From 3b175ad474db1b6208b1115e91d0b5bfde6f0288 Mon Sep 17 00:00:00 2001 From: ziane Date: Fri, 8 May 2015 11:45:54 +0200 Subject: [PATCH] petites corrections section 5 --- paper.tex | 31 +++++++------------------------ 1 file changed, 7 insertions(+), 24 deletions(-) diff --git a/paper.tex b/paper.tex index 81afcf5..60fcffc 100644 --- a/paper.tex +++ b/paper.tex @@ -442,8 +442,6 @@ In this section, experiments for both multisplitting algorithms are reported. Fi \subsection{The 3D Poisson problem} \label{3dpoisson} - - We use our two-stage algorithms to solve the well-known Poisson problem $\nabla^2\phi=f$~\cite{Polyanin01}. In three-dimensional Cartesian coordinates in $\mathbb{R}^3$, the problem takes the following form: \begin{equation} \frac{\partial^2}{\partial x^2}\phi(x,y,z)+\frac{\partial^2}{\partial y^2}\phi(x,y,z)+\frac{\partial^2}{\partial z^2}\phi(x,y,z)=f(x,y,z)\mbox{~in the domain~}\Omega @@ -489,13 +487,7 @@ and on the other hand the execution time and the number of iterations to reach t simulated in the simulator tool to run the program. The following architectures have been configured in SimGrid : 2$\times$16, 4$\times$8, 4$\times$16, 8$\times$8 and 2$\times$50. The first number represents the number of clusters in the grid and the second number represents -the number of hosts (processors/cores) in each cluster. The network has been -designed to operate with a bandwidth equals to 10Gbits (resp. 1Gbits/s) and a -latency of 8.10$^{-6}$ seconds (resp. 5.10$^{-5}$) for the intra-clusters links -(resp. inter-clusters backbone links). \\ - -%\LZK{Il me semble que le bw et lat des deux réseaux varient dans les expés d'une simu à l'autre. On vire la dernière phrase?} -%\RC{il me semble qu'on peut laisser ca} +the number of hosts (processors/cores) in each cluster. \\ \textbf{Step 5}: Conduct an extensive and comprehensive testings within these configurations by varying the key parameters, especially @@ -536,26 +528,17 @@ and between distant clusters. This parameter is application dependent. a lower speed. The network between distant clusters might be a bottleneck for the global performance of the application. -\subsection{Comparison of GMRES and Krylov two-stage algorithms in synchronous mode} - -In the scope of this paper, our first objective is to analyze when the 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. -%%RAPH : on vire ca, c'est pas clair et pas important -%For a systematic study, the experiments should figure out that, for various -%grid parameters values, the simulator will confirm Multisplitting method better performance compared to classical GMRES, particularly on poor and slow networks. -%\LZK{Pas du tout claire la dernière phrase (For a systematic...)!!} -%\RCE { Reformule autrement} +\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}$. - - -%\subsubsection{Execution of the algorithms on various computational grid architectures and scaling up the input matrix size} \subsubsection{Simulations for various grid architectures and scaling-up matrix sizes} -\ \\ +\ \\ % environment + The network of intra-clusters links has been +designed to operate with a bandwidth equals to 10Gbits and a latency of 8$\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?} \begin{table} [ht!] -- 2.39.5