From fd6a9d41eaf24ef22ee658eb5da80ca4ea0df577 Mon Sep 17 00:00:00 2001 From: David Laiymani Date: Wed, 6 May 2015 16:23:42 +0200 Subject: [PATCH] =?utf8?q?DL=20:=20corrections=20exp=C3=A9?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit --- paper.tex | 53 ++++++++++++++++++++++++++--------------------------- 1 file changed, 26 insertions(+), 27 deletions(-) diff --git a/paper.tex b/paper.tex index e60e242..42f4b5d 100644 --- a/paper.tex +++ b/paper.tex @@ -465,19 +465,19 @@ and between distant clusters. This parameter is application dependent. In the scope of this paper, our first objective is to analyze when the Krylov Multisplitting method has better performances than the classical GMRES -method. With an iterative method, better performances mean a smaller number of -iterations and execution time before reaching the convergence. For a systematic -study, the experiments should figure out that, for various grid parameters -values, the simulator will confirm the targeted outcomes, particularly for poor -and slow networks, focusing on the impact on the communication performance on -the chosen class of algorithm. +method. With a synchronous iterative method, better performances mean a +smaller number of iterations and execution time before reaching the convergence. +For a systematic study, the experiments should figure out that, for various +grid parameters values, the simulator will confirm the targeted outcomes, +particularly for poor and slow networks, focusing on the impact on the +communication performance on the chosen class of algorithm. The following paragraphs present the test conditions, the output results and our comments.\\ -\subsubsection{Execution of the the algorithms on various computational grid -architecture and scaling up the input matrix size} +\subsubsection{Execution of the algorithms on various computational grid +architectures and scaling up the input matrix size} \ \\ % environment @@ -501,9 +501,9 @@ architecture and scaling up the input matrix size} In this section, we analyze the performences of algorithms running on various -grid configuration (2x16, 4x8, 4x16 and 8x8). First, the results in Figure~\ref{fig:01} -show for all grid configuration the non-variation of the number of iterations of -classical GMRES for a given input matrix size; it is not the case for the +grid configurations (2x16, 4x8, 4x16 and 8x8). 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...} @@ -524,9 +524,9 @@ grid architectures, even with the same number of processors (for example, 2x16 and 4x8). We can observ the low sensitivity of the Krylov multisplitting method (compared with the classical GMRES) when scaling up the number of the processors in the grid: in average, the GMRES (resp. Multisplitting) algorithm performs -40\% better (resp. 48\%) less when running from 2x16=32 to 8x8=64 processors. +$40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors. -\subsubsection{Running on two different speed cluster inter-networks} +\subsubsection{Running on two different inter-clusters network speed} \ \\ \begin{figure} [ht!] @@ -536,7 +536,7 @@ in the grid: in average, the GMRES (resp. Multisplitting) algorithm performs Grid & 2x16, 4x8\\ %\hline Network & N1 : bw=10Gbs-lat=8.10$^{-6}$ \\ %\hline - & N2 : bw=1Gbs-lat=5.10$^{-5}$ \\ - Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline + Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \end{tabular} \caption{Clusters x Nodes - Networks N1 x N2} \end{center} @@ -557,9 +557,10 @@ These experiments compare the behavior of the algorithms running first on a speed inter-cluster network (N1) and also on a less performant network (N2). Figure~\ref{fig:02} shows that end users will gain to reduce the execution time for both algorithms in using a grid architecture like 4x16 or 8x8: the -performance was increased in a factor of 2. The results depict also that when +performance was increased by a factor of $2$. The results depict also that when the network speed drops down (12.5\%), the difference between the execution times can reach more than 25\%. \RC{c'est pas clair : la différence entre quoi et quoi?} +\DL{pas clair} \subsubsection{Network latency impacts on performance} \ \\ @@ -571,7 +572,7 @@ times can reach more than 25\%. \RC{c'est pas clair : la différence entre quoi Network & N1 : bw=1Gbs \\ %\hline Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \end{tabular} -\caption{Network latency impact} +\caption{Network latency impacts} \end{figure} @@ -579,20 +580,20 @@ times can reach more than 25\%. \RC{c'est pas clair : la différence entre quoi \begin{figure} [ht!] \centering \includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf} -\caption{Network latency impact on execution time} +\caption{Network latency impacts on execution time} \label{fig:03} \end{figure} -According the results in Figure~\ref{fig:03}, a degradation of the network -latency from 8.10$^{-6}$ to 6.10$^{-5}$ implies an absolute time increase more -than 75\% (resp. 82\%) of the execution for the classical GMRES (resp. Krylov +According to the results of Figure~\ref{fig:03}, a degradation of the 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. In addition, it appears that the Krylov multisplitting method tolerates more the network latency variation with a less rate increase of the execution time. Consequently, in the worst case -(lat=6.10$^{-5 }$), the execution time for GMRES is almost the double than the +($lat=6.10^{-5 }$), the execution time for GMRES is almost the double than the time of the Krylov multisplitting, even though, the performance was on the same -order of magnitude with a latency of 8.10$^{-6}$. +order of magnitude with a latency of $8.10^{-6}$. \subsubsection{Network bandwidth impacts on performance} \ \\ @@ -604,19 +605,17 @@ order of magnitude with a latency of 8.10$^{-6}$. Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \\ \end{tabular} -\caption{Network bandwidth impact} +\caption{Network bandwidth impacts} \end{figure} \begin{figure} [ht!] \centering \includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf} -\caption{Network bandwith impact on execution time} +\caption{Network bandwith impacts on execution time} \label{fig:04} \end{figure} - - The results of increasing the network bandwidth show the improvement of the performance for both algorithms by reducing the execution time (see Figure~\ref{fig:04}). However, in this case, the Krylov multisplitting method @@ -630,7 +629,7 @@ of 40\% which is only around 24\% for classical GMRES. \begin{tabular}{r c } \hline Grid & 4x8\\ %\hline - Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ + Network & N2 : bw=1Gbs - lat=5.10$^{-5}$ \\ Input matrix size & N$_{x}$ = From 40 to 200\\ \hline \end{tabular} \caption{Input matrix size impact} -- 2.39.5