X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/70f821453ece3cab916c2726ae554ca416493c41..a2c6056cb76ee160a5ad4afb5495207c9158a85c:/paper.tex

diff --git a/paper.tex b/paper.tex
index 8259385..e37e28c 100644
--- a/paper.tex
+++ b/paper.tex
@@ -717,7 +717,7 @@ of $40\%$ which is only around $24\%$ for the classical GMRES.
  \hline
  Grid Architecture & 4 $\times$ 8\\ %\hline
  Inter Network & $bw$=1Gbs - $lat$=5.10$^{-5}$ \\
- Input matrix size & $N_{x} \times N_{y} \times N_{z}$ = From 40$^{3}$ to 200$^{3}$\\ \hline
+ Input matrix size & $N_{x} \times N_{y} \times N_{z}$ = From 50$^{3}$ to 190$^{3}$\\ \hline
  \end{tabular}
 \caption{Test conditions: Input matrix size impacts}
 \label{tab:05}
@@ -731,20 +731,15 @@ of $40\%$ which is only around $24\%$ for the classical GMRES.
 \label{fig:05}
 \end{figure}
 
-In these experiments, the input matrix size  has been set from $N_{x} = N_{y}
-= N_{z} = 40$ to $200$ side elements  that is from $40^{3} = 64.000$ to $200^{3}
-= 8,000,000$  points. Obviously, as  shown in Figure~\ref{fig:05},  the execution
-time for  both algorithms increases when  the input matrix size  also increases.
-But the interesting results are:
-\begin{enumerate}
-  \item the important increase ($10$ times)  of the number of iterations needed to
-    reach the convergence for the classical GMRES algorithm particularly, when the matrix size
-    go beyond $N_{x}=150$; \RC{C'est toujours pas clair... ok le nommbre d'itérations est 10 fois plus long mais la suite de la phrase ne veut rien dire}
-    \RCE{Le nombre d'iterations augmente de 10 fois, cela surtout a partir de N=150}
-    
-\item the  classical GMRES execution time  is almost the double  for $N_{x}=140$
-  compared with the Krylov multisplitting method.
-\end{enumerate}
+In  these  experiments, the  input  matrix  size has  been  set  from $50^3$  to
+$190^3$. Obviously, as shown in Figure~\ref{fig:05}, the execution time for both
+algorithms increases when the input matrix size also increases.  For all problem
+sizes, GMRES is always slower than the Krylov multisplitting. Moreover, for this
+benchmark, it seems that  the greater the problem size is,  the bigger the ratio
+between both  algorithm execution  times is.  We can also  observ that  for some
+problem   sizes,  the   Krylov   multisplitting  convergence   varies  quite   a
+lot. Consequently the execution times in that cases also varies.
+
 
 These  findings may  help a  lot end  users to  setup the  best and  the optimal
 targeted environment for the application deployment when focusing on the problem