[cig-commits] r15239 - short/3D/PyLith/trunk/doc/userguide/boundaryconditions

[brad at geodynamics.org]

Author: brad
Date: 2009-06-14 10:27:44 -0700 (Sun, 14 Jun 2009)
New Revision: 15239

Modified:
   short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx
Log:
Updated boundary conditions.

Modified: short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx	2009-06-14 16:37:24 UTC (rev 15238)
+++ short/3D/PyLith/trunk/doc/userguide/boundaryconditions/boundaryconditions.lyx	2009-06-14 17:27:44 UTC (rev 15239)
@@ -182,44 +182,99 @@
 \end_layout
 
 \begin_layout Section
-Dirichlet Boundary Conditions
+Time-Dependent Boundary Conditions
 \end_layout
 
 \begin_layout Standard
-Dirichlet boundary conditions in PyLith prescribe the displacement of a
- subset of the vertices of the finite-element mesh,
+Several boundary conditions use a common formulation for the spatial and
+ temporal variation of the boundary condition parameters,
 \begin_inset Formula \[
-u(t)=u_{o}+(t-t_{ref})\dot{u}_{o},\]
+f(\vec{x})=f_{0}(\vec{x})+\dot{f}_{0}(\vec{x})(t-t_{0}(\vec{x}))+f_{1}(\vec{x})a(t-t_{1}(\vec{x})),\]
 
 \end_inset
 
 where 
-\begin_inset Formula $u_{o}$
+\begin_inset Formula $f(\vec{x})$
 \end_inset
 
- is the prescribed displacement at time 
-\begin_inset Formula $t_{ref}$
+ may be a scalar or vector parameter, 
+\begin_inset Formula $f_{0}(\vec{x})$
 \end_inset
 
- and 
-\begin_inset Formula $\dot{u}_{o}$
+ is a constant value, 
+\begin_inset Formula $\dot{f}_{0}(\vec{x})$
 \end_inset
 
- is the rate of change of displacement (velocity).
+ is a constant rate of change in the value, 
+\begin_inset Formula $t_{0}(\vec{x})$
+\end_inset
+
+ is the onset time for the constant rate of change, 
+\begin_inset Formula $f_{1}(\vec{x})$
+\end_inset
+
+ is the amplitude for the temporal modulation, 
+\begin_inset Formula $a(t)$
+\end_inset
+
+ is the variation in amplitude with time, 
+\begin_inset Formula $t_{1}(\vec{x})$
+\end_inset
+
+ is the onset time for the temporal modulation, and 
+\begin_inset Formula $\vec{x}$
+\end_inset
+
+ is the position of a location in space.
+ This common formulation permits easy specification of a scalar or vector
+ with a constant value, constant rate of change of a value, and/or modulation
+ of a value in time.
+ One can specify just the initial value, just the rate of change of the
+ value (along with the corresponding onset time), or just the modulation
+ in amplitude (along withthe corresponding temporal variation and onset
+ time), or any combination of the three.
+ The facilities associated with this formulation are:
+\end_layout
+
+\begin_layout Description
+db_initial Spatial database specifying the spatial variation in the initial
+ value (default is none).
+\end_layout
+
+\begin_layout Description
+db_rate Spatial database specifying rate of change in the value (default
+ is none).
+\end_layout
+
+\begin_layout Description
+db_change Spatial database specifying the amplitude of the temporal modulation
+ (default is none).
+\end_layout
+
+\begin_layout Description
+th_change Time history database specifying the temporal change in amplitude
+ (default is none).
+\end_layout
+
+\begin_layout Subsection
+Dirichlet Boundary Conditions
+\end_layout
+
+\begin_layout Standard
+Dirichlet boundary conditions in PyLith prescribe the displacement of a
+ subset of the vertices of the finite-element mesh.
  While Dirichlet boundary conditions can be applied to any vertex, usually
  they are applied to vertices on the lateral and bottom boundaries of the
  domain.
- Time dependent displacements with a uniform velocity are now supported.
- The default velocity is zero (fixed displacement).
- There are two types of Dirichlet boundary conditions, DirichletPoints and
- DirichletBoundary.
+ There are two types of Dirichlet boundary conditions, DirichletBC and Dirichlet
+Boundary.
  Both provide identical constraints on the solution, but DirichletBoundary
  is limited to vertices of a simply-connected surface, which allows diagnostic
  output of the prescribed displacements.
- DirichletPoints can be applied to a set of unconnected vertices.
+ DirichletBC can be applied to a set of unconnected vertices.
 \end_layout
 
-\begin_layout Subsection
+\begin_layout Subsubsection
 Dirichlet Boundary Condition Parameters
 \end_layout
 
@@ -233,28 +288,10 @@
 \end_layout
 
 \begin_layout Description
-db Spatial database specifying the spatial variation in the displacement
- field (default is FixedDOFDB).
-\end_layout
-
-\begin_layout Description
-rate_db Spatial database specifying rate of change in the displacement field
- (default is FixedDOFDB).
-\end_layout
-
-\begin_layout Description
-fixed_dof Array of degrees of freedom to be fixed (first degree of freedom
+bc_dof Array of degrees of freedom to be fixed (first degree of freedom
  is 0).
 \end_layout
 
-\begin_layout Description
-reference_t Reference time for rate of change of values (
-\begin_inset Formula $t_{ref},$
-\end_inset
-
- default value is 0.0 s).
-\end_layout
-
 \begin_layout Standard
 DirichletBoundary contains an additional component:
 \end_layout
@@ -316,51 +353,40 @@
 \end_layout
 
 \begin_layout LyX-Code
-fixed_dof = [2] ; fixed displacement in z direction
+bc_dof = [2] ; fixed displacement in z direction
 \end_layout
 
 \begin_layout LyX-Code
-reference_t = 3.0*yr
+db_initial = spatialdata.spatialdb.SimpleDB
 \end_layout
 
 \begin_layout LyX-Code
-db = spatialdata.spatialdb.SimpleDB ; change db to SimpleDB
+db_initial.iohandler.filename = disp_A.spatialdb
 \end_layout
 
 \begin_layout LyX-Code
-db.iohandler.filename = disp_A.spatialdb
+db_initial.query_type = nearest ; change query type to nearest point algorithm
 \end_layout
 
 \begin_layout LyX-Code
-db.query_type = nearest ; change query type to nearest point algorithm
+db_rate = spatialdata.spatialdb.UniformDB
 \end_layout
 
 \begin_layout LyX-Code
-rate_db.values = [
-\begin_inset Quotes eld
-\end_inset
-
-dof-2
-\begin_inset Quotes erd
-\end_inset
-
-]
+db_rate.values = [displacement-rate-z]
 \end_layout
 
 \begin_layout LyX-Code
-rate_db.data = [1.0e-06] ; velocity is 1.0e-06 m/s
+db_rate.data = [1.0e-06*m/s] ; velocity is 1.0e-06 m/s
 \end_layout
 
 \begin_layout Standard
 We have created an array with one boundary condition, mybc.
  The group of vertices associated with the boundary condition is group A.
- For the database associated with the displacement at the reference time
- (3.0 yr), we change the spatial database from the default FixedDOFDB to
- a SimpleDB.
+ For the database associated with the constant displacement, we use a SimpleDB.
  We set the filename and query type for the database.
- For the rate of change of values, we use the FixedDOFDB (which is a special
- case of the UniformDB) and specify the velocity in the z-direction to be
- 1.0e-06 m/s.
+ For the rate of change of values, we use a UniformDB and specify the velocity
+ in the z-direction to be 1.0e-06 m/s.
  See Section 
 \begin_inset CommandInset ref
 LatexCommand ref
@@ -399,7 +425,7 @@
 
 
 \begin_inset Tabular
-<lyxtabular version="3" rows="3" columns="3">
+<lyxtabular version="3" rows="6" columns="3">
 <features>
 <column alignment="center" valignment="top" width="0">
 <column alignment="center" valignment="top" width="0">
@@ -457,7 +483,7 @@
 \begin_layout Plain Layout
 
 \family typewriter
-initial
+initial-value
 \end_layout
 
 \end_inset
@@ -466,14 +492,14 @@
 \begin_inset Text
 
 \begin_layout Plain Layout
-Displacement vector at reference time in global coordinate system
+Initial displacement field in global coordinate system
 \end_layout
 
 \end_inset
 </cell>
 </row>
 <row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
@@ -482,13 +508,106 @@
 
 \end_inset
 </cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+rate-of-change
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Rate of change of displacement field in global coordinate system
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" 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" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+rate-start-time
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Onset time in seconds for rate of change in displacement field
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" 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" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+change-in-value
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Amplitude of change in displacement field in global coordinate system
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" 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" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
 
 \family typewriter
-rate_of_change
+change-start-time
 \end_layout
 
 \end_inset
@@ -497,7 +616,7 @@
 \begin_inset Text
 
 \begin_layout Plain Layout
-Rate of change of displacement field in global coordinate system
+Onset time in seconds for the amplitude change in the displacement field
 \end_layout
 
 \end_inset
@@ -515,7 +634,7 @@
 
 \end_layout
 
-\begin_layout Subsection
+\begin_layout Subsubsection
 Dirichlet Boundary Condition Spatial Database Files
 \end_layout
 
@@ -526,12 +645,12 @@
  freedom than those specified in the Dirichlet boundary condition settings
  using the 
 \family typewriter
-fixed_dof
+bc_dof
 \family default
  setting.
  Only those listed in 
 \family typewriter
-fixed_dof
+bc_dof
 \family default
  will be used.
  This permits using the same spatial database file for multiple Dirichlet
@@ -553,7 +672,7 @@
 \begin_inset Caption
 
 \begin_layout Plain Layout
-Values in spatial database used for Dirichlet boundary conditions.
+Values in the spatial databases used for Dirichlet boundary conditions.
 \end_layout
 
 \end_inset
@@ -563,7 +682,7 @@
 <lyxtabular version="3" rows="4" columns="2">
 <features>
 <column alignment="center" valignment="top" width="0">
-<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="4in">
 <row>
 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
@@ -571,12 +690,7 @@
 \begin_layout Plain Layout
 
 \series bold
-Value in
-\series default
- 
-\family typewriter
-\series bold
-fixed_dof
+Spatial database
 \end_layout
 
 \end_inset
@@ -598,7 +712,9 @@
 \begin_inset Text
 
 \begin_layout Plain Layout
-0
+
+\family typewriter
+db_initial
 \end_layout
 
 \end_inset
@@ -609,7 +725,7 @@
 \begin_layout Plain Layout
 
 \family typewriter
-dof-0
+displacement-x, displacement-y, displacement-z
 \end_layout
 
 \end_inset
@@ -620,7 +736,9 @@
 \begin_inset Text
 
 \begin_layout Plain Layout
-1
+
+\family typewriter
+db_rate
 \end_layout
 
 \end_inset
@@ -631,7 +749,7 @@
 \begin_layout Plain Layout
 
 \family typewriter
-dof-1
+displacement-rate-x, displacement-rate-y, displacement-rate-z, rate-start-time
 \end_layout
 
 \end_inset
@@ -642,7 +760,9 @@
 \begin_inset Text
 
 \begin_layout Plain Layout
-2
+
+\family typewriter
+db_change
 \end_layout
 
 \end_inset
@@ -653,7 +773,8 @@
 \begin_layout Plain Layout
 
 \family typewriter
-dof-2
+displacement-change-x, displacement-change-y, displacement-change-z, change-star
+t-time
 \end_layout
 
 \end_inset
@@ -671,7 +792,7 @@
 
 \end_layout
 
-\begin_layout Section
+\begin_layout Subsection
 Neumann Boundary Conditions
 \end_layout
 
@@ -696,7 +817,7 @@
  for a tutorial that uses Neumann boundary conditions.
 \end_layout
 
-\begin_layout Subsection
+\begin_layout Subsubsection
 Neumann Boundary Condition Parameters
 \end_layout
 
@@ -720,11 +841,6 @@
 \end_layout
 
 \begin_layout Description
-db The spatial database specifying the spatial variation in the applied
- tractions.
-\end_layout
-
-\begin_layout Description
 output The output manager associated with diagnostic output (traction vector).
 \end_layout
 
@@ -786,26 +902,22 @@
 \end_layout
 
 \begin_layout LyX-Code
-db = spatialdata.spatialdb.SimpleDB ; default
+db_initial = spatialdata.spatialdb.SimpleDB
 \end_layout
 
 \begin_layout LyX-Code
-db.label = Neumann BC +x edge
+db_initial.label = Neumann BC +x edge
 \end_layout
 
 \begin_layout LyX-Code
-db.iohandler.filename = axialtract.spatialdb
+db_initial.iohandler.filename = axialtract.spatialdb
 \end_layout
 
 \begin_layout LyX-Code
-db.query_type = nearest ; default
+db_initial.query_type = nearest
 \end_layout
 
 \begin_layout LyX-Code
-quadrature = pylith.feassemble.quadrature.Quadrature1Din2D
-\end_layout
-
-\begin_layout LyX-Code
 quadrature.cell = pylith.feassemble.FIATLagrange
 \end_layout
 
@@ -832,11 +944,9 @@
 \family default
 , since the default value is 
 \family typewriter
-DirichletPoints
+Dirichlet
 \family default
-.
- Because the problem is two-dimensional, we must supply a quadrature object
- to integrate over edges in two dimensions.
+BC.
  Constant tractions are used for this particular problem, so a quadrature
  order of one would have been sufficient; however, for problems involving
  more complex variations (e.g., a linear variation), a quadrature order of
@@ -958,7 +1068,7 @@
 
 \end_layout
 
-\begin_layout Subsection
+\begin_layout Subsubsection
 Neumann Boundary Condition Spatial Database Files
 \end_layout
 
@@ -974,31 +1084,31 @@
 \begin_layout Description
 one-dimensional 
 \family typewriter
-normal-traction
+normal
 \end_layout
 
 \begin_layout Description
 two-dimensional 
 \family typewriter
-shear-traction
+shear
 \family default
 , 
 \family typewriter
-normal-traction
+normal
 \end_layout
 
 \begin_layout Description
 three-dimensional 
 \family typewriter
-horiz-shear-traction
+horiz-shear
 \family default
 , 
 \family typewriter
-vert-shear-traction
+vert-shear
 \family default
 , 
 \family typewriter
-normal-traction
+normal
 \end_layout
 
 \begin_layout Standard
@@ -1025,6 +1135,410 @@
 , rather than the actual vertical direction.
 \end_layout
 
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align center
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Values in the spatial databases used for Dirichlet boundary conditions in
+ three dimensions.
+ In one- and two-dimensional problems, the names of the components are slightly
+ different as described earlier in this section.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="4in">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Spatial database
+\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
+Name in Spatial Database
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+db_initial
+\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
+
+\family typewriter
+traction-horiz-shear, traction-vert-shear, traction-normal
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+db_rate
+\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
+
+\family typewriter
+traction-rate-horiz-shear, traction-rate-vert-shear, traction-rate-normal,
+ rate-start-time
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+db_change
+\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
+
+\family typewriter
+traction-change-horiz-shear, traction-change-vert-shear, traction-change-normal,
+ change-start-time
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Point Force Boundary Conditions
+\end_layout
+
+\begin_layout Standard
+Point force boundary conditions in PyLith prescribe the application of point
+ forces to a subset of the vertices of the finite-element mesh.
+ While point force boundary conditions can be applied to any vertex, usually
+ they are applied to vertices on the lateral, top, and bottom boundaries
+ of the domain.
+\end_layout
+
+\begin_layout Subsubsection
+Point Force Parameters
+\end_layout
+
+\begin_layout Standard
+The properties and components common to both the DirichletBC and DirichletBounda
+ry boundary conditions are:
+\end_layout
+
+\begin_layout Description
+label Label of the group of vertices associated with the boundary condition.
+\end_layout
+
+\begin_layout Description
+bc_dof Array of degrees of freedom to which forces are applied (first degree
+ of freedom is 0).
+\end_layout
+
+\begin_layout Standard
+An example of setting the point force boundary condition parameters in a
+ 
+\family typewriter
+.cfg
+\family default
+ file is:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem]
+\end_layout
+
+\begin_layout LyX-Code
+bc = [mybc]
+\end_layout
+
+\begin_layout LyX-Code
+bc.mybc = pylith.bc.PointForce
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.problem.bc.mybc]
+\end_layout
+
+\begin_layout LyX-Code
+label = group A 
+\end_layout
+
+\begin_layout LyX-Code
+bc_dof = [2] ; fixed displacement in z direction
+\end_layout
+
+\begin_layout LyX-Code
+db_initial = spatialdata.spatialdb.SimpleDB
+\end_layout
+
+\begin_layout LyX-Code
+db_initial.iohandler.filename = force_A.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+db_initial.query_type = nearest ; change query type to nearest point algorithm
+\end_layout
+
+\begin_layout LyX-Code
+db_rate = spatialdata.spatialdb.UniformDB
+\end_layout
+
+\begin_layout LyX-Code
+db_rate.values = [force-rate-z]
+\end_layout
+
+\begin_layout LyX-Code
+db_rate.data = [1.0e+5*newton/s]
+\end_layout
+
+\begin_layout Standard
+We have created an array with one boundary condition, mybc.
+ The group of vertices associated with the boundary condition is group A.
+ For the database associated with the constant force, we use a SimpleDB.
+ We set the filename and query type for the database.
+ For the rate of change of values, we use a UniformDB and specify the rate
+ of change in the force to be 1.0e+5 Newton/s.
+ See Section 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:spatial:databases"
+
+\end_inset
+
+ for a discussion of the different types of spatial databases available.
+\end_layout
+
+\begin_layout Subsubsection
+Point Force Spatial Database Files
+\end_layout
+
+\begin_layout Standard
+The spatial database files for the Dirichlet boundary condition specify
+ the fixed displacements.
+ The spatial database file may contain displacements at more degrees of
+ freedom than those specified in the Dirichlet boundary condition settings
+ using the 
+\family typewriter
+bc_dof
+\family default
+ setting.
+ Only those listed in 
+\family typewriter
+bc_dof
+\family default
+ will be used.
+ This permits using the same spatial database file for multiple Dirichlet
+ boundary conditions with the same displacement field.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\noindent
+\align center
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Values in the spatial databases used for point force boundary conditions.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="4in">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\series bold
+Spatial database
+\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
+Name in Spatial Database
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+db_initial
+\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
+
+\family typewriter
+force-x, force-y, force-z
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+db_rate
+\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
+
+\family typewriter
+force-rate-x, force-rate-y, force-rate-z, rate-start-time
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+db_change
+\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
+
+\family typewriter
+force-change-x, force-change-y, force-change-z, change-start-time
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Absorbing Boundary Conditions
 \end_layout
@@ -1077,7 +1591,7 @@
 \end_layout
 
 \begin_layout Subsection
-Finite Element Implementation of Absorbing Boundary
+Finite-Element Implementation of Absorbing Boundary
 \end_layout
 
 \begin_layout Standard
@@ -1136,7 +1650,7 @@
 
 \end_inset
 
-In the case of a horizontal boundary, we can define an auxilliary direction
+In the case of a horizontal boundary, we can define an auxiliary direction
  in order to assign unique tangential directions.
  For a linear elastic isotropic material, 
 \begin_inset Formula $\sigma_{ij}=\lambda\epsilon_{kk}\delta_{ij}+2\mu\epsilon_{ij},$
@@ -1455,7 +1969,7 @@
 In order to create relative motion across the fault surface in the finite-elemen
 t mesh, additional degrees of freedom are added along with adjustment of
  the topology of the mesh.
- These additional degreees of freedom are associated with cohesive cells.
+ These additional degrees of freedom are associated with cohesive cells.
  These zero-volume cells allow control of the relative motion between vertices
  on the two sides of the fault.
  PyLith automatically adds cohesive cells for each fault surface.
@@ -1543,7 +2057,7 @@
  of two quadrilateral cells.
  The zero thickness cohesive cell (shown with dashed lines) controls slip
  on the fault.
- The Lagrange mutipliers for a kinematic earthquake source are associated
+ The Lagrange multipliers for a kinematic earthquake source are associated
  with the degrees of freedom for vertices 8 and 9.
  The constraint associated with vertex 8 controls the relative motion between
  vertices 2 and 6, and the constraint associated with vertex 9 controls