X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/Krylov_multi.git/blobdiff_plain/c9242f9fee68ee32282c6b18679048eb4c3056b4..94fdd01d0a73ca3bb8fd2c3afe8a49af5774595a:/krylov_multi_reviewed.tex?ds=sidebyside

diff --git a/krylov_multi_reviewed.tex b/krylov_multi_reviewed.tex
index 73881ba..4cad7d7 100644
--- a/krylov_multi_reviewed.tex
+++ b/krylov_multi_reviewed.tex
@@ -8,7 +8,8 @@
 \usepackage{multirow}
 \usepackage{authblk}
 
-\algnewcommand\algorithmicinput{\textbf{Input:}}
+
+\algnewcommand\algorithmicinput{\textbf{I1nput:}}
 \algnewcommand\Input{\item[\algorithmicinput]}
 
 \algnewcommand\algorithmicoutput{\textbf{Output:}}
@@ -394,6 +395,9 @@ $743^3$ & 8,192 (4x2,048)        & 704.4     & 87,822    & 4.80e-07 &  110.3   &
 \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 ranges between 4 and 6.  It can be noticed that the number of
@@ -403,6 +407,40 @@ better performance than simply using 2 clusters. In fact, we can notice that the
 precision with 2 clusters is slightly  better but in both cases the precision is
 under the specified threshold.
 
+
+%%% AJOUTE************************
+%%%*******************************
+In Figure~\ref{fig:01}, the number of iterations per second is reported for both
+GMRES and the  multisplitting methods. It should be noted that  we took only the
+inner number  of iterations (i.e.  the GMRES iterations) for  the multisplitting
+method. Iterations of CGNR are not  taken into account. From this figure, it can
+be seen that the  number of iterations per second is higher  with GMRES but it is
+not  so different  with the  multisplitting method.  For the  case  with $8,192$
+cores,  the number of  iterations per  second with  4 clusters  is approximately
+equals to 115. So it is not different from GMRES.
+
+
+\begin{figure}[htbp]
+\centering
+  \includegraphics[width=0.7\textwidth]{nb_iter_sec}
+\caption{Number of iterations per second  with the same parameters as in Table~\ref{tab1} (weak scaling) with only 2 clusters}
+\label{fig:01}
+\end{figure}
+
+
+\noindent {\bf Final remarks:}\\
+It should  be noted, on  the one  hand, that the  development of a  complete new
+method usable with any  kind of problem is a really long  and fastidious task if
+one is working from  scratch. On the other hand, using an  existing tool for the
+inner solver is also not easy because it requires to make link between the inner
+solver  and the outer  one.  We  plan to  do that  later with  engineers working
+specifically on  that point.  Moreover,  we think that  it is very  important to
+analyze the convergence  of this method compared to other  method. In this work,
+we have  focused on the  description of this  method and its performance  with a
+typical application. Many other investigations are required for this method as explained in the next section.
+%%%*******************************
+%%%*******************************
+
 \section{Conclusion and perspectives}
 We  have implemented  a  Krylov  multisplitting method  to  solve sparse  linear
 systems  on large-scale computing  platforms.  We  have developed  a synchronous