[cig-commits] r5078 - short/3D/PyLith/trunk/doc/userguide

[baagaard at geodynamics.org]

Author: baagaard
Date: 2006-10-23 09:25:15 -0700 (Mon, 23 Oct 2006)
New Revision: 5078

Modified:
   short/3D/PyLith/trunk/doc/userguide/governingeqns.lyx
Log:
Fixed line breaks.

Modified: short/3D/PyLith/trunk/doc/userguide/governingeqns.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/governingeqns.lyx	2006-10-23 15:08:05 UTC (rev 5077)
+++ short/3D/PyLith/trunk/doc/userguide/governingeqns.lyx	2006-10-23 16:25:15 UTC (rev 5078)
@@ -1002,8 +1002,9 @@
 
 which we can expand into
 \begin_inset Formula \begin{multline}
-\sum_{elements}({\frac{1}{\Delta t^{2}}\int}_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t+\Delta t)\, dV-\frac{2}{\Delta t^{2}}\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t)\, dV+\frac{1}{\Delta t^{2}}\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t-\Delta t)\, dV\\
-+{\frac{1}{2}\int}_{V^{e}}\sigma_{ij}(t)(N_{,j}^{p}+N_{,i}^{p})\: dV-\int_{V^{e}}N^{p}f_{i}(t)\: dV-\int_{S_{T}}N^{p}T_{i}\: dS)=0\end{multline}
+\sum_{elements}({\frac{1}{\Delta t^{2}}\int}_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t+\Delta t)\, dV-\frac{2}{\Delta t^{2}}\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t)\, dV\\
++\frac{1}{\Delta t^{2}}\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t-\Delta t)\, dV+{\frac{1}{2}\int}_{V^{e}}\sigma_{ij}(t)(N_{,j}^{p}+N_{,i}^{p})\: dV\\
+-\int_{V^{e}}N^{p}f_{i}(t)\: dV-\int_{S_{T}}N^{p}T_{i}\: dS)=0\end{multline}
 
 \end_inset
 
@@ -1022,8 +1023,9 @@
 
  yields
 \begin_inset Formula \begin{multline*}
-\frac{1}{\Delta t^{2}}\sum_{elements}\left(\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t+\Delta t)\, dV\right)=\frac{2}{\Delta t^{2}}\sum_{elements}\left(\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t)\, dV\right)-\frac{1}{\Delta t^{2}}\sum_{elements}\left(\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t-\Delta t)\, dV\right)\\
--\frac{1}{2}\sum_{elements}\left(\int_{V^{e}}\sigma_{ij}(t)(N_{,j}^{p}+N_{,i}^{p})\: dV\right)+\sum_{elements}\left(\int_{V^{e}}N^{p}f_{i}(t)\: dV\right)+\sum_{elements}\left(\int_{S_{T}}N^{p}T_{i}\: dS\right).\end{multline*}
+\frac{1}{\Delta t^{2}}\sum_{elements}\left(\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t+\Delta t)\, dV\right)=\frac{2}{\Delta t^{2}}\sum_{elements}\left(\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t)\, dV\right)\\
+-\frac{1}{\Delta t^{2}}\sum_{elements}\left(\int_{V^{e}}\rho N^{p}\sum_{q}N^{q}u_{i}^{q}(t-\Delta t)\, dV\right)-\frac{1}{2}\sum_{elements}\left(\int_{V^{e}}\sigma_{ij}(t)(N_{,j}^{p}+N_{,i}^{p})\: dV\right)\\
++\sum_{elements}\left(\int_{V^{e}}N^{p}f_{i}(t)\: dV\right)+\sum_{elements}\left(\int_{S_{T}}N^{p}T_{i}\: dS\right).\end{multline*}
 
 \end_inset