X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/26119b98c896e296f4ec91c15272a9575fe250a9..7122f8d886bcd6191b7eee5017e8c96944ab7e56:/IJHPCN/paper.tex

diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex
index 410b7ad..db5f791 100644
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -911,8 +911,20 @@ taken into account with TSIRM.
 
 
 %%NEW
+It  is well-known  that  preconditioners have  a very  strong  influence on  the
+convergence  of  linear  systems.   Previously,  we  have  used  some  classical
+preconditioners provided  by PETSc.  HYPRE~\cite{Falgout06} is  a very efficient
+preconditioner  based  on  structured   multigrid  and  element-based  algebraic
+multigrid algorithms. In Table~\ref{tab:06} we report an experiment that show it
+reduces  drastivally  the  number  of   iterations  but  sometimes  it  is  very
+time-consuming compared  to other simpler  precondititioners. In this  table, we
+can see that  for $512$ and $2,048$ cores, HYPRE  reduces drastically the number
+of  iterations  for FGMRES  to  reach  the  convergence.   However, it  is  very
+time-consuming compared  to TSIRM  and FGMRES with  the ASM  preconditioner. For
+$4,096$ and $8,192$ cores, FGMRES with HYPRE did not converge in less than 1000s
+where FGMRES and  TSIRM with the ASM  converge very quickly. Finally,  it can be
+noticed that TSIRM is also faster than FGMRES and it requires less iterations.
 
-{\bf example ex45/ksp à décrire et commenter en montrant que hypre est pourri avec cet exemple}
 
 \begin{table*}[htbp]
 \begin{center}
@@ -925,7 +937,7 @@ taken into account with TSIRM.
    512              & 5.54      & 685    & 2.5 &       570 & 2.21   & 128.9 & 9     \\
    2048             & 14.95     & 1,560  &  4.32 &     746 & 3.48   & 335.7 & 9 \\
    4096             & 25.13    & 2,369   & 5.61 &   859    & 4.48   & >1000  & -- \\
-   8192             & 44.35   & 3,197   &  7.6  &  1083    &  5.84  & >1000 &  --   \\
+   8192             & 44.35   & 3,197   &  7.6  &  1,083    &  5.84  & >1000 &  --   \\
 
 \hline
 
@@ -982,7 +994,7 @@ caption of the table.
 \end{center}
 \end{table*}
 
-In Table~\cite{tab:08}, the results of the experiments with the example ex20 are
+In Table~\ref{tab:08}, the results of the experiments with the example ex20 are
 reported. The block  Jacobi preconditioner has also been used  and CGLS to solve
 the minimization step for TSIRM. For this example, we can observ that the number
 of  iterations  for  FMGRES  increase  drastically  when  the  number  of  cores