[cig-commits] commit: Updated scaling tables. Small edits.
Mercurial
hg at geodynamics.org
Mon Aug 13 17:30:56 PDT 2012
changeset: 132:4d2adcbbbfe6
tag: tip
user: Brad Aagaard <baagaard at usgs.gov>
date: Mon Aug 13 17:30:52 2012 -0700
files: faultRup.tex
description:
Updated scaling tables. Small edits.
diff -r 56ed4e9edde6 -r 4d2adcbbbfe6 faultRup.tex
--- a/faultRup.tex Mon Aug 13 14:56:14 2012 -0700
+++ b/faultRup.tex Mon Aug 13 17:30:52 2012 -0700
@@ -1170,7 +1170,7 @@ the problem size (number of DOF) for the
the problem size (number of DOF) for the two different cell types
(hexahedra and tetrahedra) are nearly the same. The suite of
simulations examine problem sizes increasing by about a factor of two
-from $1.78\times 10^5$ DOF (1 process) to $1.10\times 10^7$ DOF (64
+from $1.8\times 10^5$ DOF (1 process) to $1.1\times 10^7$ DOF (64
processes). The corresponding discretization sizes are 2033 m to 500 m
for the hexahedral meshes and 2326 m to 581 m for the tetrahedral
meshes. Figure~\ref{fig:solvertest:mesh} shows the 1846 m resolution
@@ -1253,7 +1253,7 @@ for the various stages of the simulation
for the various stages of the simulation is independent of the number
of processes. For this performance benchmark we use the entire suite
of hexahedral and tetrahedral meshes described earlier that range in
-size from $1.78\times 10^5$ DOF (1 process) to $1.10\times 10^7$ DOF
+size from $1.8\times 10^5$ DOF (1 process) to $1.1\times 10^7$ DOF
(64 processes). We employ the AMG preconditioner for the elasticity
submatrix and our custom preconditioner for the Lagrange multipliers
submatrix. We ran the simulations on a Beowulf cluster comprised of 24
@@ -1566,14 +1566,13 @@ for the fault block associated with the
for the fault block associated with the Lagrange multipliers
accelerates the convergence of the Krylov solver with the fewest
number of iterations and the least sensitivity to problem
-size. \brad{Add something about poor scaling of AMG or good scaling of
- ASM?} Benchmark tests demonstrate the accuracy of our implementation
+size. Benchmark tests demonstrate the accuracy of our implementation
in PyLith with excellent agreement with the analytical solution for
viscoelastic relaxation and strike-slip faulting over multiply
earthquake cycle and excellent agreement with other codes for
supershear dynamic spontaneous rupture on a dipping normal fault
embedded in an elastoplastic domain. Consequently, we believe this
-methodology will provide a promising avenue for modeling the
+methodology provides a promising avenue for modeling the
earthquake cycle through coupling of quasi-static simulations of the
interseismic and postseismic deformation and dynamic rupture
simulations of earthquake rupture propagation.
@@ -1879,152 +1878,6 @@ simulations of earthquake rupture propag
\clearpage
\begin{table}
-\caption{Performance Benchmark Parameters\tablenotemark{a}}
-\label{tab:solvertest:parameters}
-\centering
-\begin{tabular}{llc}
- \hline
- \multicolumn{2}{l}{Parameter} & Value \\
- \hline
- \multicolumn{2}{l}{Domain} & \\
- & Length & 72 km \\
- & Width & 72 km \\
- & Height & 36 km \\
- & Angle between faults & 60 $\deg$ \\
- \multicolumn{2}{l}{Elastic properties} & \\
- & Vp & 5.774 km/s \\
- & Vs & 3.333 km/s \\
- & Density ($\rho$) & 2700. kg/m$^3$ \\
- \multicolumn{2}{l}{Middle fault} & \\
- & Length & 39.19 km \\
- & Width & 12 km \\
- & Slip & 1.0 m RL \\
- \multicolumn{2}{l}{End faults} & \\
- & Length & 43.74 km \\
- & Width & 12 km \\
- & Slip & 0.5 m LL \\
- \hline
-\end{tabular}
-\tablenotetext{a}{Simulation parameters for the performance benchmark
- with three faults embedded in a volume domain as shown in
- Figure~\ref{fig:solvertest:geometry}. We prescribe right-lateral
- (RL) slip on the middle fault and left-lateral (LL) slip on the end faults.}
-\end{table}
-
-
-\begin{table}
-\caption{Performance Benchmark Memory System Evaluation\tablenotemark{a}}
-\label{tab:solvertest:memory:events}
-\centering
-\begin{tabular}{rcc}
- \# Cores & Load Imbalance & MFlops/s \\
- \hline
- \multicolumn{3}{c}{\texttt{VecMDot}} \\
- 1 & 1.0 & 2188 \\
- 2 & 1.0 & 3969 \\
- 4 & 1.0 & 5511 \\
- 8 & 1.1 & 6007 \\
- 16 & 1.3 & 10249 \\
- 32 & 1.2 & 4270 \\
- 64 & 1.2 & 12299 \\
- \hline
- \multicolumn{3}{c}{\texttt{VecAXPY}} \\
- 1 & 1.0 & 1453 \\
- 2 & 1.1 & 2708 \\
- 4 & 1.1 & 5001 \\
- 8 & 1.1 & 4225 \\
- 16 & 1.3 & 8157 \\
- 32 & 1.2 & 13876 \\
- 64 & 1.2 & 25807 \\
- \hline
- \multicolumn{3}{c}{\texttt{VecMAXPY}} \\
- 1 & 1.0 & 1733 \\
- 2 & 1.1 & 3283 \\
- 4 & 1.1 & 4991 \\
- 8 & 1.1 & 5611 \\
- 16 & 1.3 & 11050 \\
- 32 & 1.2 & 21680 \\
- 64 & 1.2 & 42697 \\
- \hline
-\end{tabular}
-\tablenotetext{a}{Examination of memory system performance using three
- PETSc vector operations for simulations with the hexahedral meshes. \texttt{VecMDot}
- corresponds to the operation for vector reductions, \texttt{VecAXPY}
- corresponds to vector scaling and addition, and \texttt{VecMAXPY}
- corresponds to mutiple vector scaling and addition.}
-\end{table}
-
-
-\begin{table}
-\caption{Performance Benchmark Solver Evaluation\tablenotemark{a}}
-\label{tab:solvertest:solver:events}
-\centering
-\begin{tabular}{lrrr}
- Event & Calls & Time (s) & MFlops/s \\
- \hline
- \multicolumn{4}{c}{p = 8} \\
- MatMult & 168 & 2.1 & 4947 \\
- PCSetUp & 1 & 5.8 & 159 \\
- PCApply & 53 & 4.2 & 3081 \\
- KSPSolve & 1 & 12.9 & 2246 \\
- \hline
- \multicolumn{4}{c}{p = 16} \\
- MatMult & 174 & 2.2 & 9690 \\
- PCSetUp & 1 & 7.0 & 258 \\
- PCApply & 55 & 4.9 & 5629 \\
- KSPSolve & 1 & 14.9 & 4033 \\
- \hline
- \multicolumn{4}{c}{p = 32} \\
- MatMult & 189 & 3.8 & 12003 \\
- PCSetUp & 1 & 15.3 & 241 \\
- PCApply & 60 & 7.3 & 8174 \\
- KSPSolve & 1 & 26.0 & 5034 \\
- \hline
- \multicolumn{4}{c}{p = 64} \\
- MatMult & 219 & 3.2 & 34538 \\
- PCSetUp & 1 & 29.0 & 348 \\
- PCApply & 70 & 14.8 & 10229 \\
- KSPSolve & 1 & 47.5 & 7067 \\
- \hline
-\end{tabular}
-\tablenotetext{a}{Examination of solver performance using three of the
- main events comprising the linear solve for simulations with the
- hexahedral meshes and 8, 16, 32, and 64 processes. The
- \texttt{KSPSolve} event encompasses the entire linear
- solve. \texttt{MatMult} corresponds to matrix-vector
- multiplications. \texttt{PCSetUp} and \texttt{PCApply} correspond to
- the setup and application of the AMG preconditioner.}
-\end{table}
-
-
-\clearpage
-\begin{table}
-\caption{SCEC Benchmark TPV13 Parameters\tablenotemark{a}}
-\label{tab:tpv13:parameters}
-\centering
-\begin{tabular}{llc}
- \hline
- \multicolumn{2}{l}{Parameter} & Value \\
- \hline
- \multicolumn{2}{l}{Domain} & \\
- & Length & 64 km \\
- & Width & 48 km \\
- & Height & 36 km \\
- & Fault dip angle & 60 $\deg$ \\
- \multicolumn{2}{l}{Elastic properties} & \\
- & Vp & 5.716 km/s \\
- & Vs & 3.300 km/s \\
- & Density ($\rho$) & 2700. kg/m$^3$ \\
- \hline
-\end{tabular}
-\tablenotetext{a}{Simulation parameters for the performance benchmark
- with three faults embedded in a volume domain as shown in
- Figure~\ref{fig:solvertest:geometry}. We prescribe right-lateral
- (RL) slip on the middle fault and left-lateral (LL) slip on the end faults.}
-\end{table}
-
-
-\begin{table}
\caption{Preconditioner Performance\tablenotemark{a}}
\label{tab:solvertest:preconditioner:iterates}
\centering
@@ -2065,6 +1918,156 @@ simulations of earthquake rupture propag
\end{table}
+\begin{table}
+\caption{Performance Benchmark Parameters\tablenotemark{a}}
+\label{tab:solvertest:parameters}
+\centering
+\begin{tabular}{llc}
+ \hline
+ \multicolumn{2}{l}{Parameter} & Value \\
+ \hline
+ \multicolumn{2}{l}{Domain} & \\
+ & Length & 72 km \\
+ & Width & 72 km \\
+ & Height & 36 km \\
+ & Angle between faults & 60 $\deg$ \\
+ \multicolumn{2}{l}{Elastic properties} & \\
+ & Vp & 5.774 km/s \\
+ & Vs & 3.333 km/s \\
+ & Density ($\rho$) & 2700. kg/m$^3$ \\
+ \multicolumn{2}{l}{Middle fault} & \\
+ & Length & 39.19 km \\
+ & Width & 12 km \\
+ & Slip & 1.0 m RL \\
+ \multicolumn{2}{l}{End faults} & \\
+ & Length & 43.74 km \\
+ & Width & 12 km \\
+ & Slip & 0.5 m LL \\
+ \hline
+\end{tabular}
+\tablenotetext{a}{Simulation parameters for the performance benchmark
+ with three faults embedded in a volume domain as shown in
+ Figure~\ref{fig:solvertest:geometry}. We prescribe right-lateral
+ (RL) slip on the middle fault and left-lateral (LL) slip on the end faults.}
+\end{table}
+
+
+\begin{table}
+\caption{Performance Benchmark Memory System Evaluation\tablenotemark{a}}
+\label{tab:solvertest:memory:events}
+\centering
+\begin{tabular}{lrrr}
+ \hline
+ Event & \# Cores & Load Imbalance & MFlops/s \\
+ \hline
+VecMDot & 1 & 1.0 & 2188 \\
+ & 2 & 1.1 & 3968 \\
+ & 4 & 1.1 & 5510 \\
+ & 8 & 1.1 & 6008 \\
+ & 16 & 1.3 & 10249 \\
+ & 32 & 1.2 & 4270 \\
+ & 64 & 1.2 & 12300 \\
+ \hline
+VecAXPY & 1 & 1.0 & 1453 \\
+ & 2 & 1.1 & 2708 \\
+ & 4 & 1.1 & 5002 \\
+ & 8 & 1.1 & 4224 \\
+ & 16 & 1.3 & 8158 \\
+ & 32 & 1.2 & 13872 \\
+ & 64 & 1.2 & 25802 \\
+ \hline
+VecMAXPY & 1 & 1.0 & 1733 \\
+ & 2 & 1.1 & 3284 \\
+ & 4 & 1.1 & 4990 \\
+ & 8 & 1.1 & 5610 \\
+ & 16 & 1.3 & 11051 \\
+ & 32 & 1.2 & 21678 \\
+ & 64 & 1.2 & 42680 \\
+ \hline
+\end{tabular}
+\tablenotetext{a}{Examination of memory system performance using three
+ PETSc vector operations for simulations with the hexahedral
+ meshes. The performance for the tetrahedral meshes is nearly
+ the same. For ideal scaling the number of floating point operations
+ per second should scale linearly with the number of processes. \texttt{VecMDot}
+ corresponds to the operation for vector reductions, \texttt{VecAXPY}
+ corresponds to vector scaling and addition, and \texttt{VecMAXPY}
+ corresponds to mutiple vector scaling and addition.}
+\end{table}
+
+
+\begin{table}
+\caption{Performance Benchmark Solver Evaluation\tablenotemark{a}}
+\label{tab:solvertest:solver:events}
+\centering
+\begin{tabular}{lrrr}
+ \hline
+ Event & \# Calls & Time (s) & MFlops/s \\
+ \hline
+\multicolumn{4}{c}{p = 8} \\
+ MatMult & 168 & 2.1 & 4946 \\
+ PCSetUp & 1 & 5.8 & 159 \\
+ PCApply & 53 & 4.2 & 3081 \\
+ KSPSolve & 1 & 12.9 & 2246 \\
+\hline
+\multicolumn{4}{c}{p = 16} \\
+ MatMult & 174 & 2.2 & 9691 \\
+ PCSetUp & 1 & 7.0 & 258 \\
+ PCApply & 55 & 4.9 & 5629 \\
+ KSPSolve & 1 & 14.9 & 4033 \\
+\hline
+\multicolumn{4}{c}{p = 32} \\
+ MatMult & 189 & 3.8 & 12003 \\
+ PCSetUp & 1 & 15.3 & 241 \\
+ PCApply & 60 & 7.3 & 8174 \\
+ KSPSolve & 1 & 26.0 & 5034 \\
+\hline
+\multicolumn{4}{c}{p = 64} \\
+ MatMult & 219 & 3.2 & 34534 \\
+ PCSetUp & 1 & 29.0 & 348 \\
+ PCApply & 70 & 14.8 & 10228 \\
+ KSPSolve & 1 & 47.5 & 7067 \\
+\hline
+\end{tabular}
+\tablenotetext{a}{Examination of solver performance using three of the
+ main events comprising the linear solve for simulations with the
+ hexahedral meshes and 8, 16, 32, and 64 processes. The performance
+ for the tetrahedral meshes is nearly the same. For ideal scaling
+ the time for each event should be constant as the number of
+ processes incrases. The \texttt{KSPSolve} event encompasses the
+ entire linear solve. \texttt{MatMult} corresponds to matrix-vector
+ multiplications. \texttt{PCSetUp} and \texttt{PCApply} correspond to
+ the setup and application of the AMG preconditioner.}
+\end{table}
+
+
+\clearpage
+\begin{table}
+\caption{SCEC Benchmark TPV13 Parameters\tablenotemark{a}}
+\label{tab:tpv13:parameters}
+\centering
+\begin{tabular}{llc}
+ \hline
+ \multicolumn{2}{l}{Parameter} & Value \\
+ \hline
+ \multicolumn{2}{l}{Domain} & \\
+ & Length & 64 km \\
+ & Width & 48 km \\
+ & Height & 36 km \\
+ & Fault dip angle & 60 $\deg$ \\
+ \multicolumn{2}{l}{Elastic properties} & \\
+ & Vp & 5.716 km/s \\
+ & Vs & 3.300 km/s \\
+ & Density ($\rho$) & 2700. kg/m$^3$ \\
+ \hline
+\end{tabular}
+\tablenotetext{a}{Simulation parameters for the performance benchmark
+ with three faults embedded in a volume domain as shown in
+ Figure~\ref{fig:solvertest:geometry}. We prescribe right-lateral
+ (RL) slip on the middle fault and left-lateral (LL) slip on the end faults.}
+\end{table}
+
+
% ------------------------------------------------------------------
\end{article}
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