X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/GMRES2stage.git/blobdiff_plain/df562f71fc6dcfdbb4e0b77f138977ca7219df6f..49d3ad986610c9438c522b61b9c1f57ebe4b824e:/IJHPCN/paper.tex

diff --git a/IJHPCN/paper.tex b/IJHPCN/paper.tex
index 0c88f29..abe4b2d 100644
--- a/IJHPCN/paper.tex
+++ b/IJHPCN/paper.tex
@@ -511,7 +511,7 @@ Table~\ref{tab:01}.  These  latter, which are  real-world applications matrices,
 have    been   extracted    from   the    Davis   collection,    University   of
 Florida~\cite{Dav97}.
 
-\begin{table}[htbp]
+\begin{table*}[htbp]
 \begin{center}
 \begin{tabular}{|c|c|r|r|r|} 
 \hline
@@ -528,7 +528,7 @@ torso3             & 2D/3D problem & 259,156 & 4,429,042 \\
 \caption{Main characteristics of the sparse matrices chosen from the Davis collection}
 \label{tab:01}
 \end{center}
-\end{table}
+\end{table*}
 Chosen parameters  are detailed below.   
 We have  stopped  the  GMRES every  30
 iterations (\emph{i.e.}, $max\_iter_{kryl}=30$), which is the default 
@@ -550,7 +550,7 @@ fact this also depends on two parameters: the number of iterations before stoppi
 and the number of iterations to perform the minimization.
 
 
-\begin{table}[htbp]
+\begin{table*}[htbp]
 \begin{center}
 \begin{tabular}{|c|c|r|r|r|r|} 
 \hline
@@ -571,7 +571,7 @@ torso3             & fgmres / sor  & 37.70 & 565 & 34.97 & 510 \\
 \caption{Comparison between sequential standalone (F)GMRES and TSIRM with (F)GMRES (time in seconds).}
 \label{tab:02}
 \end{center}
-\end{table}
+\end{table*}
 
 
 
@@ -638,7 +638,7 @@ preconditioners in PETSc, readers are referred to~\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) having 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.}
+\caption{Comparison of FGMRES and TSIRM with FGMRES for example ex15 of PETSc/KSP with two preconditioners (mg and sor) having 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*}
@@ -710,7 +710,7 @@ 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 ($max\_iter_{kryl}=30$, $s=12$, $max\_iter_{ls}=15$, $\epsilon_{ls}=1e-40$),  time is expressed in seconds.}
+\caption{Comparison of FGMRES  and TSIRM with FGMRES algorithms for ex54 of PETSc/KSP (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*}
@@ -769,7 +769,7 @@ taken into account with TSIRM.
 \hline
 
 \end{tabular}
-\caption{Comparison of FGMRES  and TSIRM 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.}
+\caption{Comparison of FGMRES  and TSIRM for ex54 of PETSc/KSP (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*}
@@ -784,7 +784,7 @@ taken into account with TSIRM.
 
 Concerning the  experiments some  other remarks are  interesting.
 \begin{itemize}
-\item We have tested other examples  of PETSc (ex29, ex45, ex49).  For all these
+\item We have tested other examples  of PETSc/KSP (ex29, ex45, ex49).  For all these
   examples,  we have also  obtained similar  gains between  GMRES and  TSIRM but
   those  examples are  not scalable  with many  cores. In  general, we  had some
   problems with more than $4,096$ cores.
@@ -805,6 +805,82 @@ Concerning the  experiments some  other remarks are  interesting.
 %%%*********************************************************
 
 
+%%NEW
+\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 25,000 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*}
+
+
+\begin{figure}[htbp]
+\centering
+  \includegraphics[width=0.5\textwidth]{nb_iter_sec_ex45_curie}
+\caption{Number of iterations per second with ex45 and the same parameters as in Table~\ref{tab:06} (weak scaling)}
+\label{fig:03}
+\end{figure}
+
+
+
+\begin{table*}[htbp]
+\begin{center}
+\begin{tabular}{|r|r|r|r|r|r|} 
+\hline
+
+  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\\
+
+\hline
+
+\end{tabular}
+\caption{Comparison of FGMRES  and TSIRM for ex20 of PETSc/SNES with a Block Jacobi  preconditioner  having 100,000 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:07}
+\end{center}
+\end{table*}
+
+\begin{table*}[htbp]
+\begin{center}
+\begin{tabular}{|r|r|r|r|r|r|} 
+\hline
+
+  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 \\
+
+\hline
+
+\end{tabular}
+\caption{Comparison of FGMRES  and TSIRM for ex14 of PETSc/SNES with a Block Jacobi  preconditioner  having 100,000 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:08}
+\end{center}
+\end{table*}
+
+
+%%ENDNEW
 
 %%%*********************************************************
 %%%*********************************************************