X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/cebfda218ec5cc78ffbd06922f550cf3bae1a46b..a1ff3fa3715cb0844074d7927cd852f6e0cb6b3f:/paper.tex

diff --git a/paper.tex b/paper.tex
index a7d529d..e93737c 100644
--- a/paper.tex
+++ b/paper.tex
@@ -873,16 +873,15 @@ Core(TM) i7-3630QM CPU @ 2.40GHz with the version 3.5.1 of PETSc.
 
 
 In  Table~\ref{tab:02}, some  experiments comparing  the solving  of  the linear
-systems obtained with the previous matrices  with a GMRES variant and with out 2
-stage algorithm are  given. In the second column, it can  be noticed that either
-GRMES or  FGMRES (Flexible  GMRES)~\cite{Saad:1993} is used  to solve  the linear
-system.   According to  the matrices,  different preconditioner  is  used.  With
-TSIRM, the same solver and the  same preconditionner are used.  This Table shows
-that  TSIRM  can  drastically reduce  the  number  of  iterations to  reach  the
-convergence when the  number of iterations for the normal GMRES  is more or less
-greater than  500. In fact  this also depends  on tow parameters: the  number of
-iterations  to  stop  GMRES  and   the  number  of  iterations  to  perform  the
-minimization.
+systems obtained with the previous matrices  with a GMRES variant and with TSIRM
+are given. In the  second column, it can be noticed that  either GRMES or FGMRES
+(Flexible GMRES)~\cite{Saad:1993} is used to solve the linear system.  According
+to the matrices, different preconditioner  is used.  With TSIRM, the same solver
+and  the  same  preconditionner are  used.   This  Table  shows that  TSIRM  can
+drastically reduce  the number of iterations  to reach the  convergence when the
+number of iterations for  the normal GMRES is more or less  greater than 500. In
+fact this also depends on tow parameters: the number of iterations to stop GMRES
+and the number of iterations to perform the minimization.
 
 
 \begin{table}[htbp]
@@ -973,7 +972,7 @@ preconditioner in PETSc please consult~\cite{petsc-web-page}.
 \hline
 
 \end{tabular}
-\caption{Comparison of FGMRES and TSIRM with FGMRES for example ex15 of PETSc with two preconditioners (mg and sor) with 25,000 components per core on Juqueen (threshold 1e-3, restart=30, s=12),  time is expressed in seconds.}
+\caption{Comparison of FGMRES and TSIRM with FGMRES for example ex15 of PETSc with two preconditioners (mg and sor) with 25,000 components per core on Juqueen ($\epsilon_{tsirm}=1e-3$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
 \label{tab:03}
 \end{center}
 \end{table*}
@@ -1028,7 +1027,7 @@ the number of iterations. So, the overall benefit of using TSIRM is interesting.
 \begin{tabular}{|r|r|r|r|r|r|r|r|r|} 
 \hline
 
-  nb. cores & threshold   & \multicolumn{2}{c|}{FGMRES} & \multicolumn{2}{c|}{TSIRM CGLS} &  \multicolumn{2}{c|}{TSIRM LSQR} & best gain \\ 
+  nb. cores & $\epsilon_{tsirm}$  & \multicolumn{2}{c|}{FGMRES} & \multicolumn{2}{c|}{TSIRM CGLS} &  \multicolumn{2}{c|}{TSIRM LSQR} & best gain \\ 
 \cline{3-8}
              &                       & Time  & \# Iter.  & Time  & \# Iter. & Time  & \# Iter. & \\\hline \hline
   2,048      & 8e-5                  & 108.88 & 16,560  & 23.06  &  3,630  & 22.79  & 3,630   & 4.77 \\
@@ -1041,7 +1040,7 @@ the number of iterations. So, the overall benefit of using TSIRM is interesting.
 \hline
 
 \end{tabular}
-\caption{Comparison of FGMRES  and TSIRM with FGMRES algorithms for ex54 of Petsc (both with the MG preconditioner) with 25,000 components per core on Curie (restart=30, s=12),  time is expressed in seconds.}
+\caption{Comparison of FGMRES  and TSIRM with FGMRES algorithms for ex54 of Petsc (both with the MG preconditioner) with 25,000 components per core on Curie ($max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
 \label{tab:04}
 \end{center}
 \end{table*}
@@ -1099,7 +1098,7 @@ taken into account with TSIRM.
 \hline
 
 \end{tabular}
-\caption{Comparison of FGMRES  and TSIRM with FGMRES for ex54 of Petsc (both with the MG preconditioner) with 204,919,225 components on Curie with different number of cores (restart=30, s=12, threshold 5e-5),  time is expressed in seconds.}
+\caption{Comparison of FGMRES  and TSIRM with FGMRES for ex54 of Petsc (both with the MG preconditioner) with 204,919,225 components on Curie with different number of cores ($\epsilon_{tsirm}=5e-5$, $max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
 \label{tab:05}
 \end{center}
 \end{table*}
