\r
%%NEW\r
\r
+{\bf example ex45/ksp à décrire et commenter en montrant que hypre est pourri avec cet exemple}\r
+\r
+\begin{table*}[htbp]\r
+\begin{center}\r
+\begin{tabular}{|r|r|r|r|r|r|r|r|} \r
+\hline\r
+\r
+ nb. cores & \multicolumn{2}{c|}{FGMRES/ASM} & \multicolumn{2}{c|}{TSIRM CGLS/ASM} & gain& \multicolumn{2}{c|}{FGMRES/HYPRE} \\ \r
+\cline{2-5} \cline{7-8}\r
+ & Time & \# Iter. & Time & \# Iter. & & Time & \# Iter. \\\hline \hline\r
+ 512 & 5.54 & 685 & 2.5 & 570 & 2.21 & 128.9 & 9 \\\r
+ 2048 & 14.95 & 1,560 & 4.32 & 746 & 3.48 & 335.7 & 9 \\\r
+ 4096 & 25.13 & 2,369 & 5.61 & 859 & 4.48 & >1000 & -- \\\r
+ 8192 & 44.35 & 3,197 & 7.6 & 1083 & 5.84 & >1000 & -- \\\r
+\r
+\hline\r
+\r
+\end{tabular}\r
+\caption{Comparison of FGMRES and TSIRM for ex45 of PETSc/KSP with two preconditioner (ASM and HYPRE) having 5,000 components per core on Curie ($\epsilon_{tsirm}=1e-10$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$,$\epsilon_{ls}=1e-40$), time is expressed in seconds.}\r
+\label{tab:06}\r
+\end{center}\r
+\end{table*}\r
+\r
+\r
\subsection{Parallel nonlinear problems}\r
\r
With PETSc, linear solvers are used inside nonlinear solvers. The SNES\r
ex20. In ex14, the code solves the Bratu (SFI - solid fuel ignition) nonlinear\r
partial difference equations in 3 dimension. In ex20, the code solves a 3\r
dimension radiative transport test problem. For more details on these examples,\r
-interested readers are invited to see the code in the PETSc examples.\r
-\r
-In Table~\ref{tab:07} we report the result of our experiments for the example\r
-ex14. \r
+interested readers are invited to see the code in the PETSc examples. For both\r
+these examples, a weak scaling case is chosen where processors have\r
+approximately a number of components equals to 100,000.\r
+\r
+In Table~\ref{tab:07} we report the result of our experiments for the example\r
+ex14 with the block Jacobi preconditioner. For TSIRM the CGLS algorithm is used\r
+to solve the minimization step. In this table, we can see that the number of\r
+iterations used by the linear solver is smaller with TSIRM compared with FGMRES.\r
+Consequently the execution times are smaller with TSIRM. The gain between TSIRM\r
+and FGMRES is around 6 and 7. The parameters of TSIRM are expressed in the\r
+caption of the table.\r
\r
\begin{table*}[htbp]\r
\begin{center}\r
nb. cores & \multicolumn{2}{c|}{FGMRES/BJAC} & \multicolumn{2}{c|}{TSIRM CGLS/BJAC} & gain \\ \r
\cline{2-5}\r
& Time & \# Iter. & Time & \# Iter. & \\\hline \hline\r
- 1024 & 159.52 & 11,584 & 26.34 & 1,563 & 6.06 \\\r
- 2048 & 226.24 & 16,459 & 37.23 & 2,248 & 6.08\\\r
- 4096 & 391.21 & 27,794 & 50.93 & 2,911 & 7.69\\\r
- 8192 & 543.23 & 37,770 & 79.21 & 4,324 & 6.86 \\\r
+ 1,024 & 159.52 & 11,584 & 26.34 & 1,563 & 6.06 \\\r
+ 2,048 & 226.24 & 16,459 & 37.23 & 2,248 & 6.08\\\r
+ 4,096 & 391.21 & 27,794 & 50.93 & 2,911 & 7.69\\\r
+ 8,192 & 543.23 & 37,770 & 79.21 & 4,324 & 6.86 \\\r
\r
\hline\r
\r
\end{center}\r
\end{table*}\r
\r
+In Table~\cite{tab:08}, the results of the experiments with the example ex20 are\r
+reported. The block Jacobi preconditioner has also been used and CGLS to solve\r
+the minimization step for TSIRM. For this example, we can observ that the number\r
+of iterations for FMGRES increase drastically when the number of cores\r
+increases. With TSIRM, we can see that the number of iterations is initially\r
+very small compared to the FGMRES ones and when the number of cores increase,\r
+the number of iterations increases slighther with TSIRM than with FGMRES. For\r
+this example, the gain between TSIRM and FGMRES ranges between 8 with 1,024\r
+cores to more than 16 with 8,192 cores.\r
\r
\begin{table*}[htbp]\r
\begin{center}\r
nb. cores & \multicolumn{2}{c|}{FGMRES/BJAC} & \multicolumn{2}{c|}{TSIRM CGLS/BJAC} & gain \\ \r
\cline{2-5}\r
& Time & \# Iter. & Time & \# Iter. & \\\hline \hline\r
- 1024 & 667.92 & 48,732 & 81.65 & 5,087 & 8.18 \\\r
- 2048 & 966.87 & 77,177 & 90.34 & 5,716 & 10.70\\\r
- 4096 & 1,742.31 & 124,411 & 119.21 & 6,905 & 14.61\\\r
- 8192 & 2,739.21 & 187,626 & 168.9 & 9,000 & 16.22\\\r
+ 1,024 & 667.92 & 48,732 & 81.65 & 5,087 & 8.18 \\\r
+ 2,048 & 966.87 & 77,177 & 90.34 & 5,716 & 10.70\\\r
+ 4,096 & 1,742.31 & 124,411 & 119.21 & 6,905 & 14.61\\\r
+ 8,192 & 2,739.21 & 187,626 & 168.9 & 9,000 & 16.22\\\r
\r
\hline\r
\r
\r
\r
\r
+\r
+\r
+\r
+%%NEW\r
\subsection{Influence of parameters for TSIRM}\r
\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_cgls_iter_total}\r
+\caption{Number of total iterations using two different methods for the minimization: LSQR and CGLS.}\r
+\label{fig:cgls-iter} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_cgls_time}\r
+\caption{Execution time in seconds using two different methods for the minimization: LSQR and CGLS.}\r
+\label{fig:cgls-time} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_inner_restarts_iter_total}\r
+\caption{Number of total iterations with variation of restarts in the inner solver FGMRES.}\r
+\label{fig:inner_restarts_iter_total} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_inner_restarts_time}\r
+\caption{Execution time in seconds with variation of restarts in the inner solver FGMRES.}\r
+\label{fig:inner_restarts_time} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_max_inner_iter}\r
+\caption{Number of total iterations with variation of number of inner iterations.}\r
+\label{fig:max_inner_iter} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_max_inner_time}\r
+\caption{Execution time in seconds with variation of number of inner iterations.}\r
+\label{fig:max_inner_time} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_maxiter_ls_iter}\r
+\caption{Number of total iterations with variation of number of iterations in the minimization process.}\r
+\label{fig:maxiter_ls_iter} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_maxiter_ls_time}\r
+\caption{Execution time in seconds with variation of number of iterations in the minimization process.}\r
+\label{fig:maxiter_ls_time} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_size_ls_iter}\r
+\caption{Number of total iterations with variation of the size of the least-squares problem in the minimization process.}\r
+\label{fig:size_ls_iter} \r
+\end{figure}\r
+\r
+\begin{figure}[htbp]\r
+\centering\r
+ \includegraphics[angle=-90,width=0.5\textwidth]{ksp_tsirm_size_ls_time}\r
+\caption{Execution time in seconds with variation of the size of the least-squares problem in the minimization process.}\r
+\label{fig:size_ls_time} \r
+\end{figure}\r
+\r
+%%ENDNEW\r
+\r
\r
\r
\r
