From cc4027c25d11013054ab53d76fb2bfd562663820 Mon Sep 17 00:00:00 2001
From: raphael couturier <couturie@extinction>
Date: Mon, 8 Dec 2014 20:32:35 +0100
Subject: [PATCH] new

---
 krylov_multi_reviewed.tex | 46 +++++++++++++++++++++++++++++++++------
 1 file changed, 39 insertions(+), 7 deletions(-)

diff --git a/krylov_multi_reviewed.tex b/krylov_multi_reviewed.tex
index 228b2bd..1b041c9 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:}}
@@ -394,12 +395,7 @@ $743^3$ & 8,192 (4x2,048)        & 704.4     & 87,822    & 4.80e-07 &  110.3   &
 \end{table}
 
 
-\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:02}
-\end{figure}
+
 
 
 From these  experiments, it can be  observed that the  multisplitting version is
@@ -411,6 +407,42 @@ 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 iteration 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
-- 
2.39.5