin{gather*}
+-1000\leq x\leq1000\ km,\\
+-500\leq y\leq500\ km,\\
+-400\ km\leq z\leq0.
+\end{gather*}
+
+\end_inset
+
+The top (elastic) layer occupies the region
+\begin_inset Formula $-40\ km\ \leq z\leq0$
+\end_inset
+
+ and the bottom (viscoelastic) layer occupies the region
+\begin_inset Formula $-400\ km\ \leq z\leq-40\ km$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Description
+Material
+\begin_inset space ~
+\end_inset
+
+properties The material is a Poisson solid with a shear modulus (
+\begin_inset Formula $\mu$
+\end_inset
+
+) of 30 GPa.
+ The domain is modeled using an elastic isotropic material for the top layer
+ and a Maxwell viscoelastic material for the bottom layer.
+ The bottom layer has a viscosity (
+\begin_inset Formula $\eta$
+\end_inset
+
+) of 2.36682e+19 Pa-s, yielding a relaxation time (
+\begin_inset Formula $2\eta/\mu$
+\end_inset
+
+) of 50 years.
+\end_layout
+
+\begin_layout Description
+Fault The fault is a vertical, left-lateral strike-slip fault.
+ The strike is parallel to the y-direction at the center of the model:
+\begin_inset Formula
+\begin{gather*}
+x=0\ km,\\
+-500\leq y\leq500\ km,\\
+-40\ km\leq z\leq0.
+\end{gather*}
+
+\end_inset
+
+The locked portion of the fault (red section in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:benchmark:savageprescott:geometry"
+
+\end_inset
+
+) extends from
+\begin_inset Formula $-20\: km\leq z\leq0$
+\end_inset
+
+, while the creeping section (blue) extends from
+\begin_inset Formula $-40\: km\leq z\leq0$
+\end_inset
+
+.
+ Along the line where the two sections coincide (
+\begin_inset Formula $z=-20\: km$
+\end_inset
+
+), half of the coseismic displacement and half of the steady creep is applied
+ (see
+\family typewriter
+finalslip.spatialdb
+\family default
+ and
+\family typewriter
+creeprate.spatialdb
+\family default
+).
+\end_layout
+
+\begin_layout Description
+Boundary
+\begin_inset space ~
+\end_inset
+
+conditions On the bottom boundary, vertical displacements are set to zero,
+ while on the y-boundaries the x-displacements are set to zero.
+ On the x-boundaries, the x-displacements are set to zero, while constant
+ velocities of +/- 1 cm/yr are applied in the y-direction, giving a relative
+ plate motion of 2 cm/year.
+\end_layout
+
+\begin_layout Description
+Discretization For the nonuniform hexahedral mesh, the resolution at the
+ outer boundaries is 20 km.
+ An inner region is then put through one level of refinement, so that near
+ the center of the mesh the resolution is 6.7 km.
+ All meshes were generated with CUBIT.
+\end_layout
+
+\begin_layout Description
+Basis
+\begin_inset space ~
+\end_inset
+
+functions We use trilinear hexahedral cells.
+\end_layout
+
+\begin_layout Description
+Solution We compute the surface displacements and compare these to the analytica
+l solution in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:benchmark:savageprescott:solution"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figs/model_descript.pdf
+ scale 33
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Problem description for the Savage and Prescott strike-slip benchmark problem.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:benchmark:savageprescott:geometry"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Running the Benchmark
+\end_layout
+
+\begin_layout Standard
+After checking out the benchmark files from the CIG SVN repository, change
+ to the
+\family typewriter
+meshes
+\family default
+ directory.
+ Decompress the gzipped files in the
+\family typewriter
+mesh
+\family default
+ directory,
+\end_layout
+
+\begin_layout LyX-Code
+gunzip *.gz
+\end_layout
+
+\begin_layout Standard
+Alternatively, simply gunzip the mesh you want to use.
+ There are a number of
+\family typewriter
+.cfg
+\family default
+ files corresponding to the different meshes, as well as a
+\family typewriter
+pylithapp.cfg
+\family default
+ file defining parameters common to all problems.
+ Each problem uses four
+\family typewriter
+.cfg
+\family default
+ files:
+\family typewriter
+pylithapp.cfg
+\family default
+,
+\family typewriter
+fieldsplit.cfg
+\family default
+ (algrebraic multigrid preconditioner), a cell-specific file (e.g.,
+\family typewriter
+hex8.cfg
+\family default
+), and a resolution specific file (e.g., hex8_6.7km.cfg).
+ You can then run the problem by typing
+\end_layout
+
+\begin_layout LyX-Code
+pylith hex8.cfg hex8_6.7km.cfg fieldsplit.cfg
+\end_layout
+
+\begin_layout Standard
+This will run the problem for 10 earthquake cycles of 200 years each, using
+ a time-step size of 10 years, for a total simulation time of 2000 years.
+ Ground surface output occurs every 10 years, while all other outputs occur
+ every 50 years.
+\end_layout
+
+\begin_layout Standard
+Once the problem has run, results will be placed in the
+\family typewriter
+output
+\family default
+ directory.
+ These results may be viewed directly with a package such as ParaView; however,
+ to compare results to the analytical solution, some postprocessing is required.
+ First, generate the analytical results by running the
+\family typewriter
+calc_analytic.py
+\family default
+ script.
+ This will produce files with displacements and velocities (
+\family typewriter
+analytic_disp.txt
+\family default
+ and
+\family typewriter
+analytic_vel.txt
+\family default
+) in the
+\family typewriter
+output
+\family default
+ directory that are easy to use with a plotting package, such as matplotlib
+ or Matlab.
+\end_layout
+
+\begin_layout Subsection
+Benchmark Results
+\end_layout
+
+\begin_layout Standard
+Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:benchmark:savageprescott:solution"
+
+\end_inset
+
+ shows the computed surface displacements for the 10th earthquake cycle
+ compared with the analytical solution.
+ The profile results were obtained as described above, and then all results
+ (analytical and numerical) were referenced to the displacements immediately
+ following the last earthquake.
+ We find very good agreement between the analytical and numerical solutions,
+ even for meshes with uniform refinement.
+ We have not yet explored quantitative fits as a function of mesh resolution.
+ For this benchmark, it is also important to consider the distance of the
+ boundary from the region of interest.
+ Also note that the agreement between analytical and numerical solutions
+ is poor for early earthquake cycles, due to the differences in simulating
+ the problem, as noted above.
+\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/soln_profiles.pdf
+ scale 66
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Displacement profiles perpendicular to the fault for a PyLith simulation
+ with hex8 cells and the analytical solution for earthquake cycle 10.
+
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:benchmark:savageprescott:solution"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
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