suite

diff --git a/krylov_multi.tex b/krylov_multi.tex
index e51e232207ed9c08fd320d4e94d90f4c5ab2c917..a9d498f3a7dd49cc8645b41c0ca5b5f093d13459 100644 (file)
--- a/krylov_multi.tex
+++ b/krylov_multi.tex
@@ -272,23 +272,28 @@ it. In the following we presented  some experiments we could achieved out on the
 Hector architecture,  the previous UK's  high-end computing resource,  funded by
 the UK Research Councils, which has been stopped in the early 2014.
 
 Hector architecture,  the previous UK's  high-end computing resource,  funded by
 the UK Research Councils, which has been stopped in the early 2014.
 

-In the experiments  we report the size of the 3D  poisson considered\LZK[]{Suite\dots ?}
-
-
-The first column  shows the size of the  problem The size is chosen  in order to
-have approximately 50,000 components per core.  The second column represents the
+Table~\ref{tab1} shows  the result of  the experiments.  The first  column shows
+the  size of  the  3D Poisson  problem.  The size  is chosen  in  order to  have
+approximately  50,000 components  per core.   The second  column  represents the

 number of  cores used. In parenthesis,  there is the decomposition  used for the
 Krylov multisplitting. The  third column and the sixth  column respectively show
 the execution time for the GMRES  and the Kyrlow multisplitting code. The fourth
 number of  cores used. In parenthesis,  there is the decomposition  used for the
 Krylov multisplitting. The  third column and the sixth  column respectively show
 the execution time for the GMRES  and the Kyrlow multisplitting code. The fourth

-and  the   seventh  column   describes  the  number   of  iterations.   For  the
+and  the   seventh  column  describes   the  number  of  iterations.    For  the

 multisplitting  code, the  total number  of inner  iterations is  represented in
 multisplitting  code, the  total number  of inner  iterations is  represented in

-parenthesis.
+parenthesis. For  the GMRES code (alone  and in the  multisplitting version) the
+restart parameter is fixed to 16. The precision of the GMRES version is fixed to
+1e-6. For  the multisplitting,  there are two  precisions, one for  the external
+solver which is fixed to 1e-6 and another one for the inner solver (GMRES) which
+is fixed to 1e-10. It should be noted  that a high precision is used but we also
+fixed a  maximum number of  iterations for each  internal step. In  practise, we
+limit the  number of internal step to  10. So an internal  iteration is finished
+when the precision is reached or  when the maximum internal number of iterations
+is reached.
+

 
 

- We  also give  the other parameters:  the restart  for the GRMES method....\\

 
 

-\LZK{La seule remarque que j'ai pu tirée des deux tableaux c'est le fait qu'il y a plus de procs dans un cluster pour 2x4096 et c'est pour cette configuration qu'on a un bon speedup avec préconditionnement!!! Mais je ne sais pas toujours pourquoi?}

 
 

-\begin{table}[p]
+\begin{table}[htbp]

 \begin{center}
 \begin{tabular}{|c|c||c|c|c||c|c|c||c|} 
 \hline
 \begin{center}
 \begin{tabular}{|c|c||c|c|c||c|c|c||c|} 
 \hline


@@ -296,7 +301,8 @@ parenthesis.
  \cline{3-8}
            &                   &  Time (s) & nb Iter. & $\Delta$  &   Time (s)& nb Iter. & $\Delta$ & \\
 \hline
  \cline{3-8}
            &                   &  Time (s) & nb Iter. & $\Delta$  &   Time (s)& nb Iter. & $\Delta$ & \\
 \hline

-
+$468^3$ & 2048 (2x1024)        &  299.7    & 41,028    & 5.02e-8  &  48.4    & 691(6,146) & 8.24e-08  & 6.19   \\
+\hline

 $590^3$ & 4096 (2x2048)        &  433.1    & 55,494    & 4.92e-7  &  74.1    & 1,101(8,211) & 6.62e-08  & 5.84   \\
 \hline
 $743^3$ & 8192 (2x4096)        & 704.4     & 87,822    & 4.80e-07 &  151.2   & 3,061(14,914) & 5.87e-08 & 4.65    \\
 $590^3$ & 4096 (2x2048)        &  433.1    & 55,494    & 4.92e-7  &  74.1    & 1,101(8,211) & 6.62e-08  & 5.84   \\
 \hline
 $743^3$ & 8192 (2x4096)        & 704.4     & 87,822    & 4.80e-07 &  151.2   & 3,061(14,914) & 5.87e-08 & 4.65    \\


@@ -305,33 +311,17 @@ $743^3$ & 8192 (4x2048)        & 704.4     & 87,822    & 4.80e-07 &  110.3   & 1
 \hline
 
 \end{tabular}
 \hline
 
 \end{tabular}

-\caption{Results without preconditioner}
+\caption{Results}

 \label{tab1}
 \end{center}
 \end{table}
 
 
 \label{tab1}
 \end{center}
 \end{table}
 
 

-\begin{table}[p]
-\begin{center}
-\begin{tabular}{|c|c||c|c|c||c|c|c||c|} 
-\hline
-\multirow{2}{*}{Pb size}&\multirow{2}{*}{Nb. cores} &  \multicolumn{3}{c||}{GMRES} &  \multicolumn{3}{c||}{Krylov Multisplitting} & \multirow{2}{*}{Ratio}\\
- \cline{3-8}
-           &                   &  Time (s) & nb Iter. & $\Delta$  &   Time (s)& nb Iter. & $\Delta$ & \\
-\hline
-
-$590^3$ & 4096 (2x2048)        &  433.0    & 55,494    & 4.92e-7  &  80.4    & 1,091(9,545) & 7.64e-08  & 5.39   \\
-\hline
-$743^3$ & 8192 (2x4096)        & 704.4     & 87,822    & 4.80e-07 &  110.2   & 1,401(12,379) & 1.11e-07 & 6.39    \\
-\hline
-$743^3$ & 8192 (4x2048)        & 704.4     & 87,822    & 4.80e-07 &  139.8   & 1,891(15,960) & 1.60e-07& 5.03  \\
-\hline
-
-\end{tabular}
-\caption{Results with preconditioner}
-\label{tab2}
-\end{center}
-\end{table}
+From these  experiments, it can be  observed that the  multisplitting version is
+always  faster   than  the  GMRES   version.   The  acceleration  gain   of  the
+multisplitting version is between 4 and 6.  It can be noticed that the number of
+iteration is drastically reduced with  the multisplitting version even it is not
+neglectable.

 
 \section{Conclusion and perspectives}
 
 
 \section{Conclusion and perspectives}