X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/fadf3e9c2be61f86ddebab4672ca769096168535..d9f21083ce58fea2feb0ad4a9d6e3c7944aa644f:/hpcc.tex

diff --git a/hpcc.tex b/hpcc.tex
index b4d0be3..9fcb5d8 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -1,417 +1,200 @@
-
-%% bare_conf.tex
-%% V1.3
-%% 2007/01/11
-%% by Michael Shell
-%% See:
-%% http://www.michaelshell.org/
-%% for current contact information.
-%%
-%% This is a skeleton file demonstrating the use of IEEEtran.cls
-%% (requires IEEEtran.cls version 1.7 or later) with an IEEE conference paper.
-%%
-%% Support sites:
-%% http://www.michaelshell.org/tex/ieeetran/
-%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
-%% and
-%% http://www.ieee.org/
-
-%%*************************************************************************
-%% Legal Notice:
-%% This code is offered as-is without any warranty either expressed or
-%% implied; without even the implied warranty of MERCHANTABILITY or
-%% FITNESS FOR A PARTICULAR PURPOSE! 
-%% User assumes all risk.
-%% In no event shall IEEE or any contributor to this code be liable for
-%% any damages or losses, including, but not limited to, incidental,
-%% consequential, or any other damages, resulting from the use or misuse
-%% of any information contained here.
-%%
-%% All comments are the opinions of their respective authors and are not
-%% necessarily endorsed by the IEEE.
-%%
-%% This work is distributed under the LaTeX Project Public License (LPPL)
-%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
-%% distributed and modified. A copy of the LPPL, version 1.3, is included
-%% in the base LaTeX documentation of all distributions of LaTeX released
-%% 2003/12/01 or later.
-%% Retain all contribution notices and credits.
-%% ** Modified files should be clearly indicated as such, including  **
-%% ** renaming them and changing author support contact information. **
-%%
-%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
-%%                    bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex
-%%*************************************************************************
-
-% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
-% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
-% *** with production work. IEEE's font choices can trigger bugs that do  ***
-% *** not appear when using other class files.                            ***
-% The testflow support page is at:
-% http://www.michaelshell.org/tex/testflow/
-
-
-
-% Note that the a4paper option is mainly intended so that authors in
-% countries using A4 can easily print to A4 and see how their papers will
-% look in print - the typesetting of the document will not typically be
-% affected with changes in paper size (but the bottom and side margins will).
-% Use the testflow package mentioned above to verify correct handling of
-% both paper sizes by the user's LaTeX system.
-%
-% Also note that the "draftcls" or "draftclsnofoot", not "draft", option
-% should be used if it is desired that the figures are to be displayed in
-% draft mode.
-%
 \documentclass[conference]{IEEEtran}
-% Add the compsoc option for Computer Society conferences.
-%
-% If IEEEtran.cls has not been installed into the LaTeX system files,
-% manually specify the path to it like:
-% \documentclass[conference]{../sty/IEEEtran}
-
-
-
-
-
-% Some very useful LaTeX packages include:
-% (uncomment the ones you want to load)
-
-
-% *** CITATION PACKAGES ***
-%
-%\usepackage{cite}
-% cite.sty was written by Donald Arseneau
-% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
-% \cite{} output to follow that of IEEE. Loading the cite package will
-% result in citation numbers being automatically sorted and properly
-% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
-% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
-% \cite will automatically add leading space, if needed. Use cite.sty's
-% noadjust option (cite.sty V3.8 and later) if you want to turn this off.
-% cite.sty is already installed on most LaTeX systems. Be sure and use
-% version 4.0 (2003-05-27) and later if using hyperref.sty. cite.sty does
-% not currently provide for hyperlinked citations.
-% The latest version can be obtained at:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
-% The documentation is contained in the cite.sty file itself.
-
-
-
-
-
-
-% *** GRAPHICS RELATED PACKAGES ***
-%
-\ifCLASSINFOpdf
-  % \usepackage[pdftex]{graphicx}
-  % declare the path(s) where your graphic files are
-  % \graphicspath{{../pdf/}{../jpeg/}}
-  % and their extensions so you won't have to specify these with
-  % every instance of \includegraphics
-  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
-\else
-  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
-  % will default to the driver specified in the system graphics.cfg if no
-  % driver is specified.
-  % \usepackage[dvips]{graphicx}
-  % declare the path(s) where your graphic files are
-  % \graphicspath{{../eps/}}
-  % and their extensions so you won't have to specify these with
-  % every instance of \includegraphics
-  % \DeclareGraphicsExtensions{.eps}
-\fi
-% graphicx was written by David Carlisle and Sebastian Rahtz. It is
-% required if you want graphics, photos, etc. graphicx.sty is already
-% installed on most LaTeX systems. The latest version and documentation can
-% be obtained at: 
-% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
-% Another good source of documentation is "Using Imported Graphics in
-% LaTeX2e" by Keith Reckdahl which can be found as epslatex.ps or
-% epslatex.pdf at: http://www.ctan.org/tex-archive/info/
-%
-% latex, and pdflatex in dvi mode, support graphics in encapsulated
-% postscript (.eps) format. pdflatex in pdf mode supports graphics
-% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
-% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
-% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
-% which can result in "jaggedy"/blurry rendering of lines and letters as
-% well as large increases in file sizes.
-%
-% You can find documentation about the pdfTeX application at:
-% http://www.tug.org/applications/pdftex
-
-
-
-
-
-% *** MATH PACKAGES ***
-%
-%\usepackage[cmex10]{amsmath}
-% A popular package from the American Mathematical Society that provides
-% many useful and powerful commands for dealing with mathematics. If using
-% it, be sure to load this package with the cmex10 option to ensure that
-% only type 1 fonts will utilized at all point sizes. Without this option,
-% it is possible that some math symbols, particularly those within
-% footnotes, will be rendered in bitmap form which will result in a
-% document that can not be IEEE Xplore compliant!
-%
-% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
-% thus preventing page breaks from occurring within multiline equations. Use:
-%\interdisplaylinepenalty=2500
-% after loading amsmath to restore such page breaks as IEEEtran.cls normally
-% does. amsmath.sty is already installed on most LaTeX systems. The latest
-% version and documentation can be obtained at:
-% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/
-
-
-
-
-
-% *** SPECIALIZED LIST PACKAGES ***
-%
-%\usepackage{algorithmic}
-% algorithmic.sty was written by Peter Williams and Rogerio Brito.
-% This package provides an algorithmic environment fo describing algorithms.
-% You can use the algorithmic environment in-text or within a figure
-% environment to provide for a floating algorithm. Do NOT use the algorithm
-% floating environment provided by algorithm.sty (by the same authors) or
-% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
-% algorithm float types and packages that provide these will not provide
-% correct IEEE style captions. The latest version and documentation of
-% algorithmic.sty can be obtained at:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
-% There is also a support site at:
-% http://algorithms.berlios.de/index.html
-% Also of interest may be the (relatively newer and more customizable)
-% algorithmicx.sty package by Szasz Janos:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/
-
-
-
-
-% *** ALIGNMENT PACKAGES ***
-%
-%\usepackage{array}
-% Frank Mittelbach's and David Carlisle's array.sty patches and improves
-% the standard LaTeX2e array and tabular environments to provide better
-% appearance and additional user controls. As the default LaTeX2e table
-% generation code is lacking to the point of almost being broken with
-% respect to the quality of the end results, all users are strongly
-% advised to use an enhanced (at the very least that provided by array.sty)
-% set of table tools. array.sty is already installed on most systems. The
-% latest version and documentation can be obtained at:
-% http://www.ctan.org/tex-archive/macros/latex/required/tools/
-
-
-%\usepackage{mdwmath}
-%\usepackage{mdwtab}
-% Also highly recommended is Mark Wooding's extremely powerful MDW tools,
-% especially mdwmath.sty and mdwtab.sty which are used to format equations
-% and tables, respectively. The MDWtools set is already installed on most
-% LaTeX systems. The lastest version and documentation is available at:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/mdwtools/
-
-
-% IEEEtran contains the IEEEeqnarray family of commands that can be used to
-% generate multiline equations as well as matrices, tables, etc., of high
-% quality.
-
-
-%\usepackage{eqparbox}
-% Also of notable interest is Scott Pakin's eqparbox package for creating
-% (automatically sized) equal width boxes - aka "natural width parboxes".
-% Available at:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/eqparbox/
-
-
-
-
-
-% *** SUBFIGURE PACKAGES ***
-%\usepackage[tight,footnotesize]{subfigure}
-% subfigure.sty was written by Steven Douglas Cochran. This package makes it
-% easy to put subfigures in your figures. e.g., "Figure 1a and 1b". For IEEE
-% work, it is a good idea to load it with the tight package option to reduce
-% the amount of white space around the subfigures. subfigure.sty is already
-% installed on most LaTeX systems. The latest version and documentation can
-% be obtained at:
-% http://www.ctan.org/tex-archive/obsolete/macros/latex/contrib/subfigure/
-% subfigure.sty has been superceeded by subfig.sty.
-
-
-
-%\usepackage[caption=false]{caption}
-%\usepackage[font=footnotesize]{subfig}
-% subfig.sty, also written by Steven Douglas Cochran, is the modern
-% replacement for subfigure.sty. However, subfig.sty requires and
-% automatically loads Axel Sommerfeldt's caption.sty which will override
-% IEEEtran.cls handling of captions and this will result in nonIEEE style
-% figure/table captions. To prevent this problem, be sure and preload
-% caption.sty with its "caption=false" package option. This is will preserve
-% IEEEtran.cls handing of captions. Version 1.3 (2005/06/28) and later 
-% (recommended due to many improvements over 1.2) of subfig.sty supports
-% the caption=false option directly:
-%\usepackage[caption=false,font=footnotesize]{subfig}
-%
-% The latest version and documentation can be obtained at:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/
-% The latest version and documentation of caption.sty can be obtained at:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/caption/
-
-
-
-
-% *** FLOAT PACKAGES ***
-%
-%\usepackage{fixltx2e}
-% fixltx2e, the successor to the earlier fix2col.sty, was written by
-% Frank Mittelbach and David Carlisle. This package corrects a few problems
-% in the LaTeX2e kernel, the most notable of which is that in current
-% LaTeX2e releases, the ordering of single and double column floats is not
-% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
-% single column figure to be placed prior to an earlier double column
-% figure. The latest version and documentation can be found at:
-% http://www.ctan.org/tex-archive/macros/latex/base/
-
-
-
-%\usepackage{stfloats}
-% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
-% the ability to do double column floats at the bottom of the page as well
-% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
-% LaTeX2e). It also provides a command:
-%\fnbelowfloat
-% to enable the placement of footnotes below bottom floats (the standard
-% LaTeX2e kernel puts them above bottom floats). This is an invasive package
-% which rewrites many portions of the LaTeX2e float routines. It may not work
-% with other packages that modify the LaTeX2e float routines. The latest
-% version and documentation can be obtained at:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
-% Documentation is contained in the stfloats.sty comments as well as in the
-% presfull.pdf file. Do not use the stfloats baselinefloat ability as IEEE
-% does not allow \baselineskip to stretch. Authors submitting work to the
-% IEEE should note that IEEE rarely uses double column equations and
-% that authors should try to avoid such use. Do not be tempted to use the
-% cuted.sty or midfloat.sty packages (also by Sigitas Tolusis) as IEEE does
-% not format its papers in such ways.
-
-
-
-
-
-% *** PDF, URL AND HYPERLINK PACKAGES ***
-%
-%\usepackage{url}
-% url.sty was written by Donald Arseneau. It provides better support for
-% handling and breaking URLs. url.sty is already installed on most LaTeX
-% systems. The latest version can be obtained at:
-% http://www.ctan.org/tex-archive/macros/latex/contrib/misc/
-% Read the url.sty source comments for usage information. Basically,
-% \url{my_url_here}.
-
-% *** Do not adjust lengths that control margins, column widths, etc. ***
-% *** Do not use packages that alter fonts (such as pslatex).         ***
-% There should be no need to do such things with IEEEtran.cls V1.6 and later.
-% (Unless specifically asked to do so by the journal or conference you plan
-% to submit to, of course. )
-
-
 
 \usepackage[T1]{fontenc}
 \usepackage[utf8]{inputenc}
-%\usepackage{amsmath}
+\usepackage{amsfonts,amssymb}
+\usepackage{amsmath}
+\usepackage{algorithm}
+\usepackage{algpseudocode}
 %\usepackage{amsthm}
-%\usepackage{amsfonts}
-%\usepackage{graphicx}
+\usepackage{graphicx}
 %\usepackage{xspace}
 \usepackage[american]{babel}
-% Extension pour les graphiques EPS
-%\usepackage[dvips]{graphicx}
-\usepackage[pdftex,final]{graphicx}
 % Extension pour les liens intra-documents (tagged PDF)
 % et l'affichage correct des URL (commande \url{http://example.com})
 %\usepackage{hyperref}
 
+\algnewcommand\algorithmicinput{\textbf{Input:}}
+\algnewcommand\Input{\item[\algorithmicinput]}
 
-\begin{document}
-%
-% paper title
-% can use linebreaks \\ within to get better formatting as desired
-\title{Simulation of Asynchronous Iterative Numerical Algorithms Using SimGrid}
+\algnewcommand\algorithmicoutput{\textbf{Output:}}
+\algnewcommand\Output{\item[\algorithmicoutput]}
 
 
-% author names and affiliations
-% use a multiple column layout for up to three different
-% affiliations
-\author{\IEEEauthorblockN{RaphaÃ«l Couturier and Arnaud Giersch and David Laiymani and Charles-Emile Ramamonjisoa}
-\IEEEauthorblockA{Femto-ST Institute - DISC Department\\
-UniversitÃ© de Franche-ComtÃ©\\
-Belfort\\
-Email: raphael.couturier@univ-fcomte.fr}
-%\and
-%\IEEEauthorblockN{Arnaud Giersch}
-%\IEEEauthorblockA{Twentieth Century Fox\\
-%Springfield, USA\\
-%Email: homer@thesimpsons.com}
-%\and
-%\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
-%\IEEEauthorblockA{Starfleet Academy\\
-%San Francisco, California 96678-2391\\
-%Telephone: (800) 555--1212\\
-%Fax: (888) 555--1212
-}
+\begin{document}
 
+\title{Simulation of Asynchronous Iterative Numerical Algorithms Using SimGrid}
 
+\author{%
+  \IEEEauthorblockN{%
+    RaphaÃ«l Couturier,
+    Arnaud Giersch,
+    David Laiymani and
+    Charles Emile Ramamonjisoa
+  }
+  \IEEEauthorblockA{%
+    Femto-ST Institute - DISC Department\\
+    UniversitÃ© de Franche-ComtÃ©\\
+    Belfort\\
+    Email: raphael.couturier@univ-fcomte.fr
+  }
+}
 
-% make the title area
 \maketitle
 
-
 \begin{abstract}
-%\boldmath
 The abstract goes here.
 \end{abstract}
-% IEEEtran.cls defaults to using nonbold math in the Abstract.
-% This preserves the distinction between vectors and scalars. However,
-% if the conference you are submitting to favors bold math in the abstract,
-% then you can use LaTeX's standard command \boldmath at the very start
-% of the abstract to achieve this. Many IEEE journals/conferences frown on
-% math in the abstract anyway.
 
-% no keywords
+\section{Introduction}
+
+Parallel computing and high performance computing (HPC) are becoming 
+more and more imperative for solving various problems raised by 
+researchers on various scientific disciplines but also by industrial in 
+the field. Indeed, the increasing complexity of these requested 
+applications combined with a continuous increase of their sizes lead to 
+write distributed and parallel algorithms requiring significant hardware 
+resources ( grid computing , clusters, broadband network ,etc... ) but 
+also a non- negligible CPU execution time. We consider in this paper a 
+class of highly efficient parallel algorithms called iterative executed 
+in a distributed environment. As their name suggests, these algorithm 
+solves a given problem that might be NP- complete complex by successive 
+iterations (X$_{n +1 }$= f (X$_{n}$) ) from an initial value X
+$_{0}$ to find an approximate value X* of the solution with a very low 
+residual error. Several well-known methods demonstrate the convergence 
+of these algorithms. Generally, to reduce the complexity and the 
+execution time, the problem is divided into several "pieces" that will 
+be solved in parallel on multiple processing units. The latter will 
+communicate each intermediate results before a new iteration starts 
+until the approximate solution is reached. These distributed parallel 
+computations can be performed either in "synchronous" communication mode 
+where a new iteration begin only when all nodes communications are 
+completed, either "asynchronous" mode where processors can continue 
+independently without or few synchronization points. Despite the 
+effectiveness of iterative approach, a major drawback of the method is 
+the requirement of huge resources in terms of computing capacity, 
+storage and high speed communication network. Indeed, limited physical 
+resources are blocking factors for large-scale deployment of parallel 
+algorithms. 
+
+In recent years, the use of a simulation environment to execute parallel 
+iterative algorithms found some interests in reducing the highly cost of 
+access to computing resources: (1) for the applications development life 
+cycle and in code debugging (2) and in production to get results in a 
+reasonable execution time with a simulated infrastructure not accessible 
+with physical resources. Indeed, the launch of distributed iterative 
+asynchronous algorithms to solve a given problem on a large-scale 
+simulated environment challenges to find optimal configurations giving 
+the best results with a lowest residual error and in the best of 
+execution time. According our knowledge, no testing of large-scale 
+simulation of the class of algorithm solving to achieve real results has 
+been undertaken to date. We had in the scope of this work implemented a 
+program for solving large non-symmetric linear system of equations by 
+numerical method GMRES (Generalized Minimal Residual ) in the simulation 
+environment Simgrid . The simulated platform had allowed us to launch 
+the application from a modest computing infrastructure by simulating 
+different distributed architectures composed by clusters nodes 
+interconnected by variable speed networks. In addition, it has been 
+permitted to show the effectiveness of asynchronous mode algorithm by 
+comparing its performance with the synchronous mode time. With selected 
+parameters on the network platforms (bandwidth, latency of inter cluster 
+network) and on the clusters architecture (number, capacity calculation 
+power) in the simulated environment , the experimental results have 
+demonstrated not only the algorithm convergence within a reasonable time 
+compared with the physical environment performance, but also a time 
+saving of up to 40 \% in asynchronous mode.
+
+This article is structured as follows: after this introduction, the next 
+section will give a brief description of iterative asynchronous model. 
+Then, the simulation framework SIMGRID will be presented with the 
+settings to create various distributed architectures. The algorithm of 
+the multi -splitting method used by GMRES written with MPI primitives 
+and its adaptation to Simgrid with SMPI (Simulation MPI ) will be in the 
+next section . At last, the experiments results carried out will be 
+presented before the conclusion which we will announce the opening of 
+our future work after the results.
+ 
+\section{The asynchronous iteration model}
+
+DÃ©crire le modÃ¨le asynchrone. Je m'en charge (DL)
 
+\section{SimGrid}
 
+DÃ©crire SimGrid (Arnaud)
 
 
-% For peer review papers, you can put extra information on the cover
-% page as needed:
-% \ifCLASSOPTIONpeerreview
-% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
-% \fi
-%
-% For peerreview papers, this IEEEtran command inserts a page break and
-% creates the second title. It will be ignored for other modes.
-\IEEEpeerreviewmaketitle
 
 
 
-\section{Introduction}
 
-PrÃ©senter un bref Ã©tat de l'art sur la simulation d'algos parallÃ¨les. PrÃ©senter rapidement les algos itÃ©ratifs asynchrones et leurs avantages. Parler de leurs inconvÃ©nients en particulier la difficultÃ© de dÃ©ploiement Ã  grande Ã©chelle donc il serait bien de simuler. Dire qu'Ã  notre connaissance il n'existe pas de simulation de ce type d'algo.
-PrÃ©senter les travaux et les rÃ©sultats obtenus. Annoncer le plan.
- 
-\section{The asynchronous iteration model}
 
-DÃ©crire le modÃ¨le asynchrone. Je m'en charge (DL)
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Simulation of the multisplitting method}
+%DÃ©crire le problÃ¨me (algo) traitÃ© ainsi que le processus d'adaptation Ã  SimGrid.
+Let $Ax=b$ be a large sparse system of $n$ linear equations in $\mathbb{R}$, where $A$ is a sparse square and nonsingular matrix, $x$ is the solution vector and $y$ is the right-hand side vector. We use a multisplitting method based on the block Jacobi partitioning to solve this linear system on a large scale platform composed of $L$ clusters of processors. In this case, we apply a row-by-row splitting without overlapping  
+\[
+\left(\begin{array}{ccc}
+A_{11} & \cdots & A_{1L} \\
+\vdots & \ddots & \vdots\\
+A_{L1} & \cdots & A_{LL}
+\end{array} \right)
+\times 
+\left(\begin{array}{c}
+X_1 \\
+\vdots\\
+X_L
+\end{array} \right)
+=
+\left(\begin{array}{c}
+Y_1 \\
+\vdots\\
+Y_L
+\end{array} \right)\] 
+in such a way that successive rows of matrix $A$ and both vectors $x$ and $b$ are assigned to one cluster, where for all $l,i\in\{1,\ldots,L\}$ $A_{li}$ is a rectangular block of $A$ of size $n_l\times n_i$, $X_l$ and $Y_l$ are sub-vectors of $x$ and $y$, respectively, each of size $n_l$ and $\sum_{l} n_l=\sum_{i} n_i=n$.
+
+The multisplitting method proceeds by iteration to solve in parallel the linear system by $L$ clusters of processors, in such a way each sub-system
+\begin{equation}
+\left\{
+\begin{array}{l}
+A_{ll}X_l = Y_l \mbox{,~such that}\\
+Y_l = B_l - \displaystyle\sum_{i=1,i\neq l}^{L}A_{li}X_i,
+\end{array}
+\right.
+\label{eq:4.1}
+\end{equation}
+is solved independently by a cluster and communication are required to update the right-hand side sub-vectors $Y_l$, such that the sub-vectors $X_i$ represent the data dependencies between the clusters. As each sub-system (\ref{eq:4.1}) is solved in parallel by a cluster of processors, our multisplitting method uses an iterative method as an inner solver which is easier to parallelize and more scalable than a direct method. In this work, we use the parallel GMRES method~\cite{ref1} which is one of the most used iterative method by many researchers. 
+
+\begin{algorithm}
+\caption{A multisplitting solver with inner iteration GMRES method}
+\begin{algorithmic}[1]
+\Input $A_l$ (local sparse matrix), $B_l$ (local right-hand side), $x^0$ (initial guess)
+\Output $X_l$ (local solution vector)\vspace{0.2cm}
+\State Load $A_l$, $B_l$, $x^0$
+\State Initialize the shared vector $\hat{x}=x^0$
+\For {$k=1,2,3,\ldots$ until the global convergence}
+\State $x^0=\hat{x}$
+\State Inner iteration solver: \Call{InnerSolver}{$x^0$, $k$}
+\State Exchange the local solution ${X}_l^k$ with the neighboring clusters and copy the shared vector elements in $\hat{x}$
+\EndFor
+
+\Statex
+
+\Function {InnerSolver}{$x^0$, $k$}
+\State Compute the local right-hand side: $Y_l = B_l - \sum^L_{i=1,i\neq l}A_{li}X_i^0$
+\State Solving the local splitting $A_{ll}X_l^k=Y_l$ using the parallel GMRES method, such that $X_l^0$ is the local initial guess
+\State \Return $X_l^k$
+\EndFunction
+\end{algorithmic}
+\label{algo:01}
+\end{algorithm}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
 
-\section{SimGrid}
 
-DÃ©crire SimGrid (Arnaud)
 
-\section{Simulation of the multi-splitting method}
 
-DÃ©crire le problÃ¨me (algo) traitÃ© ainsi que le processus d'adaptation Ã  SimGrid.
 
 \section{Experimental results}
 
@@ -479,21 +262,22 @@ lat latency , ... ).
   \centering
   \caption{2 clusters X 50 nodes}
   \label{tab.cluster.2x50}
-  \includegraphics[width=209pt]{img-1.eps}
+  \includegraphics[width=209pt]{img1.jpg}
 \end{table}
 
 \begin{table}
   \centering
-  \caption{3 clusters X 33 n\oe{}uds}
+  \caption{3 clusters X 33 nodes}
   \label{tab.cluster.3x33}
-  \includegraphics[width=209pt]{img-1.eps}
+  \includegraphics[width=209pt]{img2.jpg}
 \end{table}
 
 \begin{table}
   \centering
-  \caption{3 clusters X 67 noeuds}
+  \caption{3 clusters X 67 nodes}
   \label{tab.cluster.3x67}
-  \includegraphics[width=128pt]{img-2.eps}
+%  \includegraphics[width=160pt]{img3.jpg}
+  \includegraphics[scale=0.5]{img3.jpg}
 \end{table}
 
 \paragraph*{Interpretations and comments}
@@ -531,142 +315,24 @@ with a bandwidth of 1 Mbits/s as shown in Table~\ref{tab.cluster.3x67}.
 
 \section{Conclusion}
 
-
-% An example of a floating figure using the graphicx package.
-% Note that \label must occur AFTER (or within) \caption.
-% For figures, \caption should occur after the \includegraphics.
-% Note that IEEEtran v1.7 and later has special internal code that
-% is designed to preserve the operation of \label within \caption
-% even when the captionsoff option is in effect. However, because
-% of issues like this, it may be the safest practice to put all your
-% \label just after \caption rather than within \caption{}.
-%
-% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
-% option should be used if it is desired that the figures are to be
-% displayed while in draft mode.
-%
-%\begin{figure}[!t]
-%\centering
-%\includegraphics[width=2.5in]{myfigure}
-% where an .eps filename suffix will be assumed under latex, 
-% and a .pdf suffix will be assumed for pdflatex; or what has been declared
-% via \DeclareGraphicsExtensions.
-%\caption{Simulation Results}
-%\label{fig_sim}
-%\end{figure}
-
-% Note that IEEE typically puts floats only at the top, even when this
-% results in a large percentage of a column being occupied by floats.
-
-
-% An example of a double column floating figure using two subfigures.
-% (The subfig.sty package must be loaded for this to work.)
-% The subfigure \label commands are set within each subfloat command, the
-% \label for the overall figure must come after \caption.
-% \hfil must be used as a separator to get equal spacing.
-% The subfigure.sty package works much the same way, except \subfigure is
-% used instead of \subfloat.
-%
-%\begin{figure*}[!t]
-%\centerline{\subfloat[Case I]\includegraphics[width=2.5in]{subfigcase1}%
-%\label{fig_first_case}}
-%\hfil
-%\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
-%\label{fig_second_case}}}
-%\caption{Simulation results}
-%\label{fig_sim}
-%\end{figure*}
-%
-% Note that often IEEE papers with subfigures do not employ subfigure
-% captions (using the optional argument to \subfloat), but instead will
-% reference/describe all of them (a), (b), etc., within the main caption.
-
-
-% An example of a floating table. Note that, for IEEE style tables, the 
-% \caption command should come BEFORE the table. Table text will default to
-% \footnotesize as IEEE normally uses this smaller font for tables.
-% The \label must come after \caption as always.
-%
-%\begin{table}[!t]
-%% increase table row spacing, adjust to taste
-%\renewcommand{\arraystretch}{1.3}
-% if using array.sty, it might be a good idea to tweak the value of
-% \extrarowheight as needed to properly center the text within the cells
-%\caption{An Example of a Table}
-%\label{table_example}
-%\centering
-%% Some packages, such as MDW tools, offer better commands for making tables
-%% than the plain LaTeX2e tabular which is used here.
-%\begin{tabular}{|c||c|}
-%\hline
-%One & Two\\
-%\hline
-%Three & Four\\
-%\hline
-%\end{tabular}
-%\end{table}
-
-
-% Note that IEEE does not put floats in the very first column - or typically
-% anywhere on the first page for that matter. Also, in-text middle ("here")
-% positioning is not used. Most IEEE journals/conferences use top floats
-% exclusively. Note that, LaTeX2e, unlike IEEE journals/conferences, places
-% footnotes above bottom floats. This can be corrected via the \fnbelowfloat
-% command of the stfloats package.
-
-
-
-
-
-
-
-% conference papers do not normally have an appendix
-
-
-% use section* for acknowledgement
 \section*{Acknowledgment}
 
 
 The authors would like to thank...
 
 
-
-
-
 % trigger a \newpage just before the given reference
 % number - used to balance the columns on the last page
 % adjust value as needed - may need to be readjusted if
 % the document is modified later
-%\IEEEtriggeratref{8}
-% The "triggered" command can be changed if desired:
-%\IEEEtriggercmd{\enlargethispage{-5in}}
-
-% references section
-
-% can use a bibliography generated by BibTeX as a .bbl file
-% BibTeX documentation can be easily obtained at:
-% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
-% The IEEEtran BibTeX style support page is at:
-% http://www.michaelshell.org/tex/ieeetran/bibtex/
 \bibliographystyle{IEEEtran}
-% argument is your BibTeX string definitions and bibliography database(s)
-\bibliography{bib/hpccBib}
-%
-% <OR> manually copy in the resultant .bbl file
-% set second argument of \begin to the number of references
-% (used to reserve space for the reference number labels box)
-%\begin{thebibliography}{1}
-%
-%\bibitem{IEEEhowto:kopka}
-%H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
-%  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
-%
-%\end{thebibliography}
-
+\bibliography{hpccBib}
 
-
-
-% that's all folks
 \end{document}
 
-
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% fill-column: 80
+%%% ispell-local-dictionary: "american"
+%%% End:
