[cig-commits] commit: Updated scaling figure.
Mercurial
hg at geodynamics.org
Tue Aug 14 13:29:54 PDT 2012
changeset: 136:78953462162c
parent: 133:007ad2fd2670
user: Brad Aagaard <baagaard at usgs.gov>
date: Tue Aug 14 08:44:47 2012 -0700
files: faultRup.tex figs/solvertest_scaling.pdf
description:
Updated scaling figure.
diff -r 007ad2fd2670 -r 78953462162c faultRup.tex
--- a/faultRup.tex Mon Aug 13 17:38:47 2012 -0700
+++ b/faultRup.tex Tue Aug 14 08:44:47 2012 -0700
@@ -1205,16 +1205,18 @@ with the results summarized in
with the results summarized in
Table~\ref{tab:solvertest:preconditioner:iterates}.
-The family of field split preconditioners using algebraic multigrid
-methods minimize the increase in the number of iterations with problem
-size. For these preconditioners the number of iterations increases by
-only about 20\% for a four times increase in the number of degrees of
-freedom, compared to 60\% for the ASM preconditioner. Within the
-family of field split preconditioners, the one with multiplicative
-composition minimizes the number of iterations. The custom
-preconditioner for the Lagrange multiplier submatrix greatly
-accelerates the convergence with an 80\% reduction in the
-number of iterations required for convergence.
+The Schur complement and family of field split preconditioners using
+algebraic multigrid methods minimize the increase in the number of
+iterations with problem size. For these preconditioners the number of
+iterations increases by only about 20\% for a four times increase in
+the number of degrees of freedom, compared to 60\% for the ASM
+preconditioner. Within the family of field split preconditioners using
+algebraic multigrid methods, the one with multiplicative composition
+minimizes the number of iterations. The custom preconditioner for the
+Lagrange multiplier submatrix greatly accelerates the convergence with
+an 80\% reduction in the number of iterations required for
+convergence. This preconditioner also provides the fastest runtime of
+all of these preconditioners.
\subsection{Parallel Scaling Performance}
@@ -1666,12 +1668,19 @@ simulations of earthquake rupture propag
\end{figure}
\begin{figure}
- \brad{update figure after solver tuning}
\noindent\includegraphics{figs/solvertest_scaling}
- \caption{Plot of parallel scaling for the performance benchmark. \brad{add more here}}
+ \caption{Plot of parallel scaling for the performance benchmark with
+ the algebraic multigrid preconditioner and fault block custom
+ preconditioner. The finite-element integrations for the Jacobian
+ and residual exhibit good weak scaling with minimal sensitivity to
+ the problem size. The linear solve does not scale as well, which
+ we attribute to the poor scaling of the algebraic multigrid setup
+ and application as well as limited memory and interconnect
+ bandwidth.}
\label{fig:solvertest:scaling}
\end{figure}
+\clearpage
\begin{figure}
\noindent\includegraphics[width=84mm]{figs/savageprescott_soln}
\caption{Deformation (exaggerated by a factor of 5000) 95\% of the
@@ -1710,6 +1719,7 @@ simulations of earthquake rupture propag
\label{fig:savage:prescott:profiles}
\end{figure}
+\clearpage
\begin{figure}
\noindent\includegraphics{figs/tpv13_geometry}
\caption{Geometry for SCEC spontaneous rupture benchmark TPV13 involving
@@ -1829,7 +1839,6 @@ simulations of earthquake rupture propag
% ------------------------------------------------------------------
% TABLES
% ------------------------------------------------------------------
-\clearpage
\begin{table}
\caption{Example Preconditioners for the Saddle Point Problem in
Equation~(\ref{eqn:saddle:point})\tablenotemark{a}}
@@ -1869,12 +1878,7 @@ simulations of earthquake rupture propag
\tablenotetext{a}{Four examples of preconditioners often used to
accelerate convergence in saddle point problems. Below the
mathematical expression for the preconditioner, we show the PyLith
- parameters used to construct the preconditioner. In the performance
- benchmark we consider the AMG preconditioner with multiplicative
- relaxation, the Schur complement preconditioner with upper
- factorization, and the Schur complement preconditioner with full
- factorization. The AMG preconditioner with additive relaxation is
- shown for completeness.}
+ parameters used to construct the preconditioner. }
\end{table}
\clearpage
@@ -1883,27 +1887,28 @@ simulations of earthquake rupture propag
\label{tab:solvertest:preconditioner:iterates}
\centering
\begin{tabular}{lcrrr}
+ \hline
Preconditioner & Cell & \multicolumn{3}{c}{Problem Size} \\
& & S1 & S2 & S4 \\
\hline
ASM
- & Tet4 & 239 & 287 & 434 \\
- & Hex8 & 184 & 236 & 298 \\
+ & Tet4 & 184 & 217 & 270 \\
+ & Hex8 & 143 & 179 & 221 \\
Schur (full)
- & Tet4 & 131 & 173 & 205 \\
- & Hex8 & 101 & 131 & 155 \\
+ & Tet4 & 82 & 84 & 109 \\
+ & Hex8 & 54 & 60 & 61 \\
Schur (upper)
- & Tet4 & 222 & 269 & 356 \\
- & Hex8 & 175 & 215 & 274 \\
+ & Tet4 & 79 & 78 & 87 \\
+ & Hex8 & 53 & 59 & 57 \\
FieldSplit (add)
- & Tet4 & 301 & 330 & 333 \\
- & Hex8 & 205 & 203 & 232 \\
+ & Tet4 & 241 & 587 & 585 \\
+ & Hex8 & 159 & 193 & 192 \\
FieldSplit (mult)
- & Tet4 & 451 & 503 & 517 \\
- & Hex8 & 258 & 264 & 331 \\
+ & Tet4 & 284 & 324 & 383 \\
+ & Hex8 & 165 & 177 & 194 \\
FieldSplit (mult,custom)
- & Tet4 & 60 & 63 & 70 \\
- & Hex8 & 48 & 51 & 59 \\
+ & Tet4 & 42 & 48 & 51 \\
+ & Hex8 & 35 & 39 & 43 \\
\hline
\end{tabular}
\tablenotetext{a}{Number of iterations for Additive Schwarz (ASM),
@@ -1911,11 +1916,14 @@ simulations of earthquake rupture propag
and multiplicative with custom fault block preconditioner),
preconditioners for tetrahedral and hexahedral discretizations and
three problem sizes (S1 with $1.8\times 10^5$ DOF, S2 with
- $3.5\times 10^5$ DOF, and S3 with $6.9\times 10^5$ DOF). The field
- split preconditioner with multiplicative composition and the custom
- fault block preconditioner yields good performance with only a
+ $3.5\times 10^5$ DOF, and S3 with $6.9\times 10^5$ DOF). The Schur
+ complement preconditioners and the field split preconditioner with
+ multiplicative factorization and the custom fault block
+ preconditioner yield the best performance with only a
fraction of the iterates as the other preconditioners and a small
- increase with problem size.}
+ increase with problem size. Furthermore, the the field
+ split preconditioner with multiplicative factorization and the custom
+ fault block preconditioner provides the shortest runtime.}
\end{table}
diff -r 007ad2fd2670 -r 78953462162c figs/solvertest_scaling.pdf
Binary file figs/solvertest_scaling.pdf has changed
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