X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/3f095ff7f3fff2553897be9e8dce25d2c3e9298f..38a7609896d59a80d0149b4698596417805bbe3f:/IJHPCN/paper.tex

diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex
index 999ce37..063abb3 100644
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -786,6 +786,30 @@ taken into account with TSIRM.
 
 %%NEW
 
+{\bf example ex45/ksp Ã  dÃ©crire et commenter en montrant que hypre est pourri avec cet exemple}
+
+\begin{table*}[htbp]
+\begin{center}
+\begin{tabular}{|r|r|r|r|r|r|r|r|} 
+\hline
+
+  nb. cores   & \multicolumn{2}{c|}{FGMRES/ASM} & \multicolumn{2}{c|}{TSIRM CGLS/ASM} & gain& \multicolumn{2}{c|}{FGMRES/HYPRE}   \\ 
+\cline{2-5} \cline{7-8}
+                    & Time  & \# Iter.  & Time  & \# Iter. &        & Time  & \# Iter.   \\\hline \hline
+   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 &  --   \\
+
+\hline
+
+\end{tabular}
+\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.}
+\label{tab:06}
+\end{center}
+\end{table*}
+
+
 \subsection{Parallel nonlinear problems}
 
 With  PETSc,  linear  solvers  are  used inside  nonlinear  solvers.   The  SNES
@@ -799,10 +823,17 @@ classical solvers. Consequently, we have chosen  two of these examples: ex14 and
 ex20.  In ex14, the code solves the  Bratu (SFI - solid fuel ignition) nonlinear
 partial  difference equations  in 3  dimension.  In  ex20, the  code solves  a 3
 dimension radiative transport test problem.  For more details on these examples,
-interested readers are invited to see the code in the PETSc examples.
-
-In Table~\ref{tab:07} we  report the result of our experiments  for the example
-ex14. 
+interested readers are invited  to see the code in the  PETSc examples. For both
+these  examples,   a  weak  scaling   case  is  chosen  where   processors  have
+approximately a number of components equals to 100,000.
+
+In Table~\ref{tab:07}  we report the result  of our experiments for  the example
+ex14 with the block Jacobi preconditioner.  For TSIRM the CGLS algorithm is used
+to solve  the minimization step. In  this table, we  can see that the  number of
+iterations used by the linear solver is smaller with TSIRM compared with FGMRES.
+Consequently the execution times are smaller  with TSIRM. The gain between TSIRM
+and FGMRES  is around  6 and  7. The parameters  of TSIRM  are expressed  in the
+caption of the table.
 
 \begin{table*}[htbp]
 \begin{center}
@@ -812,10 +843,10 @@ ex14.
   nb. cores   & \multicolumn{2}{c|}{FGMRES/BJAC} & \multicolumn{2}{c|}{TSIRM CGLS/BJAC} & gain  \\ 
 \cline{2-5}
                     & Time         & \# Iter.  & Time   & \# Iter. &  \\\hline \hline
-   1024              & 159.52      & 11,584    &  26.34  &     1,563  &  6.06  \\
-   2048             & 226.24       & 16,459    &  37.23 &     2,248   &  6.08\\
-   4096             & 391.21     & 27,794   &  50.93 &   2,911  &  7.69\\
-   8192             & 543.23     & 37,770   &  79.21  &  4,324  & 6.86 \\
+   1,024              & 159.52      & 11,584    &  26.34  &     1,563  &  6.06  \\
+   2,048             & 226.24       & 16,459    &  37.23 &     2,248   &  6.08\\
+   4,096             & 391.21     & 27,794   &  50.93 &   2,911  &  7.69\\
+   8,192             & 543.23     & 37,770   &  79.21  &  4,324  & 6.86 \\
 
 \hline
 
@@ -825,6 +856,15 @@ ex14.
 \end{center}
 \end{table*}
 
+In Table~\cite{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
+increases. With  TSIRM, we can  see that the  number of iterations  is initially
+very small compared  to the FGMRES ones  and when the number  of cores increase,
+the number  of iterations increases slighther  with TSIRM than with  FGMRES. For
+this example,  the gain  between TSIRM  and FGMRES ranges  between 8  with 1,024
+cores to more than 16 with 8,192 cores.
 
 \begin{table*}[htbp]
 \begin{center}
@@ -834,10 +874,10 @@ ex14.
   nb. cores   & \multicolumn{2}{c|}{FGMRES/BJAC} & \multicolumn{2}{c|}{TSIRM CGLS/BJAC} & gain   \\ 
 \cline{2-5}
                     & Time         & \# Iter.  & Time   & \# Iter.  &  \\\hline \hline
-   1024              & 667.92      & 48,732    & 81.65  &     5,087 &  8.18 \\
-   2048             & 966.87       & 77,177    &  90.34 &     5,716 &  10.70\\
-   4096             & 1,742.31     & 124,411   &  119.21 &   6,905  & 14.61\\
-   8192             & 2,739.21     & 187,626   &  168.9  &  9,000   & 16.22\\
+   1,024              & 667.92      & 48,732    & 81.65  &     5,087 &  8.18 \\
+   2,048             & 966.87       & 77,177    &  90.34 &     5,716 &  10.70\\
+   4,096             & 1,742.31     & 124,411   &  119.21 &   6,905  & 14.61\\
+   8,192             & 2,739.21     & 187,626   &  168.9  &  9,000   & 16.22\\
 
 \hline
 
