From 5933ab9497ff790a931894f60fa16b9949111ff9 Mon Sep 17 00:00:00 2001 From: couturie Date: Sat, 9 May 2015 18:24:17 +0200 Subject: [PATCH] suite --- paper.tex | 39 +++++++++++++++++++-------------------- 1 file changed, 19 insertions(+), 20 deletions(-) diff --git a/paper.tex b/paper.tex index 67599b9..4309369 100644 --- a/paper.tex +++ b/paper.tex @@ -488,7 +488,7 @@ SimGrid to simulate the grid environment. \paragraph{Simulation parameters for SimGrid} \ \\ \noindent Before running a SimGrid benchmark, many parameters for the computation platform must be defined. For our experiments, we consider platforms -in which several clusters are geographically distant, so there are intra and +in which several clusters are geographically distant, so that there are intra and inter-cluster communications. In the following, these parameters are described: \begin{itemize} @@ -563,8 +563,8 @@ the application to be tested. Numerical parallel iterative algorithms have been chosen for the study in this paper. \\ \textbf{Step 2}: Collect the software materials needed for the experimentation. -In our case, we have two variants algorithms for the resolution of the -3D-Poisson problem: (1) using the classical GMRES; (2) and the multisplitting +In our case, we have two variants for the resolution of the +3D-Poisson problem: (1) using the classical GMRES; (2) using the multisplitting method. In addition, the SimGrid simulator has been chosen to simulate the behaviors of the distributed applications. SimGrid is running in a virtual machine on a simple laptop. \\ @@ -580,7 +580,7 @@ have been configured in SimGrid : 2$\times$16, 4$\times$8, 4$\times$16, 8$\times represents the number of clusters in the grid and the second number represents the number of hosts (processors/cores) in each cluster. \\ -\textbf{Step 5}: Conduct an extensive and comprehensive testings +\textbf{Step 5}: Conduct extensive and comprehensive testings within these configurations by varying the key parameters, especially the CPU power capacity, the network parameters and also the size of the input data. \\ @@ -600,39 +600,38 @@ Another important factor impacting the overall performance of the application is the network configuration. Two main network parameters can modify drastically the program output results: \begin{enumerate} -\item the network bandwidth ($bw$ in bits/s) also known as "the data-carrying - capacity" of the network is defined as the maximum of data that can transit +\item the network bandwidth ($bw$ in Gbits/s) also known as "the data-carrying + capacity" of the network is defined as the maximum amount of data that can transit from one point to another in a unit of time. \item the network latency ($lat$ in microseconds) defined as the delay from the - start time to send a simple data from a source to a destination. + starting time to send a simple data from a source to a destination. \end{enumerate} -Upon the network characteristics, another impacting factor is the volume of data exchanged between the nodes in the cluster +Among the network characteristics, another impacting factor is the volume of data exchanged between the nodes in the cluster and between distant clusters. This parameter is application dependent. - In a grid environment, it is common to distinguish, on one hand, the + In a grid environment, it is common to distinguish, on the one hand, the \textit{intra-network} which refers to the links between nodes within a cluster and on the other hand, the \textit{inter-network} which is the backbone link between clusters. In practice, these two networks have different speeds. The intra-network generally works like a high speed - local network with a high bandwidth and very low latency. In opposite, the - inter-network connects clusters sometime via heterogeneous networks components - through internet with a lower speed. The network between distant clusters + local network with a high bandwidth and very low latency. On the contrary, the + inter-network connects clusters sometimes via heterogeneous networks components the through internet with a lower speed. The network between distant clusters might be a bottleneck for the global performance of the application. \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 +when the synchronous Krylov two-stage method has better performances than the +classical GMRES method. With a synchronous iterative method, better performances +mean a smaller number of iterations and execution time before reaching the convergence. Table~\ref{tab:01} summarizes the parameters used in the different simulations: the grid architectures (i.e. the number of clusters and the number of nodes per cluster), 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 +parameters of the intra-clusters links: the bandwidth $bw$=10Gbit/s and the latency $lat=8\mu$s. In what follows, we will present the test conditions, the output results and our comments. @@ -641,8 +640,8 @@ results and our comments. \begin{tabular}{ll} \hline Grid architecture & 2$\times$16, 4$\times$8, 4$\times$16 and 8$\times$8\\ -\multirow{2}{*}{Network inter-clusters} & $N1$: $bw$=10Gbs, $lat=8\mu$s \\ - & $N2$: $bw$=1Gbs, $lat=50\mu$s \\ +\multirow{2}{*}{Network inter-clusters} & $N1$: $bw$=10Gbit/s, $lat=8\mu$s \\ + & $N2$: $bw$=1Gbit/s, $lat=50\mu$s \\ \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$170 \\ \hline \end{tabular} @@ -705,7 +704,7 @@ efficient for distributed systems with high latency networks. \end{figure} \subsubsection{Network latency impacts on performances\\} -Figure~\ref{fig:03} shows the impact of the network latency on the performances of both algorithms. The simulation is conducted on a computational grid of 2 clusters of 16 processors each (i.e. configuration 2$\times$16) interconnected by a network of bandwidth $bw$=1Gbs to solve a 3D Poisson problem of size $150^3$. According to the results, a degradation of the network latency from $8\mu$s to $60\mu$s implies an absolute execution time increase for both algorithms, but not with the same rate of degradation. The GMRES algorithm is more sensitive to the latency degradation than the Krylov two-stage algorithm. +Figure~\ref{fig:03} shows the impact of the network latency on the performances of both algorithms. The simulation is conducted on a computational grid of 2 clusters of 16 processors each (i.e. configuration 2$\times$16) interconnected by a network of bandwidth $bw$=1Gbit/s to solve a 3D Poisson problem of size $150^3$. According to the results, a degradation of the network latency from $8\mu$s to $60\mu$s implies an absolute execution time increase for both algorithms, but not with the same rate of degradation. The GMRES algorithm is more sensitive to the latency degradation than the Krylov two-stage algorithm. \begin{figure}[ht] \centering @@ -719,7 +718,7 @@ Figure~\ref{fig:03} shows the impact of the network latency on the performances Figure~\ref{fig:04} reports the results obtained for the simulation of a grid of $2\times16$ processors interconnected by a network of latency $lat=50\mu$s to solve a 3D Poisson problem of size $150^3$. The results of increasing the -network bandwidth from $1$Gbs to $10$Gbs show the performances improvement for +network bandwidth from $1$Gbit/s to $10$Gbit/s show the performances improvement for both algorithms by reducing the execution times. However, the Krylov two-stage algorithm presents a better performance gain in the considered bandwidth interval with a gain of $40\%$ compared to only about $24\%$ for the classical -- 2.39.5