petites modifs 5.4.2

[rce2015.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 1fdc62bbe39f1bac97fac168282818107e6b9e58..24ddab9a5181b4cac5b4f9e5264ebaa158981912 100644 (file)
--- 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}
 
 \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
 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$^3$}
 \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}
 
 \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. $N2$}
 
 \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}
 
 \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 }
 \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
 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 }
 \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.
 
 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 }
 \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.
 
 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
 
 \begin{table} [htbp]
 \centering