[cig-commits] [commit] master: Recover changes from stress (f28db4c)
cig_noreply at geodynamics.org
cig_noreply at geodynamics.org
Fri May 9 15:25:56 PDT 2014
Repository : https://github.com/geodynamics/cigma
On branch : master
Link : https://github.com/geodynamics/cigma/compare/65c02138d3ae8b87c088cc14fe4f98e21e3f0805...a26f592c25c89a40622404999ba1effcdf6df9e3
>---------------------------------------------------------------
commit f28db4c7cc18ad7f81cc80bc6f60890958d47724
Author: Luis Armendariz <luis>
Date: Fri Mar 27 19:53:17 2009 +0000
Recover changes from stress
>---------------------------------------------------------------
f28db4c7cc18ad7f81cc80bc6f60890958d47724
main2.lyx | 1048 +++++++++++++++++++++++++++++++------------------------------
1 file changed, 528 insertions(+), 520 deletions(-)
diff --git a/main2.lyx b/main2.lyx
index 0dc3e23..ff09947 100644
--- a/main2.lyx
+++ b/main2.lyx
@@ -3762,263 +3762,261 @@ In this chapter, we show how to use Cigma to run specific comparisons on
\end_layout
\begin_layout Section
-Mantle Convection
-\end_layout
-
-\begin_layout Standard
-For this example, we use CitcomCU to solve a thermal convection problem
- in a three-dimensional domain.
- The initial temperature field is a linear gradient from the top surface
- to the bottom surface.
- The temperature is fixed at 1 at the bottom of the cube, and fixed at 0
- at the top of the cube.
- In this case, we have solved for the velocity field for three different
- resolutions and stored it in three rectilinear vtk files called
-\family typewriter
-citcomcu.case8.vtr
-\family default
-,
-\family typewriter
-citcomcu.case16.vtr
-\family default
-, and
-\family typewriter
-citcomcu.case32.vtr
-\family default
-.
+Laplace Problem
\end_layout
\begin_layout Standard
-Now, we run the first comparison, comparing the highest resolution,
-\end_layout
-
-\begin_layout LyX-Code
-$ cigma compare
-\backslash
-
-\end_layout
+Here we obtain a sequence of solutions over five refinement levels by solving
+ the Laplace problem
+\begin_inset Formula $\nabla^{2}\phi(x,y)=4x^{4}+4y^{4}$
+\end_inset
-\begin_layout LyX-Code
- -a citcomcu.case32.vtr:velocity
-\backslash
+ inside
+\begin_inset Formula $\Omega=[-1,1]^{2}$
+\end_inset
-\end_layout
+, subject to
+\begin_inset Formula $\phi(x_{0},y_{0})=x_{0}^{2}+y_{0}^{2}$
+\end_inset
-\begin_layout LyX-Code
- -b citcomcu.case8.vtr:velocity
-\backslash
+ for points
+\begin_inset Formula $(x_{0},y_{0})$
+\end_inset
-\end_layout
+ in the boundary
+\begin_inset Formula $\partial\Omega$
+\end_inset
-\begin_layout LyX-Code
- -o citcomcu.h5:/case_32_08
+.
+ This problem can easily be solved using the Deal.II library, and is available
+ under Step 4 in the documentation.
\end_layout
\begin_layout LyX-Code
+$ levels=
+\begin_inset Quotes erd
+\end_inset
-\end_layout
+2 3 4 5
+\begin_inset Quotes erd
+\end_inset
-\begin_layout LyX-Code
-Summary of comparison:
-\end_layout
-\begin_layout LyX-Code
- L2 = 0.0500057391169
\end_layout
\begin_layout LyX-Code
- Linf = 0.146940986884
+$ for i in ${levels}; do
\end_layout
\begin_layout LyX-Code
- volume = 1
-\end_layout
+ cigma compare
+\backslash
-\begin_layout LyX-Code
- L2/volume = 0.0500057391169
\end_layout
\begin_layout LyX-Code
- L2/sqrt(volume) = 0.0500057391169
-\end_layout
+ square6.vtk square${i}.vtk
+\backslash
-\begin_layout LyX-Code
- h1 = 0.0541265877365
\end_layout
\begin_layout LyX-Code
- h2 = 0.216506350946
-\end_layout
-
-\begin_layout Standard
-Since we did not specify an integration mesh, the mesh from the first field
- is used for the integration of the
-\begin_inset Formula $L_{2}$
-\end_inset
-
- norm.
- Additionally, the above command creates the HDF5 file
-\family typewriter
-citcomcu.h5
-\family default
-, and stores the results of the comparison into an array called
-\family typewriter
-case32_08
-\family default
-.
-
+ -o square.h5:/error_6_${i}
\end_layout
\begin_layout LyX-Code
-$ cigma compare
+ vtk-residuals --output-log-values
\backslash
\end_layout
\begin_layout LyX-Code
- -a citcomcu.case32.vtr:velocity
+ -m square6.vtk
\backslash
\end_layout
\begin_layout LyX-Code
- -b citcomcu.case16.vtr:velocity
+ -i square.h5:/error_6_${i}
\backslash
\end_layout
\begin_layout LyX-Code
- -o citcomcu.h5:/case_32_16
+ -o log_error_square_6_${i}.vtk:log_error
\end_layout
\begin_layout LyX-Code
-
+ done
\end_layout
-\begin_layout LyX-Code
-Summary of comparison:
+\begin_layout Standard
+From output of the above commands we can collect the following table
\end_layout
-\begin_layout LyX-Code
- L2 = 0.0100758230674
-\end_layout
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="3">
+<features>
+<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" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
-\begin_layout LyX-Code
- Linf = 0.0322452153235
+\begin_layout Plain Layout
+Case
\end_layout
-\begin_layout LyX-Code
- volume = 1
-\end_layout
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
-\begin_layout LyX-Code
- L2/volume = 0.0100758230674
-\end_layout
+\begin_layout Plain Layout
+\begin_inset Formula $h$
+\end_inset
-\begin_layout LyX-Code
- L2/sqrt(volume) = 0.0100758230674
-\end_layout
-\begin_layout LyX-Code
- h1 = 0.0541265877365
\end_layout
-\begin_layout LyX-Code
- h2 = 0.108253175473
-\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
+\begin_inset Formula $L_{2}$
+\end_inset
-\begin_layout LyX-Code
\end_layout
-\begin_layout Standard
-From these two results, we can estimate how fast we are converging to a
- common answer between levels
-\begin_inset Formula $a$
\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+err_6_2
+\end_layout
- and
-\begin_inset Formula $b$
\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
- by using
+\begin_layout Plain Layout
+0.70717
\end_layout
-\begin_layout Standard
-\begin_inset Formula \begin{eqnarray*}
-\alpha & \sim & \frac{\log(\varepsilon_{b}/\varepsilon_{a})}{\log(h_{b}/h_{a})}\\
- & \sim & \frac{\log(0.01/0.05)}{\log(0.108/0.217)}\\
- & \sim & 2.3\end{eqnarray*}
-
\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.08280
+\end_layout
-where we have assumed that the highest resolution field is equivalent to
- the exact solution in our approximation for
-\begin_inset Formula $\alpha$
\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
-.
+\begin_layout Plain Layout
+err_6_3
\end_layout
-\begin_layout Standard
-Using a logarithmic scale to view the residual field for these two comparisons,
- we generate two vtk files using the comands
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+0.35355
\end_layout
-\begin_layout LyX-Code
-$ vtk-residuals
-\backslash
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+\begin_layout Plain Layout
+0.02462
\end_layout
-\begin_layout LyX-Code
- --output-log-values
-\backslash
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+\begin_layout Plain Layout
+err_6_4
\end_layout
-\begin_layout LyX-Code
- -m citcomcu.case32.vtr:velocity
-\backslash
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+\begin_layout Plain Layout
+0.17677
\end_layout
-\begin_layout LyX-Code
- -i citcomcu.h5:/case_32_08
-\backslash
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+\begin_layout Plain Layout
+0.00631
\end_layout
-\begin_layout LyX-Code
- -o log-res-vel-32-08.vtk
+\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
+err_6_5
\end_layout
-\begin_layout LyX-Code
-$ vtk-residuals
-\backslash
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+\begin_layout Plain Layout
+0.08838
\end_layout
-\begin_layout LyX-Code
- --output-log-values
-\backslash
+\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
+0.00137
\end_layout
-\begin_layout LyX-Code
- -m citcomcucase32.vtr:velocity
-\backslash
-
-\end_layout
+\end_inset
+</cell>
+</row>
+</lyxtabular>
-\begin_layout LyX-Code
- -i citcomcu.h5:/case_32_16
-\backslash
+\end_inset
-\end_layout
-\begin_layout LyX-Code
- -o log-res-vel-32-16.vtk
\end_layout
\begin_layout Standard
@@ -4030,9 +4028,9 @@ status collapsed
\begin_layout Plain Layout
\begin_inset Graphics
- filename figures2/log_res_citcomcu_velocity_32_08.png
- lyxscale 40
- scale 40
+ filename figures2/laplace_square6.png
+ lyxscale 80
+ scale 25
\end_inset
@@ -4040,7 +4038,7 @@ status collapsed
\begin_inset Caption
\begin_layout Plain Layout
-Caption for 5.1 here
+Caption for 5.4 here
\end_layout
\end_inset
@@ -4051,10 +4049,9 @@ Caption for 5.1 here
\end_inset
-\begin_inset space ~
-\end_inset
-
+\end_layout
+\begin_layout Standard
\begin_inset Float figure
placement H
wide false
@@ -4063,9 +4060,9 @@ status collapsed
\begin_layout Plain Layout
\begin_inset Graphics
- filename figures2/log_res_citcomcu_velocity_32_16.png
+ filename figures2/log_res_square_6_2.png
lyxscale 40
- scale 40
+ scale 18
\end_inset
@@ -4073,7 +4070,7 @@ status collapsed
\begin_inset Caption
\begin_layout Plain Layout
-Caption for 5.2 here
+Caption for 5.4 here
\end_layout
\end_inset
@@ -4087,68 +4084,35 @@ Caption for 5.2 here
\end_layout
\begin_layout Standard
-In the figures above, we show three cross sections of the error in the velocity
- field.
- The convergence behavior of these two comparisons can almost be confirmed
- visually by observing the overall color shift between the two figures,
- which use the same absolute color scale.
-\end_layout
-
-\begin_layout Section
-Circular Inclusion Benchmark
-\end_layout
-
-\begin_layout Standard
-We begin by analyzing a two-dimensional example benchmark problem for which
- we know an exact analytical solution.
-\end_layout
-
-\begin_layout LyX-Code
-
-\end_layout
-
-\begin_layout LyX-Code
-$ cigma compare
-\backslash
-
-\end_layout
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status collapsed
-\begin_layout LyX-Code
- -a p256.vts:PressureField
-\backslash
+\begin_layout Plain Layout
+\begin_inset Graphics
+ filename figures2/log_res_square_6_3.png
+ lyxscale 40
+ scale 18
-\end_layout
+\end_inset
-\begin_layout LyX-Code
- -b p128.vts:PressureField
-\backslash
-\end_layout
+\begin_inset Caption
-\begin_layout LyX-Code
- -o circ_inc.h5:/pressure_256_128
+\begin_layout Plain Layout
+Caption for 5.4 here
\end_layout
-\begin_layout LyX-Code
-$ cigma compare
-\backslash
-
-\end_layout
+\end_inset
-\begin_layout LyX-Code
- -a p256.vts:PressureField
-\backslash
\end_layout
-\begin_layout LyX-Code
- -b p64.vts:PressureField
-\backslash
+\end_inset
-\end_layout
-\begin_layout LyX-Code
- -o circ_inc.h5:/pressure_256_064
\end_layout
\begin_layout Standard
@@ -4160,7 +4124,7 @@ status collapsed
\begin_layout Plain Layout
\begin_inset Graphics
- filename figures2/log_res_circular_inclusion_256_064.png
+ filename figures2/log_res_square_6_4.png
lyxscale 40
scale 18
@@ -4170,7 +4134,7 @@ status collapsed
\begin_inset Caption
\begin_layout Plain Layout
-Caption for 5.3 here
+Caption for 5.4 here
\end_layout
\end_inset
@@ -4181,10 +4145,9 @@ Caption for 5.3 here
\end_inset
-\begin_inset space ~
-\end_inset
-
+\end_layout
+\begin_layout Standard
\begin_inset Float figure
placement H
wide false
@@ -4193,7 +4156,7 @@ status collapsed
\begin_layout Plain Layout
\begin_inset Graphics
- filename figures2/log_res_circular_inclusion_256_128.png
+ filename figures2/log_res_square_6_5.png
lyxscale 40
scale 18
@@ -4217,399 +4180,298 @@ Caption for 5.4 here
\end_layout
\begin_layout Standard
-The analytic solution is registered under the somewhat verbose name
-\end_layout
-
-\begin_layout LyX-Code
-
-\family typewriter
-bm.gale.circular_inclusion.pressure
-\end_layout
-
-\begin_layout Standard
-which we shorten by storing it in a shell variable,
-\end_layout
-
-\begin_layout LyX-Code
-$ export p=PressureField
-\end_layout
-
-\begin_layout LyX-Code
-$ export bm=bm.gale.circular_inclusion
-\end_layout
-
-\begin_layout LyX-Code
-$ cigma compare ${bm}.pressure p256.vts:${p} -o circ_inc.h5:/pressure_256
-\end_layout
-
-\begin_layout LyX-Code
-$ cigma compare ${bm}.pressure p128.vts:${p} -o circ_inc.h5:/pressure_128
-\end_layout
-
-\begin_layout LyX-Code
-$ cigma compare ${bm}.pressure p64.vts:${p} -o circ_inc.h5:/pressure_064
-\end_layout
+\begin_inset space ~
+\end_inset
-\begin_layout Section
-Strikeslip Benchmark Convergence
-\end_layout
-\begin_layout Standard
-This benchmark problem computes the viscoelastic (Maxwell) relaxation of
- stresses from a single, finite strike-slip earthquake in 3D without gravity.
- In order to obtain several data points, we use the CUBIT mesh generator
- to create a sequence of meshes with a 1.2 refinement ratio on which to solve.
- In this case, we also calculate the displacement field over 100 timesteps,
- saving every 10th field.
-\end_layout
+\begin_inset Float figure
+placement H
+wide false
+sideways false
+status open
-\begin_layout LyX-Code
-$ export a=hex8_0500m
-\end_layout
+\begin_layout Plain Layout
+\begin_inset Graphics
+ filename figures2/alpha_square.png
+ scale 30
-\begin_layout LyX-Code
-$ export b=hex8_1000m
-\end_layout
+\end_inset
-\begin_layout LyX-Code
-$ export d=displacements
-\end_layout
-\begin_layout LyX-Code
-$ export steps=`seq -f '%04g' 0 10 100` # generates list 0000 0010 0020
- ...
- 0100
-\end_layout
+\begin_inset Caption
-\begin_layout LyX-Code
-$ for n in ${steps}; do
+\begin_layout Plain Layout
+Caption for 5.4 here
\end_layout
-\begin_layout LyX-Code
- for b in
-\begin_inset Quotes eld
\end_inset
-hex8_1000m hex8_0833m hex8_0694m hex8_0578m
-\begin_inset Quotes erd
-\end_inset
-; do
\end_layout
-\begin_layout LyX-Code
- echo
-\begin_inset Quotes eld
-\end_inset
-
-Calculating ${a}-${b}-${n}
-\begin_inset Quotes erd
\end_inset
\end_layout
-\begin_layout LyX-Code
- cigma compare
-\backslash
-
+\begin_layout Section
+Mantle Convection
\end_layout
-\begin_layout LyX-Code
- -a strikeslip_${a}_t${n}.vtk:${d}
-\backslash
-
+\begin_layout Standard
+For this example, we use CitcomCU to solve a thermal convection problem
+ in a three-dimensional domain.
+ The initial temperature field is a linear gradient from the top surface
+ to the bottom surface.
+ The temperature is fixed at 1 at the bottom of the cube, and fixed at 0
+ at the top of the cube.
+ In this case, we have solved for the velocity field for three different
+ resolutions and stored it in three rectilinear vtk files called
+\family typewriter
+citcomcu.case8.vtr
+\family default
+,
+\family typewriter
+citcomcu.case16.vtr
+\family default
+, and
+\family typewriter
+citcomcu.case32.vtr
+\family default
+.
\end_layout
-\begin_layout LyX-Code
- -b strikeslip_${b}_t${n}.vtk:${d}
-\backslash
-
+\begin_layout Standard
+Now, we run the first comparison, comparing the highest resolution,
\end_layout
\begin_layout LyX-Code
- -o
-\begin_inset Quotes eld
-\end_inset
-
-strikeslipnog.h5:/${d}-${a}-${b}-${n}
-\begin_inset Quotes erd
-\end_inset
+$ cigma compare
+\backslash
+\end_layout
+\begin_layout LyX-Code
+ -a citcomcu.case32.vtr:velocity
\backslash
\end_layout
\begin_layout LyX-Code
- --verbose
+ -b citcomcu.case8.vtr:velocity
+\backslash
+
\end_layout
\begin_layout LyX-Code
- done
+ -o citcomcu.h5:/case_32_08
\end_layout
\begin_layout LyX-Code
- done
+
\end_layout
-\begin_layout Section
-Laplace Problem
+\begin_layout LyX-Code
+Summary of comparison:
\end_layout
-\begin_layout Standard
-Here we obtain a sequence of solutions over five refinement levels by solving
- the Laplace problem
-\begin_inset Formula $\nabla^{2}\phi(x,y)=4x^{4}+4y^{4}$
-\end_inset
+\begin_layout LyX-Code
+ L2 = 0.0500057391169
+\end_layout
- inside
-\begin_inset Formula $\Omega=[-1,1]^{2}$
-\end_inset
+\begin_layout LyX-Code
+ Linf = 0.146940986884
+\end_layout
-, subject to
-\begin_inset Formula $\phi(x_{0},y_{0})=x_{0}^{2}+y_{0}^{2}$
-\end_inset
+\begin_layout LyX-Code
+ volume = 1
+\end_layout
- for points
-\begin_inset Formula $(x_{0},y_{0})$
-\end_inset
+\begin_layout LyX-Code
+ L2/volume = 0.0500057391169
+\end_layout
- in the boundary
-\begin_inset Formula $\partial\Omega$
-\end_inset
+\begin_layout LyX-Code
+ L2/sqrt(volume) = 0.0500057391169
+\end_layout
-.
- This problem can easily be solved using the Deal.II library, and is available
- under Step 4 in the documentation.
+\begin_layout LyX-Code
+ h1 = 0.0541265877365
\end_layout
\begin_layout LyX-Code
-$ levels=
-\begin_inset Quotes erd
-\end_inset
+ h2 = 0.216506350946
+\end_layout
-2 3 4 5
-\begin_inset Quotes erd
+\begin_layout Standard
+Since we did not specify an integration mesh, the mesh from the first field
+ is used for the integration of the
+\begin_inset Formula $L_{2}$
\end_inset
+ norm.
+ Additionally, the above command creates the HDF5 file
+\family typewriter
+citcomcu.h5
+\family default
+, and stores the results of the comparison into an array called
+\family typewriter
+case32_08
+\family default
+.
\end_layout
\begin_layout LyX-Code
-$ for i in ${levels}; do
+$ cigma compare
+\backslash
+
\end_layout
\begin_layout LyX-Code
- cigma compare
+ -a citcomcu.case32.vtr:velocity
\backslash
\end_layout
\begin_layout LyX-Code
- square6.vtk square${i}.vtk
+ -b citcomcu.case16.vtr:velocity
\backslash
\end_layout
\begin_layout LyX-Code
- -o square.h5:/error_6_${i}
+ -o citcomcu.h5:/case_32_16
\end_layout
\begin_layout LyX-Code
- vtk-residuals --output-log-values
-\backslash
\end_layout
\begin_layout LyX-Code
- -m square6.vtk
-\backslash
-
+Summary of comparison:
\end_layout
\begin_layout LyX-Code
- -i square.h5:/error_6_${i}
-\backslash
-
+ L2 = 0.0100758230674
\end_layout
\begin_layout LyX-Code
- -o log_error_square_6_${i}.vtk:log_error
+ Linf = 0.0322452153235
\end_layout
\begin_layout LyX-Code
- done
+ volume = 1
\end_layout
-\begin_layout Standard
-From output of the above commands we can collect the following table
+\begin_layout LyX-Code
+ L2/volume = 0.0100758230674
\end_layout
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="3">
-<features>
-<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" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-Case
+\begin_layout LyX-Code
+ L2/sqrt(volume) = 0.0100758230674
\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
-\begin_inset Formula $h$
-\end_inset
-
-
+\begin_layout LyX-Code
+ h1 = 0.0541265877365
\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
-
-\begin_inset Formula $L_{2}$
-\end_inset
-
-
+\begin_layout LyX-Code
+ h2 = 0.108253175473
\end_layout
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
+\begin_layout LyX-Code
-\begin_layout Plain Layout
-err_6_2
\end_layout
+\begin_layout Standard
+From these two results, we can estimate how fast we are converging to a
+ common answer between levels
+\begin_inset Formula $a$
\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-0.70717
-\end_layout
+ and
+\begin_inset Formula $b$
\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-\begin_layout Plain Layout
-0.08280
+ by using
\end_layout
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
+\begin_layout Standard
+\begin_inset Formula \begin{eqnarray*}
+\alpha & \sim & \frac{\log(\varepsilon_{b}/\varepsilon_{a})}{\log(h_{b}/h_{a})}\\
+ & \sim & \frac{\log(0.01/0.05)}{\log(0.108/0.217)}\\
+ & \sim & 2.3\end{eqnarray*}
-\begin_layout Plain Layout
-err_6_3
-\end_layout
+\end_inset
+where we have assumed that the highest resolution field is equivalent to
+ the exact solution in our approximation for
+\begin_inset Formula $\alpha$
\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-\begin_layout Plain Layout
-0.35355
+.
\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
-0.02462
+\begin_layout Standard
+Using a logarithmic scale to view the residual field for these two comparisons,
+ we generate two vtk files using the comands
\end_layout
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
+\begin_layout LyX-Code
+$ vtk-residuals
+\backslash
-\begin_layout Plain Layout
-err_6_4
\end_layout
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
+\begin_layout LyX-Code
+ --output-log-values
+\backslash
-\begin_layout Plain Layout
-0.17677
\end_layout
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
+\begin_layout LyX-Code
+ -m citcomcu.case32.vtr:velocity
+\backslash
-\begin_layout Plain Layout
-0.00631
\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 LyX-Code
+ -i citcomcu.h5:/case_32_08
+\backslash
-\begin_layout Plain Layout
-err_6_5
\end_layout
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
+\begin_layout LyX-Code
+ -o log-res-vel-32-08.vtk
+\end_layout
+
+\begin_layout LyX-Code
+$ vtk-residuals
+\backslash
-\begin_layout Plain Layout
-0.08838
\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 LyX-Code
+ --output-log-values
+\backslash
-\begin_layout Plain Layout
-0.00137
\end_layout
-\end_inset
-</cell>
-</row>
-</lyxtabular>
+\begin_layout LyX-Code
+ -m citcomcucase32.vtr:velocity
+\backslash
-\end_inset
+\end_layout
+
+\begin_layout LyX-Code
+ -i citcomcu.h5:/case_32_16
+\backslash
+\end_layout
+\begin_layout LyX-Code
+ -o log-res-vel-32-16.vtk
\end_layout
\begin_layout Standard
@@ -4621,9 +4483,9 @@ status collapsed
\begin_layout Plain Layout
\begin_inset Graphics
- filename figures2/laplace_square6.png
- lyxscale 80
- scale 25
+ filename figures2/log_res_citcomcu_velocity_32_08.png
+ lyxscale 40
+ scale 40
\end_inset
@@ -4631,7 +4493,7 @@ status collapsed
\begin_inset Caption
\begin_layout Plain Layout
-Caption for 5.4 here
+Caption for 5.1 here
\end_layout
\end_inset
@@ -4642,9 +4504,10 @@ Caption for 5.4 here
\end_inset
-\end_layout
+\begin_inset space ~
+\end_inset
+
-\begin_layout Standard
\begin_inset Float figure
placement H
wide false
@@ -4653,9 +4516,9 @@ status collapsed
\begin_layout Plain Layout
\begin_inset Graphics
- filename figures2/log_res_square_6_2.png
+ filename figures2/log_res_citcomcu_velocity_32_16.png
lyxscale 40
- scale 18
+ scale 40
\end_inset
@@ -4663,7 +4526,7 @@ status collapsed
\begin_inset Caption
\begin_layout Plain Layout
-Caption for 5.4 here
+Caption for 5.2 here
\end_layout
\end_inset
@@ -4677,35 +4540,68 @@ Caption for 5.4 here
\end_layout
\begin_layout Standard
-\begin_inset Float figure
-placement H
-wide false
-sideways false
-status collapsed
+In the figures above, we show three cross sections of the error in the velocity
+ field.
+ The convergence behavior of these two comparisons can almost be confirmed
+ visually by observing the overall color shift between the two figures,
+ which use the same absolute color scale.
+\end_layout
-\begin_layout Plain Layout
-\begin_inset Graphics
- filename figures2/log_res_square_6_3.png
- lyxscale 40
- scale 18
+\begin_layout Section
+Circular Inclusion Benchmark
+\end_layout
-\end_inset
+\begin_layout Standard
+We begin by analyzing a two-dimensional example benchmark problem for which
+ we know an exact analytical solution.
+\end_layout
+\begin_layout LyX-Code
-\begin_inset Caption
+\end_layout
+
+\begin_layout LyX-Code
+$ cigma compare
+\backslash
-\begin_layout Plain Layout
-Caption for 5.4 here
\end_layout
-\end_inset
+\begin_layout LyX-Code
+ -a p256.vts:PressureField
+\backslash
+
+\end_layout
+\begin_layout LyX-Code
+ -b p128.vts:PressureField
+\backslash
\end_layout
-\end_inset
+\begin_layout LyX-Code
+ -o circ_inc.h5:/pressure_256_128
+\end_layout
+
+\begin_layout LyX-Code
+$ cigma compare
+\backslash
+
+\end_layout
+
+\begin_layout LyX-Code
+ -a p256.vts:PressureField
+\backslash
+
+\end_layout
+
+\begin_layout LyX-Code
+ -b p64.vts:PressureField
+\backslash
+\end_layout
+\begin_layout LyX-Code
+ -o circ_inc.h5:/pressure_256_064
\end_layout
\begin_layout Standard
@@ -4717,7 +4613,7 @@ status collapsed
\begin_layout Plain Layout
\begin_inset Graphics
- filename figures2/log_res_square_6_4.png
+ filename figures2/log_res_circular_inclusion_256_064.png
lyxscale 40
scale 18
@@ -4727,7 +4623,7 @@ status collapsed
\begin_inset Caption
\begin_layout Plain Layout
-Caption for 5.4 here
+Caption for 5.3 here
\end_layout
\end_inset
@@ -4738,9 +4634,10 @@ Caption for 5.4 here
\end_inset
-\end_layout
+\begin_inset space ~
+\end_inset
+
-\begin_layout Standard
\begin_inset Float figure
placement H
wide false
@@ -4749,7 +4646,7 @@ status collapsed
\begin_layout Plain Layout
\begin_inset Graphics
- filename figures2/log_res_square_6_5.png
+ filename figures2/log_res_circular_inclusion_256_128.png
lyxscale 40
scale 18
@@ -4773,33 +4670,144 @@ Caption for 5.4 here
\end_layout
\begin_layout Standard
-\begin_inset space ~
-\end_inset
+The analytic solution is registered under the somewhat verbose name
+\end_layout
+\begin_layout LyX-Code
-\begin_inset Float figure
-placement H
-wide false
-sideways false
+\family typewriter
+bm.gale.circular_inclusion.pressure
+\end_layout
+
+\begin_layout Standard
+which we shorten by storing it in a shell variable,
+\end_layout
+
+\begin_layout LyX-Code
+$ export p=PressureField
+\end_layout
+
+\begin_layout LyX-Code
+$ export bm=bm.gale.circular_inclusion
+\end_layout
+
+\begin_layout LyX-Code
+$ cigma compare ${bm}.pressure p256.vts:${p} -o circ_inc.h5:/pressure_256
+\end_layout
+
+\begin_layout LyX-Code
+$ cigma compare ${bm}.pressure p128.vts:${p} -o circ_inc.h5:/pressure_128
+\end_layout
+
+\begin_layout LyX-Code
+$ cigma compare ${bm}.pressure p64.vts:${p} -o circ_inc.h5:/pressure_064
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Note Note
status open
+\begin_layout Section
+Strikeslip Benchmark Convergence
+\end_layout
+
\begin_layout Plain Layout
-\begin_inset Graphics
- filename figures2/alpha_square.png
- scale 30
+This benchmark problem computes the viscoelastic (Maxwell) relaxation of
+ stresses from a single, finite strike-slip earthquake in 3D without gravity.
+ In order to obtain several data points, we use the CUBIT mesh generator
+ to create a sequence of meshes with a 1.2 refinement ratio on which to solve.
+ In this case, we also calculate the displacement field over 100 timesteps,
+ saving every 10th field.
+\end_layout
+
+\begin_layout LyX-Code
+$ export a=hex8_0500m
+\end_layout
+
+\begin_layout LyX-Code
+$ export b=hex8_1000m
+\end_layout
+
+\begin_layout LyX-Code
+$ export d=displacements
+\end_layout
+
+\begin_layout LyX-Code
+$ export steps=`seq -f '%04g' 0 10 100` # generates list 0000 0010 0020
+ ...
+ 0100
+\end_layout
+\begin_layout LyX-Code
+$ for n in ${steps}; do
+\end_layout
+
+\begin_layout LyX-Code
+ for b in
+\begin_inset Quotes eld
\end_inset
+hex8_1000m hex8_0833m hex8_0694m hex8_0578m
+\begin_inset Quotes erd
+\end_inset
-\begin_inset Caption
+; do
+\end_layout
+
+\begin_layout LyX-Code
+ echo
+\begin_inset Quotes eld
+\end_inset
+
+Calculating ${a}-${b}-${n}
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+ cigma compare
+\backslash
+
+\end_layout
+
+\begin_layout LyX-Code
+ -a strikeslip_${a}_t${n}.vtk:${d}
+\backslash
+
+\end_layout
+
+\begin_layout LyX-Code
+ -b strikeslip_${b}_t${n}.vtk:${d}
+\backslash
-\begin_layout Plain Layout
-Caption for 5.4 here
\end_layout
+\begin_layout LyX-Code
+ -o
+\begin_inset Quotes eld
+\end_inset
+
+strikeslipnog.h5:/${d}-${a}-${b}-${n}
+\begin_inset Quotes erd
\end_inset
+\backslash
+
+\end_layout
+
+\begin_layout LyX-Code
+ --verbose
+\end_layout
+
+\begin_layout LyX-Code
+ done
+\end_layout
+
+\begin_layout LyX-Code
+ done
\end_layout
\end_inset
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