modif

[GMRES2stage.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 1db9b1980a50848a191aba70abdea17c496bc16a..c66f8c71ae1ec2704b0db181df987640f4a3d97f 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -353,6 +353,7 @@
 \usepackage{algpseudocode}
 \usepackage{amsmath}
 \usepackage{amssymb}
 \usepackage{algpseudocode}
 \usepackage{amsmath}
 \usepackage{amssymb}

+\usepackage{multirow}

 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}
 
 \algnewcommand\algorithmicinput{\textbf{Input:}}
 \algnewcommand\Input{\item[\algorithmicinput]}


@@ -667,7 +668,8 @@ reused with the new values of the residuals.
 In order to see the influence of our algorithm with only one processor, we first
 show  a comparison  with the  standard version  of GMRES  and our  algorithm. In
 table~\ref{tab:01},  we  show  the  matrices  we  have used  and  some  of  them
 In order to see the influence of our algorithm with only one processor, we first
 show  a comparison  with the  standard version  of GMRES  and our  algorithm. In
 table~\ref{tab:01},  we  show  the  matrices  we  have used  and  some  of  them

-characteristics.
+characteristics. For all  the matrices, the name, the field,  the number of rows
+and the number of nonzero elements is given.

 
 \begin{table}
 \begin{center}
 
 \begin{table}
 \begin{center}


@@ -688,29 +690,43 @@ torso3             & 2D/3D problem & 259,156 & 4,429,042 \\
 \end{center}
 \end{table}
 
 \end{center}
 \end{table}
 

+In  table~\ref{tab:02}, some  experiments comparing  the sovling  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
+gmres or fgmres is used to  solve the linear system.  According to the matrices,
+different preconditioner is used.  With the 2  stage algorithm, the same
+solver and the same preconditionner is used.

 
 
 
 

+\begin{table}
+\begin{center}
+\begin{tabular}{|c|c|r|r|r|r|} 
+\hline
+
+ \multirow{2}{*}{Matrix name}  & Solver /   & \multicolumn{2}{c|}{gmres variant} & \multicolumn{2}{c|}{2 stage} \\
+       &  precond             & Time  & \# Iter.  & Time  & \# Iter.  \\\hline \hline

 
 

-%% \begin{table}
-%% \begin{center}
-%% \begin{tabular}{|c|c|r|r|r|} 
-%% \hline
+crashbasis         & gmres / none             &  15.65     & 518  &  14.12 & 450  \\
+parabolic\_fem     & gmres / ilu           & 1009.94   & 7573 & 401.52 & 2970 \\
+epb3               & fgmres / sor             &  8.67     & 600  &  8.21 & 540  \\
+atmosmodj          &  fgmres / sor & 104.23  & 451 & 88.97 & 366  \\
+bfwa398            & gmres / none  & 1.42 & 9612 & 0.28 & 1650 \\
+torso3             & fgmres/sor  & 565  & 37.70 & 34.97 & 510 \\
+\hline

 
 

-%%  Matrix name       & GMRES version             &\# Rows   & \# Nonzeros   \\\hline \hline
+\end{tabular}
+\caption{Comparison of GMRES and 2 stage GMRES algorithms in sequential with some matrices, time is expressed in seconds.}
+\label{tab:02}
+\end{center}
+\end{table}

 
 

-%% crashbasis         & GMRES              & Optimization      & 160,000  &  1,750,416  \\
-%% parabolic\_fem     &                    & Computational fluid dynamics  & 525,825 & 2,100,225 \\
-%% epb3               &                    & Thermal problem   & 84,617  & 463,625  \\
-%% atmosmodj          & Computational fluid dynamics  & 1,270,432 & 8,814,880 \\
-%% bfwa398            & Electromagnetics problem & 398 & 3,678 \\
-%% torso3             & 2D/3D problem & 259,156 & 4,429,042 \\
-%% \hline

 
 

-%% \end{tabular}
-%% \caption{Comparison of GMRES and 2 stage GMRES algorithms in sequential with some matrices}
-%% \label{tab:01}
-%% \end{center}
-%% \end{table}
+Param : retart 30 iters
+cols = 8
+iter cgls = 20
+cgls prec = 1e-40
+prec = 1e-10
+Intel(R) Core(TM) i7-3630QM CPU @ 2.40GHz

 
 
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