[cig-commits] commit: Small changes for submission.

[Mercurial]

changeset:   152:c86f883e07c3
tag:         tip
user:        Brad Aagaard <baagaard at usgs.gov>
date:        Thu Sep 13 12:28:12 2012 -0700
files:       faultRup.tex
description:
Small changes for submission.


diff -r 1892d1447fdf -r c86f883e07c3 faultRup.tex
--- a/faultRup.tex	Thu Sep 13 08:36:22 2012 -0700
+++ b/faultRup.tex	Thu Sep 13 12:28:12 2012 -0700
@@ -3,7 +3,6 @@
 \documentclass[jgr]{agutex}
 
 \usepackage{lineno}
-\usepackage{array}
 \usepackage{rotating}
 \usepackage[centertags]{amsmath}
 \usepackage{bm}
@@ -73,6 +72,18 @@
   Chicago, Illinois, USA.}
 
 \altaffiltext{3}{GNS Science, Lower Hutt, New Zealand.}
+
+% ------------------------------------------------------------------
+% Main points
+%
+% We employ domain decomposition to implement fault slip in a
+% finite-element code.
+%
+% We develop a preconditioner to accelerate convergence in
+% quasi-static problems.
+%
+% Benchmarks for quasi-static and dynamic problems verify the
+% implementation.
 
 % ------------------------------------------------------------------
 \begin{abstract}
@@ -477,7 +488,7 @@ rather than $t+\Delta t$ yields
     \\
     + \int_{V} \bm{N}_m^T \cdot \bm{f}(t) \, dV \\
       - \int_{V} \rho \bm{N}_m^T \cdot \bm{N}_n \cdot 
-          \frac{\partial^2 \bm{u}_n}{\partial t^2}(t) \, dV
+          \frac{\partial^2 \bm{u}_n(t)}{\partial t^2} \, dV
     =\bm{0}.
   \end{split}
 \end{equation}
@@ -490,19 +501,19 @@ time using explicit time stepping via Ne
 \citep{Newmark:1959} with a central difference scheme wherein the
 acceleration and velocity are given by
 \begin{gather}
-  \frac{\partial^2 \bm{u}}{\partial t^2}(t) = 
+  \frac{\partial^2 \bm{u}(t)}{\partial t^2} = 
   \frac{1}{\Delta t^2} \left(
     \bm{du} - \bm{u}(t) + \bm{u}(t-\Delta t)
   \right), \\
 %
-  \frac{\partial \bm{u}}{\partial t}(t) = \frac{1}{2\Delta t} \left(
+  \frac{\partial \bm{u}(t)}{\partial t} = \frac{1}{2\Delta t} \left(
     \bm{du} + \bm{u}(t) - \bm{u}(t-\Delta t)
     \right).
 \end{gather}
 Expanding the inertial term yields
 \begin{equation}
   \begin{split}
-    - \int_{V} \rho \bm{N}_m^T \cdot \bm{N}_n \cdot \frac{\partial^2 \bm{u}_n}{\partial
+    - \int_{V} \rho \bm{N}_m^T \cdot \bm{N}_n \cdot \frac{\partial^2 \bm{u}_n(t)}{\partial
       t^2} \, dV = \\
     - \frac{1}{\Delta t^2} \int_{V} \rho \bm{N}_m^T \cdot
     \bm{N}_n \cdot 
@@ -1828,6 +1839,7 @@ rupture propagation.
 % TABLES
 % ------------------------------------------------------------------
 \begin{table}
+%\scriptsize % :SUBMIT:
   \caption{Example Preconditioners for the Saddle Point Problem in
     Equation~(\ref{eqn:saddle:point})\tablenotemark{a}}
   \label{tab:preconditioner:options}
@@ -1950,6 +1962,7 @@ rupture propagation.
 
 
 \begin{table}
+%\scriptsize % :SUBMIT:
 \caption{Performance Benchmark Memory System Evaluation\tablenotemark{a}}
 \label{tab:solvertest:memory:events}
 \centering
@@ -1996,6 +2009,7 @@ VecMAXPY &    1 & 1.0 &   1819 \\
 
 
 \begin{table}
+\scriptsize
 \caption{Performance Benchmark Solver Evaluation\tablenotemark{a}}
 \label{tab:solvertest:solver:events}
 \centering
@@ -2003,25 +2017,25 @@ VecMAXPY &    1 & 1.0 &   1819 \\
   \hline
   Event & \# Calls & Time (s) & MFlops/s \\
   \hline
-\multicolumn{4}{c}{p = 12} \\
+\multicolumn{4}{c}{{\it p = 12}} \\
   MatMult & 180 &      2.7 &     6113 \\
   PCSetUp &   1 &      5.7 &      232 \\
   PCApply &  57 &      5.5 &     3690 \\
   KSPSolve &   1 &     15.1 &     3013 \\
 \hline
-\multicolumn{4}{c}{p = 24} \\
+\multicolumn{4}{c}{{\it p = 24}} \\
   MatMult & 207 &      3.1 &    12293 \\
   PCSetUp &   1 &      5.2 &      526 \\
   PCApply &  66 &      6.6 &     7285 \\
   KSPSolve &   1 &     16.4 &     6666 \\
 \hline
-\multicolumn{4}{c}{p = 48} \\
+\multicolumn{4}{c}{{\it p = 48}} \\
   MatMult & 222 &      4.0 &    21136 \\
   PCSetUp &   1 &     10.1 &      628 \\
   PCApply &  71 &      9.4 &    12032 \\
   KSPSolve &   1 &     25.1 &    10129 \\
 \hline
-\multicolumn{4}{c}{p = 96} \\
+\multicolumn{4}{c}{{\it p = 96}} \\
   MatMult & 234 &      4.0 &    42130 \\
   PCSetUp &   1 &     11.8 &     1943 \\
   PCApply &  75 &     11.6 &    20422 \\
@@ -2040,7 +2054,6 @@ VecMAXPY &    1 & 1.0 &   1819 \\
 \end{table}
 
 
-\clearpage
 \begin{table}
 \caption{Savage and Prescott Benchmark Parameters\tablenotemark{a}}
 \label{tab:Savage:Prescott:parameters}
@@ -2095,6 +2108,7 @@ VecMAXPY &    1 & 1.0 &   1819 \\
   the parameters can be found in \citet{Harris:etal:SRL:2011}.}
 \end{table}
 
+\clearpage
 
 % ------------------------------------------------------------------
 \end{article}