From: couturie <raphael.couturier@univ-fcomte.Fr>
Date: Wed, 6 May 2015 08:59:47 +0000 (+0200)
Subject: Merge branch 'master' of ssh://bilbo.iut-bm.univ-fcomte.fr/rce2015
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rce2015.git/commitdiff_plain/c3bff7fe72edcd1226a6248d1c1d799bd98e9e34?ds=sidebyside;hp=-c

Merge branch 'master' of ssh://bilbo.iut-bm.univ-fcomte.fr/rce2015
---

c3bff7fe72edcd1226a6248d1c1d799bd98e9e34
diff --combined paper.tex
index 31e2676,a1c1889..6affca8
--- a/paper.tex
+++ b/paper.tex
@@@ -317,12 -317,10 +317,12 @@@ suppress all global variables by replac
  Simgrid      selector       called      "runtime       automatic      switching"
  (smpi/privatize\_global\_variables). Indeed, global  variables can generate side
  effects on runtime between the threads running in the same process, generated by
 -Simgrid  to simulate the  grid environment.  \RC{On vire cette  phrase ?} \RCE {Si c'est la phrase d'avant sur les threads, je pense qu'on peut la retenir car c'est l'explication du pourquoi Simgrid n'aime pas les variables globales. Si c'est pas bien dit, on peut la reformuler. Si c'est la phrase ci-apres, effectivement, on peut la virer si elle preterais a discussion}The
 -last modification on the  MPI program pointed out for some  cases, the review of
 -the sequence of  the MPI\_Isend, MPI\_Irecv and  MPI\_Waitall instructions which
 -might cause an infinite loop.
 +Simgrid  to simulate the  grid environment.
 +
 +%\RC{On vire cette  phrase ?} \RCE {Si c'est la phrase d'avant sur les threads, je pense qu'on peut la retenir car c'est l'explication du pourquoi Simgrid n'aime pas les variables globales. Si c'est pas bien dit, on peut la reformuler. Si c'est la phrase ci-apres, effectivement, on peut la virer si elle preterais a discussion}The
 +%last modification on the  MPI program pointed out for some  cases, the review of
 +%the sequence of  the MPI\_Isend, MPI\_Irecv and  MPI\_Waitall instructions which
 +%might cause an infinite loop.
  
  
  \paragraph{Simgrid Simulator parameters}
@@@ -352,7 -350,7 +352,7 @@@ In addition, the following arguments ar
  	\item matrix diagonal value = 6.0 for synchronous Krylov multisplitting experiments and 6.2 for asynchronous block Jacobi experiments; \RC{CE tu vérifies, je dis ca de tête}
  	\item matrix off-diagonal value;
  	\item execution mode: synchronous or asynchronous;
 -	\RCE {C'est ok la liste des arguments du programme mais si Lilia ou toi pouvez preciser pour les  arguments pour CGLS ci dessous}
 +	\RCE {C'est ok la liste des arguments du programme mais si Lilia ou toi pouvez preciser pour les  arguments pour CGLS ci dessous} \RC{Vu que tu n'as pas fait varier ce paramètre, on peut ne pas en parler}
  	\item Size of matrix S;
  	\item Maximum number of iterations and tolerance threshold for CGLS. 
  \end{itemize}
@@@ -365,10 -363,7 +365,10 @@@ It should also be noticed that both sol
  \section{Experimental Results}
  \label{sec:expe}
  
 -In this section, experiments for both Multisplitting algorithms are reported. First the problem used in our experiments is described.
 +In this section, experiments for both Multisplitting algorithms are reported. First the 3D Poisson problem used in our experiments is described.
 +
 +\subsection{3D Poisson}
 +
  
  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}
@@@ -382,16 -377,13 +382,13 @@@ such tha
  where the real-valued function $\phi(x,y,z)$ is the solution sought, $f(x,y,z)$ is a known function and $\Omega=[0,1]^3$. The 3D discretization of the Laplace operator $\nabla^2$ with the finite difference scheme includes 7 points stencil on the computational grid. The numerical approximation of the Poisson problem on three-dimensional grid is repeatedly computed as $\phi=\phi^\star$ such that      
  \begin{equation}
  \begin{array}{ll}
- \phi^\star(x,y,z)= & \frac{1}{6}(\phi(x-h,y,z)+\phi(x+h,y,z) \\
-                   & +\phi(x,y-h,z)+\phi(x,y+h,z) \\
-                   & +\phi(x,y,z-h)+\phi(x,y,z+h)\\
-                   & -h^2f(x,y,z))
+ \phi^\star(x,y,z)=&\frac{1}{6}(\phi(x-h,y,z)+\phi(x,y-h,z)+\phi(x,y,z-h)\\&+\phi(x+h,y,z)+\phi(x,y+h,z)+\phi(x,y,z+h)\\&-h^2f(x,y,z))
  \end{array}
  \label{eq:08}
  \end{equation}
  until convergence where $h$ is the grid spacing between two adjacent elements in the 3D computational grid. 
  
- In the parallel context, the 3D Poisson problem is partitioned into $L\times p$ sub-problems such that $L$ is the number of clusters and $p$ is the number of processors in each cluster. We apply the three-dimensional partitioning instead of the row-by-row one in order to reduce the size of the data shared at the sub-problems boundaries. In this case, each processor is in charge of parallelepipedic sub-problem and has at most six neighbors in the same cluster or in distant clusters with which it shares data at boundaries. 
+ In the parallel context, the 3D Poisson problem is partitioned into $L\times p$ sub-problems such that $L$ is the number of clusters and $p$ is the number of processors in each cluster. We apply the three-dimensional partitioning instead of the row-by-row one in order to reduce the size of the data shared at the sub-problems boundaries. In this case, each processor is in charge of parallelepipedic block of the problem and has at most six neighbors in the same cluster or in distant clusters with which it shares data at boundaries. 
  
  \subsection{Study setup and Simulation Methodology}
  
@@@ -464,25 -456,28 +461,25 @@@ transit between the clusters and nodes 
   speed.  The network  between distant  clusters might  be a  bottleneck for  the
   global performance of the application.
  
 -\subsection{Comparing GMRES and Multisplitting algorithms in
 +\subsection{Comparison of GMRES and Krylov Multisplitting algorithms in
  synchronous mode}
  
 -In the scope of this paper, our first objective is to demonstrate the
 -Algo-2 (Multisplitting method) shows a better performance in grid
 -architecture compared with Algo-1 (Classical GMRES) both running in
 -\textit{synchronous mode}. Better algorithm performance
 -should means a less number of iterations output and a less 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.
 +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.
  
  The following paragraphs present the test conditions, the output results
  and our comments.\\
  
  
 -\textit{3.a Executing the algorithms on various computational grid
 +\subsubsection{Execution of the the algorithms on various computational grid
  architecture and scaling up the input matrix size}
 -\\
 -
 +\ \\
  % environment
  \begin{footnotesize}
  \begin{tabular}{r c }