X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/f63c6fdeff0469b90e60afdbaaf960959126aefc..538afc25a7a90630d2f90891d0a4d700bfe3460f:/paper.tex

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@@ -530,49 +530,55 @@ and  between distant  clusters.  This parameter is application dependent.
 
 
 \subsection{Comparison between GMRES and two-stage multisplitting algorithms in synchronous mode}
-In the scope of this paper, our first objective is to analyze when the synchronous Krylov two-stage method has better performance than the classical GMRES method. With a synchronous iterative method, better performance means a smaller number of iterations and execution time before reaching the convergence. In what follows, we will present the test conditions, the output results and our comments. For all simulations, we fix the network parameters of the intra-cluster links: the bandwidth $bw$=10Gbs and the latency $lat$=8$\times$10$^{-6}$.
+In the scope of this paper, our first objective is to analyze when the synchronous Krylov two-stage method has better performance than the classical GMRES method. With a synchronous iterative method, better performance means a smaller number of iterations and execution time before reaching the convergence.
 
-\subsubsection{Simulations for various grid architectures and scaling-up matrix sizes}
-\  \\
-% environment
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- The network of intra-clusters links has been
-designed to  operate with a bandwidth  equals to 10Gbits and a latency of 8$\times$10$^{-6}$ seconds. \\
-
-\RC{Je ne comprends plus rien CE : pourquoi dans 5.4.1 il y a 2 network et aussi dans 5.4.2. Quelle est la différence? Dans la figure 3 de la section 5.4.1 pourquoi il n'y a pas N1 et N2?}
+Table~\ref{tab:01} summarizes the parameters used in the different simulations: the grid architectures, the network of inter-clusters backbone links and the matrix sizes of the 3D Poisson problem. However, for all simulations we fix the network parameters of the intra-clusters links: the bandwidth $bw$=10Gbs and the latency $lat$=8$\times$10$^{-6}$. In what follows, we will present the test conditions, the output results and our comments. 
 
 \begin{table} [ht!]
 \begin{center}
-\begin{tabular}{ll }
- \hline
- Grid architecture & 2$\times$16, 4$\times$8, 4$\times$16 and 8$\times$8\\ %\hline
- \multirow{2}{*}{Network} & Inter (N2): $bw$=1Gbs, $lat$=5$\times$10$^{-5}$ \\ %\hline
-                          & Intra (N1): $bw$=10Gbs, $lat$=8$\times$10$^{-6}$ \\
- \multirow{2}{*}{Matrix size}  & N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$ =150 $\times$ 150 $\times$ 150\\ %\hline
-  &  N$_{x}$ $\times$ N$_{y}$ $\times$ N$_{z}$  =170 $\times$ 170 $\times$ 170    \\ \hline
- \end{tabular}
-\caption{Test conditions: various grid configurations with the matrix sizes 150$^3$ or 170$^3$}
-%\LZK{Ce sont les caractéristiques du réseau intra ou inter clusters? Ce n'est pas précisé...}
-%\RCE{oui c est precise}
+\begin{tabular}{ll}
+\hline
+Grid architecture                       & 2$\times$16, 4$\times$8, 4$\times$16 and 8$\times$8\\ 
+\multirow{2}{*}{Network inter-clusters} & $N1$: $bw$=1Gbs, $lat$=5$\times$10$^{-5}$ \\ 
+                                        & $N2$: $bw$=10Gbs, $lat$=8$\times$10$^{-6}$ \\
+\multirow{2}{*}{Matrix size}            & $Mat1$: N$_{x}\times$N$_{y}\times$N$_{z}$=150$\times$150$\times$150\\
+                                        & $Mat2$: N$_{x}\times$N$_{y}\times$N$_{z}$=170$\times$170$\times$170 \\ \hline
+\end{tabular}
+\caption{Parameters for the different simulations}
 \label{tab:01}
 \end{center}
 \end{table}
+
+\subsubsection{Simulations for various grid architectures and scaling-up matrix sizes}
+\  \\
+% environment
+In this section, we analyze the simulations conducted on various grid configurations and for different sizes of the 3D Poisson problem. The parameters of the network between clusters is fixed to $N1$ (see Table~\ref{tab:01}. Figure~\ref{fig:01} shows, for all grid configurations and a given matrix size 170$^3$ elements, a non-variation in the number of iterations for the classical GMRES algorithm, which is not the case of the Krylov two-stage algorithm.
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-In  this  section,  we  analyze   the  simulations  conducted  on  various  grid
-configurations presented  in Table~\ref{tab:01}. It  should be noticed  that two
-networks are considered: N1 is  the network between clusters (inter-cluster) and
-N2 is the network inside  a cluster (intra-cluster).  Figure~\ref{fig:01} shows,
-for all  grid configurations  and a  given matrix size,  a non-variation  in the
-number of iterations for the classical GMRES algorithm, which is not the case of
-the Krylov two-stage algorithm.
-%% First,  the results in  Figure~\ref{fig:01}
-%% show for all grid configurations the non-variation of the number of iterations of
-%% classical  GMRES for  a given  input matrix  size; it is not  the case  for the
-%% multisplitting method.
-%\RC{CE attention tu n'as pas mis de label dans tes figures, donc c'est le bordel, j'en mets mais vérifie...}
-%\RC{Les légendes ne sont pas explicites...}
-%\RCE{Corrige}
 
 \begin{figure} [htbp]
   \begin{center}