\r
\r
%%NEW\r
+It is well-known that preconditioners have a very strong influence on the\r
+convergence of linear systems. Previously, we have used some classical\r
+preconditioners provided by PETSc. HYPRE~\cite{Falgout06} is a very efficient\r
+preconditioner based on structured multigrid and element-based algebraic\r
+multigrid algorithms. In Table~\ref{tab:06} we report an experiment that show it\r
+reduces drastivally the number of iterations but sometimes it is very\r
+time-consuming compared to other simpler precondititioners. In this table, we\r
+can see that for $512$ and $2,048$ cores, HYPRE reduces drastically the number\r
+of iterations for FGMRES to reach the convergence. However, it is very\r
+time-consuming compared to TSIRM and FGMRES with the ASM preconditioner. For\r
+$4,096$ and $8,192$ cores, FGMRES with HYPRE did not converge in less than 1000s\r
+where FGMRES and TSIRM with the ASM converge very quickly. Finally, it can be\r
+noticed that TSIRM is also faster than FGMRES and it requires less iterations.\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
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
+ 8192 & 44.35 & 3,197 & 7.6 & 1,083 & 5.84 & >1000 & -- \\\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
+In Table~\ref{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
