[cig-commits] r15769 - doc/geodynamics.org/benchmarks/trunk/long

[luis at geodynamics.org]

Author: luis
Date: 2009-10-05 15:49:11 -0700 (Mon, 05 Oct 2009)
New Revision: 15769

Modified:
   doc/geodynamics.org/benchmarks/trunk/long/divergence.html
   doc/geodynamics.org/benchmarks/trunk/long/divergence.rst
Log:
Fixes to long/divergence.rst

Modified: doc/geodynamics.org/benchmarks/trunk/long/divergence.html
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/divergence.html	2009-10-05 22:49:04 UTC (rev 15768)
+++ doc/geodynamics.org/benchmarks/trunk/long/divergence.html	2009-10-05 22:49:11 UTC (rev 15769)
@@ -16,23 +16,41 @@
 square domain, and the velocity on the corners is set to enforce a
 spreading from the center of the square. Figure [fig:Divergence_v_sri]
 shows the velocity and strain rate invariant for a numerical solution.
-For a constant divergence $d$, the analytic solution for this setup is
-$$v_x = x cdot d/2, v_y = y cdot d/2$$</p>
-<p>In 3D, the analytic solution is
-$$v_x = x cdot d/3, v_y = y cdot d/3, v_z = z cdot d/3$$</p>
-<p>In both cases, the strain rate invariant equals $sqrt{d/2}$. As shown in
+For a constant divergence [;d;], the analytic solution for this setup is</p>
+<blockquote>
+[;v_x = x \cdot d/2, v_y = y \cdot d/2;]</blockquote>
+<p>In 3D, the analytic solution is</p>
+<blockquote>
+[;v_x = x \cdot d/3, v_y = y \cdot d/3, v_z = z \cdot d/3;]</blockquote>
+<p>In both cases, the strain rate invariant equals [;\sqrt{d/2};]. As shown in
 Figure [fig:Divergence_2D_error], the main source of error in 2D comes
 from inaccuracies in the solver. Figure [fig:Divergence_3D_error] paints
 a different picture in 3D, where the main source of error comes from
 having a finite number of particles.</p>
 <div class="figure">
-<img alt="images/divergence_v.pngFigure[fig:Divergence_v_sri]VelocityandStrainRateInvariantsolutionforthe2DDivergencebenchmark.Thevariationinthestrainrateinvariantisuniformlysmall." src="images/divergence_v.pngFigure[fig:Divergence_v_sri]VelocityandStrainRateInvariantsolutionforthe2DDivergencebenchmark.Thevariationinthestrainrateinvariantisuniformlysmall." />
+<img alt="images/divergence_v.png" src="images/divergence_v.png" />
+<p class="caption">Figure [fig:Divergence_v_sri]</p>
+<div class="legend">
+Velocity and Strain Rate Invariant solution for the 2D Divergence
+benchmark. The variation in the strain rate invariant is uniformly
+small.</div>
 </div>
 <div class="figure">
-<img alt="images/divergence_2D_error.epsFigure[fig:Divergence_2D_error]Maximumerrorinthestrainrateinvariantforthe2DDivergencebenchmarkvs.toleranceinthelinearsolver.Theresolutioniskeptat$32\times32$,andthenumberofparticlespercelliskeptat30." src="images/divergence_2D_error.epsFigure[fig:Divergence_2D_error]Maximumerrorinthestrainrateinvariantforthe2DDivergencebenchmarkvs.toleranceinthelinearsolver.Theresolutioniskeptat$32\times32$,andthenumberofparticlespercelliskeptat30." />
+<img alt="images/divergence_2D_error.png" src="images/divergence_2D_error.png" />
+<p class="caption">Figure [fig:Divergence_2D_error]</p>
+<div class="legend">
+Maximum error in the strain rate invariant for the 2D Divergence
+benchmark vs. tolerance in the linear solver. The resolution is kept at
+[;32 times 32;], and the number of particles per cell is kept at 30.</div>
 </div>
 <div class="figure">
-<img alt="images/divergence_3D_error.epsFigure[fig:Divergence_3D_error]Maximumerrorinthestrainrateinvariantforthe3DDivergencebenchmarkvs.thenumberofparticlesineachcell.Theresolutioniskeptat$16\times16\times16$,andthetoleranceinthelinearsolveriskeptat$10^{-7}$." src="images/divergence_3D_error.epsFigure[fig:Divergence_3D_error]Maximumerrorinthestrainrateinvariantforthe3DDivergencebenchmarkvs.thenumberofparticlesineachcell.Theresolutioniskeptat$16\times16\times16$,andthetoleranceinthelinearsolveriskeptat$10^{-7}$." />
+<img alt="images/divergence_3D_error.png" src="images/divergence_3D_error.png" />
+<p class="caption">Figure [fig:Divergence_3D_error]</p>
+<div class="legend">
+Maximum error in the strain rate invariant for the 3D Divergence
+benchmark vs. the number of particles in each cell. The resolution is
+kept at [;16 \times 16 \times 16;], and the tolerance in the linear
+solver is kept at [;10^{-7};].</div>
 </div>
 </div>
 </body>

Modified: doc/geodynamics.org/benchmarks/trunk/long/divergence.rst
===================================================================
--- doc/geodynamics.org/benchmarks/trunk/long/divergence.rst	2009-10-05 22:49:04 UTC (rev 15768)
+++ doc/geodynamics.org/benchmarks/trunk/long/divergence.rst	2009-10-05 22:49:11 UTC (rev 15769)
@@ -7,34 +7,42 @@
 square domain, and the velocity on the corners is set to enforce a
 spreading from the center of the square. Figure [fig:Divergence_v_sri]
 shows the velocity and strain rate invariant for a numerical solution.
-For a constant divergence $d$, the analytic solution for this setup is
-$$v_x = x \cdot d/2, v_y = y \cdot d/2$$
+For a constant divergence [;d;], the analytic solution for this setup is
 
+    [;v_x = x \\cdot d/2, v_y = y \\cdot d/2;]
+
 In 3D, the analytic solution is
-$$v_x = x \cdot d/3, v_y = y \cdot d/3, v_z = z \cdot d/3$$
 
-In both cases, the strain rate invariant equals $\sqrt{d/2}$. As shown in
+    [;v_x = x \\cdot d/3, v_y = y \\cdot d/3, v_z = z \\cdot d/3;]
+
+In both cases, the strain rate invariant equals [;\\sqrt{d/2};]. As shown in
 Figure [fig:Divergence_2D_error], the main source of error in 2D comes
 from inaccuracies in the solver. Figure [fig:Divergence_3D_error] paints
 a different picture in 3D, where the main source of error comes from
 having a finite number of particles.
 
 .. figure:: images/divergence_v.png
+
    Figure [fig:Divergence_v_sri]
+
    Velocity and Strain Rate Invariant solution for the 2D Divergence
    benchmark. The variation in the strain rate invariant is uniformly
    small.
 
-.. figure:: images/divergence_2D_error.eps
+.. figure:: images/divergence_2D_error.png
+
    Figure [fig:Divergence_2D_error]
+
    Maximum error in the strain rate invariant for the 2D Divergence
    benchmark vs. tolerance in the linear solver. The resolution is kept at
-   $32 \times 32$, and the number of particles per cell is kept at 30.
+   [;32 \times 32;], and the number of particles per cell is kept at 30.
 
-.. figure:: images/divergence_3D_error.eps
+.. figure:: images/divergence_3D_error.png
+
    Figure [fig:Divergence_3D_error]
+
    Maximum error in the strain rate invariant for the 3D Divergence
    benchmark vs. the number of particles in each cell. The resolution is
-   kept at $16 \times 16 \times 16$, and the tolerance in the linear
-   solver is kept at $10^{-7}$.
+   kept at [;16 \\times 16 \\times 16;], and the tolerance in the linear
+   solver is kept at [;10^{-7};].