X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/blobdiff_plain/ac4df02370b008c7b6b76f2127b30eb5e745f842..f191ea095298626cf15138076b2e26ee4dec9b15:/paper.tex?ds=inline

diff --git a/paper.tex b/paper.tex
index 1fdc62b..24ddab9 100644
--- a/paper.tex
+++ b/paper.tex
@@ -549,9 +549,8 @@ Grid architecture                       & 2$\times$16, 4$\times$8, 4$\times$16 a
 \end{center}
 \end{table}
 
-\subsubsection{Simulations for various grid architectures and scaling-up matrix sizes}
-\  \\
-% environment
+\subsubsection{Simulations for various grid architectures and scaling-up matrix sizes\\}
+
 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    $N2$    (see
@@ -570,22 +569,33 @@ The execution times between both algorithms is significant with different grid a
 \includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
 \end{center}
 \caption{Various grid configurations with the matrix sizes 150$^3$ and 170$^3$}
+\LZK{CE, la légende de la Figure 3 est trop large. Remplacer les N$_x\times$N$_y\times$N$_z$ par $Mat1$=150$^3$ et $Mat2$=170$^3$ comme dans la Table 1}
 \label{fig:01}
 \end{figure}
 
-\subsubsection{Simulations for two different inter-clusters network speeds \\}
-
-In this section, the experiments  compare the  behavior of  the algorithms  running on a
-speeder inter-cluster  network (N2) and  also on  a less performant  network (N1) respectively defined in the test conditions Table~\ref{tab:02}.
-%\RC{Il faut définir cela avant...}
-Figure~\ref{fig:02} shows that end users will reduce the execution time
-for  both  algorithms when using  a  grid  architecture  like  4 $\times$ 16 or  8 $\times$ 8: the reduction factor is around $2$. The results depict  also that when
-the  network speed  drops down (variation of 12.5\%), the  difference between  the two Multisplitting algorithms execution times can reach more than 25\%.
+\subsubsection{Simulations for two different inter-clusters network speeds\\}
+In  Figure~\ref{fig:02} we  present the  execution times  of both  algorithms to
+solve a  3D Poisson problem of  size $150^3$ on two  different simulated network
+$N1$ and $N2$ (see Table~\ref{tab:01}). As previously mentioned, we can see from
+this figure  that the Krylov two-stage  algorithm is sensitive to  the number of
+clusters (i.e. it is better to have a small number of clusters). However, we can
+notice an  interesting behavior of  the Krylov  two-stage algorithm. It  is less
+sensitive to bad network bandwidth and latency for the inter-clusters links than
+the  GMRES algorithms.  This  means  that the  multisplitting  methods are  more
+efficient for distributed systems with high latency networks.
+
+%% In this section, the experiments  compare the  behavior of  the algorithms  running on a
+%% speeder inter-cluster  network (N2) and  also on  a less performant  network (N1) respectively defined in the test conditions Table~\ref{tab:02}.
+%% %\RC{Il faut définir cela avant...}
+%% Figure~\ref{fig:02} shows that end users will reduce the execution time
+%% for  both  algorithms when using  a  grid  architecture  like  4 $\times$ 16 or  8 $\times$ 8: the reduction factor is around $2$. The results depict  also that when
+%% the  network speed  drops down (variation of 12.5\%), the  difference between  the two Multisplitting algorithms execution times can reach more than 25\%.
 
 \begin{figure}[t]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
 \caption{Various grid configurations with networks $N1$ vs. $N2$}
+\LZK{CE, remplacer les ``,'' des décimales par un ``.''}
 \label{fig:02}
 \end{figure}
 
@@ -610,8 +620,21 @@ the  network speed  drops down (variation of 12.5\%), the  difference between  t
 
 
 
-\subsubsection{Network latency impacts on performance}
-\ \\
+
+
+
+
+
+
+
+
+
+
+
+
+
+\subsubsection{Network latency impacts on performance\\}
+
 \begin{table} [ht!]
 \centering
 \begin{tabular}{r c }
@@ -639,11 +662,11 @@ network  latency  from  $8.10^{-6}$  to $6.10^{-5}$  implies  an  absolute  time
 increase of more than $75\%$ (resp.   $82\%$) of the execution for the classical
 GMRES  (resp.   Krylov  multisplitting)  algorithm. The  execution  time  factor
 between the two algorithms  varies from 2.2 to 1.5 times  with a network latency
-decreasing from $8.10^{-6}$ to $6.10^{-5}$.
+decreasing from $8.10^{-6}$ to $6.10^{-5}$ second.
 
 
-\subsubsection{Network bandwidth impacts on performance}
-\ \\
+\subsubsection{Network bandwidth impacts on performance\\}
+
 \begin{table} [ht!]
 \centering
 \begin{tabular}{r c }
@@ -675,8 +698,8 @@ Figure~\ref{fig:04}). However,  in this  case, the Krylov  multisplitting method
 presents a better  performance in the considered bandwidth interval  with a gain
 of $40\%$ which is only around $24\%$ for the classical GMRES.
 
-\subsubsection{Input matrix size impacts on performance}
-\ \\
+\subsubsection{Input matrix size impacts on performance\\}
+
 \begin{table} [ht!]
 \centering
 \begin{tabular}{r c }
@@ -712,7 +735,8 @@ targeted environment for the application deployment when focusing on the problem
 size scale up.  It  should be noticed that the same test has  been done with the
 grid 4 $\times$ 8 leading to the same conclusion.
 
-\subsubsection{CPU Power impacts on performance}
+\subsubsection{CPU Power impacts on performance\\}
+
 
 \begin{table} [htbp]
 \centering