X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/hpcc2014.git/blobdiff_plain/2367662d760a73d98ca68d37a3912c211972afe3..abad274bfc60959441fa058f1e08bbeefed30b34:/hpcc.tex?ds=inline

diff --git a/hpcc.tex b/hpcc.tex
index 968b235..62922bc 100644
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -1,720 +1,761 @@
-
-%% 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{amsfonts,amssymb}
 \usepackage{amsmath}
-%\usepackage{amsmath}
+%\usepackage{algorithm}
+\usepackage{algpseudocode}
 %\usepackage{amsthm}
-%\usepackage{amsfonts}
-%\usepackage{graphicx}
-%\usepackage{xspace}
+\usepackage{graphicx}
 \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}
 
+\usepackage{url}
+\DeclareUrlCommand\email{\urlstyle{same}}
 
-\begin{document}
-%
-% paper title
-% can use linebreaks \\ within to get better formatting as desired
-\title{Simulation of Asynchronous Iterative Numerical Algorithms Using SimGrid}
-
-
-% 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
-}
-
-
-
-% make the title area
-\maketitle
+\usepackage[autolanguage,np]{numprint}
+\AtBeginDocument{%
+  \renewcommand*\npunitcommand[1]{\text{#1}}
+  \npthousandthpartsep{}}
 
+\usepackage{xspace}
+\usepackage[textsize=footnotesize]{todonotes}
+\newcommand{\AG}[2][inline]{%
+  \todo[color=green!50,#1]{\sffamily\textbf{AG:} #2}\xspace}
+\newcommand{\DL}[2][inline]{%
+  \todo[color=yellow!50,#1]{\sffamily\textbf{DL:} #2}\xspace}
+\newcommand{\LZK}[2][inline]{%
+  \todo[color=blue!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}
+\newcommand{\RC}[2][inline]{%
+  \todo[color=red!10,#1]{\sffamily\textbf{RC:} #2}\xspace}
+\newcommand{\CER}[2][inline]{%
+  \todo[color=pink!10,#1]{\sffamily\textbf{CER:} #2}\xspace}
 
-\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.
+\algnewcommand\algorithmicinput{\textbf{Input:}}
+\algnewcommand\Input{\item[\algorithmicinput]}
 
-% no keywords
+\algnewcommand\algorithmicoutput{\textbf{Output:}}
+\algnewcommand\Output{\item[\algorithmicoutput]}
 
+\newcommand{\MI}{\mathit{MaxIter}}
+\newcommand{\Time}[1]{\mathit{Time}_\mathit{#1}}
 
+\begin{document}
 
+\title{Simulation of Asynchronous Iterative Algorithms Using SimGrid}
+
+\author{%
+  \IEEEauthorblockN{%
+    Charles Emile Ramamonjisoa\IEEEauthorrefmark{1},
+    Lilia Ziane Khodja\IEEEauthorrefmark{2},
+    David Laiymani\IEEEauthorrefmark{1},
+    Arnaud Giersch\IEEEauthorrefmark{1} and
+    RaphaÃ«l Couturier\IEEEauthorrefmark{1}
+  }
+  \IEEEauthorblockA{\IEEEauthorrefmark{1}%
+    Femto-ST Institute -- DISC Department\\
+    UniversitÃ© de Franche-ComtÃ©,
+    IUT de Belfort-MontbÃ©liard\\
+    19 avenue du MarÃ©chal Juin, BP 527, 90016 Belfort cedex, France\\
+    Email: \email{{charles.ramamonjisoa,david.laiymani,arnaud.giersch,raphael.couturier}@univ-fcomte.fr}
+  }
+  \IEEEauthorblockA{\IEEEauthorrefmark{2}%
+    Inria Bordeaux Sud-Ouest\\
+    200 avenue de la Vieille Tour, 33405 Talence cedex, France \\
+    Email: \email{lilia.ziane@inria.fr}
+  }
+}
 
-% 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
+\maketitle
 
+\begin{abstract}
 
+Synchronous  iterative  algorithms  are  often less  scalable  than  asynchronous
+iterative  ones.  Performing  large  scale experiments  with  different kind  of
+network parameters is not easy  because with supercomputers such parameters are
+fixed. So, one  solution consists in using simulations first  in order to analyze
+what parameters  could influence or not  the behaviors of an  algorithm. In this
+paper, we show  that it is interesting to use SimGrid  to simulate the behaviors
+of asynchronous  iterative algorithms. For that,  we compare the  behavior of a
+synchronous  GMRES  algorithm  with  an  asynchronous  multisplitting  one  with
+simulations  which let us easily choose  some parameters.   Both  codes  are real  MPI
+codes and simulations allow us to see when the asynchronous multisplitting algorithm can be more
+efficient than the GMRES one to solve a 3D Poisson problem.
+
+
+% no keywords for IEEE conferences
+% Keywords: Algorithm distributed iterative asynchronous simulation SimGrid
+\end{abstract}
 
 \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{SimGrid}
+Parallel computing and high performance computing (HPC) are becoming  more and more imperative to solve various
+problems raised by  researchers on various scientific disciplines but also by industrialists 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 \emph{iterative algorithms} executed in a distributed environment. As their name
+suggests, these algorithms solve a given problem 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~\cite{BT89,Bahi07}.
+
+Parallelization of such algorithms generally involves the division of the problem
+into  several  \emph{blocks}  that  will  be  solved  in  parallel  on  multiple
+processing units. The latter will communicate each intermediate results before a
+new  iteration starts  and until  the  approximate solution  is reached.   These
+parallel computations can be performed either in a \emph{synchronous} mode, where a
+new iteration  begins only  when all nodes  communications are completed,  or in an
+\emph{asynchronous}  mode where  processors can  continue independently  with no
+synchronization points~\cite{bcvc06:ij}. In this case, local computations do not
+need to  wait for  required data. Processors  can then perform  their iterations
+with the  data present at that time.  Even if the number of required iterations 
+before  the convergence  is generally  greater  than in  the synchronous  case,
+asynchronous  iterative algorithms  can significantly  reduce  overall execution
+times by  suppressing idle  times due to  synchronizations especially in  a grid
+computing context (see~\cite{Bahi07} for more details).
+
+Parallel applications  based on a synchronous or  asynchronous iteration model
+may have different configuration and deployment requirements.  Quantifying their
+resource  allocation  policies and  application  scheduling  algorithms in  grid
+computing environments under varying load,  CPU power and network speeds are very
+costly,       very        labor       intensive       and        very       time
+consuming~\cite{Calheiros:2011:CTM:1951445.1951450}.   The case  of asynchronous
+iterative algorithms  is even more problematic  since they are  very sensitive to
+the  execution environment  context.  For instance,  variations  in the  network
+bandwidth (intra and  inter-clusters), in the number and the  power of nodes, in
+the number  of clusters\dots{} can lead  to very different  number of iterations
+and so  to very  different execution times.   Then, it  appears that the  use of
+simulation tools to explore various  platform scenarios and to run large numbers
+of  experiments quickly  can  be very  promising.  
+
+Thus, using a simulation environment to execute parallel iterative algorithms can prove to be very interesting to reduce 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, to  find optimal  configurations
+giving  the best  results  with  a lowest  residual  error and  in  the best 
+execution time is very challenging  for large scale distributed  iterative asynchronous  algorithms
+
+
+To our knowledge,  there is no existing work on the  large-scale simulation of a
+real asynchronous  iterative application.  {\bf The contribution  of the present
+  paper can be  summarized in two main points}.  First we  give a first approach
+of the simulation  of asynchronous iterative algorithms using  a simulation tool
+(i.e.    the   SimGrid   toolkit~\cite{SimGrid}).    Second,  we   confirm   the
+efficiency  of the  asynchronous  multisplitting algorithm  by comparing  its
+performances   with  the   synchronous  GMRES   (Generalized   Minimal  Residual) method
+\cite{ref1}.  Both  these codes can  be used to  solve large linear  systems. In
+this  paper, we  focus  on  a 3D  Poisson  problem.  We  show  that, with  minor
+modifications of the initial MPI code,  the SimGrid toolkit allows us to perform
+a  test campaign  of  a  real asynchronous  iterative  application on  different
+computing architectures.
+% The  simulated results  we
+%obtained are  in line with real  results exposed in  ??\AG[]{ref?}. 
+SimGrid  has  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.  Parameters  of the
+network  platforms  are   the  bandwidth  and  the  latency   of  inter  cluster
+network. Parameters on the cluster's architecture are the number of machines and
+the  computation power  of a  machine.  Simulations show  that the  asynchronous
+multisplitting algorithm  can solve the  3D Poisson problem  approximately twice
+faster than GMRES with two distant clusters. In this way, we present an original solution to optimize the use of a simulation 
+tool to run efficiently an  asynchronous iterative parallel algorithm in a grid architecture
+
+
+
+This article is structured as follows: after this introduction, the next section
+will  give a  brief  description  of the iterative  asynchronous  model.  Then,  the
+simulation framework  SimGrid is presented  with the settings to  create various
+distributed architectures.  Then, the  multisplitting method is presented, it is
+based  on GMRES to  solve each  block obtained  from the  splitting. This  code is
+written with MPI  primitives and its adaptation to  SimGrid with SMPI (Simulated
+MPI) is  detailed in the next  section. At last, the  simulation results carried
+out will be presented before some concluding remarks and future works.
 
-DÃ©crire SimGrid (Arnaud)
+ 
+\section{Motivations and scientific context}
+
+As exposed in  the introduction, parallel iterative methods  are now widely used
+in  many scientific  domains.   They can  be  classified in  three main  classes
+depending on  how iterations  and communications are  managed (for  more details
+readers  can refer  to~\cite{bcvc06:ij}). In  the synchronous  iterations model,
+data are exchanged  at the end of each iteration. All  the processors must begin
+the same iteration  at the same time and important idle  times on processors are
+generated.  It is possible to use asynchronous communications, in this case, the
+model can be  compared to the previous one except that  data required on another
+processor are  sent asynchronously i.e.  without  stopping current computations.
+This technique  allows communications to be partially  overlapped by  computations but
+unfortunately, the overlapping is only  partial and important idle times remain.
+It is clear that, in a grid computing context, where the number of computational
+nodes is large,  heterogeneous and widely distributed, the  idle times generated
+by synchronizations are very penalizing. One  way to overcome this problem is to
+use the asynchronous iterations model.   Here, local computations do not need to
+wait for  required data. Processors can  then perform their  iterations with the
+data present  at that time.  Figure~\ref{fig:aiac} illustrates  this model where
+the gray blocks represent the  computation phases.  With this algorithmic model,
+the number  of iterations required  before the convergence is  generally greater
+than  for the  two former  classes.  But,  and as  detailed in~\cite{bcvc06:ij},
+asynchronous  iterative algorithms  can significantly  reduce  overall execution
+times by  suppressing idle  times due to  synchronizations especially in  a grid
+computing context.
+
+\begin{figure}[!t]
+  \centering
+    \includegraphics[width=8cm]{AIAC.pdf}
+  \caption{The asynchronous iterations model}
+  \label{fig:aiac}
+\end{figure}
+
+
+%% It is very challenging to develop efficient applications for large scale,
+%% heterogeneous and distributed platforms such as computing grids. Researchers and
+%% engineers have to develop techniques for maximizing application performance of
+%% these multi-cluster platforms, by redesigning the applications and/or by using
+%% novel algorithms that can account for the composite and heterogeneous nature of
+%% the platform. Unfortunately, the deployment of such applications on these very
+%% large scale systems is very costly, labor intensive and time consuming. In this
+%% context, it appears that the use of simulation tools to explore various platform
+%% scenarios at will and to run enormous numbers of experiments quickly can be very
+%% promising. Several works\dots{}
+
+%% \AG{Several works\dots{} what?\\
+%  Le paragraphe suivant se trouve dÃ©jÃ  dans l'intro ?}
+In the context of asynchronous algorithms, the number of iterations to reach the
+convergence depends on  the delay of the messages. With  synchronous iterations, the
+number of  iterations is exactly  the same than  in the sequential mode  (if the
+parallelization process does  not change the algorithm). So  the difficulty with
+asynchronous iterative algorithms comes from the fact that it is necessary to run the algorithm
+with real data. Indeed, from one execution to the other the order of messages will
+change and the  number of iterations to reach the  convergence will also change.
+According  to all  the parameters  of the  platform (number  of nodes,  power of
+nodes,  inter  and  intra clusters  bandwidth  and  latency, etc.) and  of  the
+algorithm  (number   of  splittings  with  the   multisplitting  algorithm),  the
+multisplitting code  will obtain the solution  more or less  quickly. Of course,
+the GMRES method also depends on the same parameters. As it is difficult to have
+access to  many clusters,  grids or supercomputers  with many  different network
+parameters,  it  is  interesting  to  be  able  to  simulate  the  behaviors  of
+asynchronous iterative algorithms before being able to run real experiments.
 
 
 
 
 
 
+\section{SimGrid}
 
-%%%%%
+SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid} is a simulation
+framework to study the behavior of large-scale distributed systems.  As its name
+suggests, it emanates from the grid computing community, but is nowadays used to
+study grids, clouds, HPC or peer-to-peer systems.  The early versions of SimGrid
+date back from 1999, but it is still actively developed and distributed as an open
+source software.  Today, it is one of the major generic tools in the field of
+simulation for large-scale distributed systems.
+
+SimGrid provides several programming interfaces: MSG to simulate Concurrent
+Sequential Processes, SimDAG to simulate DAGs of (parallel) tasks, and SMPI to
+run real applications written in MPI~\cite{MPI}.  Apart from the native C
+interface, SimGrid provides bindings for the C++, Java, Lua and Ruby programming
+languages.  SMPI is the interface that has been used for the work exposed in
+this paper.  The SMPI interface implements about \np[\%]{80} of the MPI 2.0
+standard~\cite{bedaride+degomme+genaud+al.2013.toward}, and supports
+applications written in C or Fortran, with little or no modifications.
+
+Within SimGrid, the execution of a distributed application is simulated by a
+single process.  The application code is really executed, but some operations,
+like communications, are intercepted, and their running time is computed
+according to the characteristics of the simulated execution platform.  The
+description of this target platform is given as an input for the execution, by
+the mean of an XML file.  It describes the properties of the platform, such as
+the computing nodes with their computing power, the interconnection links with
+their bandwidth and latency, and the routing strategy.  The scheduling of the
+simulated processes, as well as the simulated running time of the application
+are computed according to these properties.
+
+To compute the durations of the operations in the simulated world, and to take
+into account resource sharing (e.g. bandwidth sharing between competing
+communications), SimGrid uses a fluid model.  This allows users to run relatively fast
+simulations, while still keeping accurate
+results~\cite{bedaride+degomme+genaud+al.2013.toward,
+  velho+schnorr+casanova+al.2013.validity}.  Moreover, depending on the
+simulated application, SimGrid/SMPI allows to skip long lasting computations and
+to only take their duration into account.  When the real computations cannot be
+skipped, but the results are unimportant for the simulation results, it is
+also possible to share dynamically allocated data structures between
+several simulated processes, and thus to reduce the whole memory consumption.
+These two techniques can help to run simulations on a very large scale.
+
+The validity of simulations with SimGrid has been asserted by several studies.
+See, for example, \cite{velho+schnorr+casanova+al.2013.validity} and articles
+referenced therein for the validity of the network models.  Comparisons between
+real execution of MPI applications on the one hand, and their simulation with
+SMPI on the other hand, are presented in~\cite{guermouche+renard.2010.first,
+  clauss+stillwell+genaud+al.2011.single,
+  bedaride+degomme+genaud+al.2013.toward}.  All these works conclude that
+SimGrid is able to simulate pretty accurately the real behavior of the
+applications.
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Simulation of the multisplitting method}
+
+\subsection{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
+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 $b$ is the right-hand side vector. We use a multisplitting method based on the block Jacobi splitting to solve this linear system on a large scale platform composed of $L$ clusters of processors~\cite{o1985multi}. In this case, we apply a row-by-row splitting without overlapping  
+\begin{equation*}
+  \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}
+      B_1 \\
+      \vdots\\
+      B_L
+    \end{array} \right)
+\end{equation*}
+in such a way that successive rows of matrix $A$ and both vectors $x$ and $b$
+are assigned to one cluster, where for all $\ell,m\in\{1,\ldots,L\}$, $A_{\ell
+  m}$ is a rectangular block of $A$ of size $n_\ell\times n_m$, $X_\ell$ and
+$B_\ell$ are sub-vectors of $x$ and $b$, respectively, of size $n_\ell$ each,
+and $\sum_{\ell} n_\ell=\sum_{m} n_m=n$.
+
+The multisplitting method proceeds by iteration to solve in parallel the linear system on $L$ clusters of processors, in such a way each sub-system
+\begin{equation}
+  \label{eq:4.1}
+  \left\{
+    \begin{array}{l}
+      A_{\ell\ell}X_\ell = Y_\ell \text{, such that}\\
+      Y_\ell = B_\ell - \displaystyle\sum_{\substack{m=1\\ m\neq \ell}}^{L}A_{\ell m}X_m
+    \end{array}
+  \right.
+\end{equation}
+is solved independently by a cluster and communications are required to update
+the right-hand side sub-vector $Y_\ell$, such that the sub-vectors $X_m$
+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 algorithm of GMRES method~\cite{ref1} which is one of the most
+used iterative method by many researchers.
+
+\begin{figure}[!t]
+  %%% IEEE instructions forbid to use an algorithm environment here, use figure
+  %%% instead
+\begin{algorithmic}[1]
+\Input $A_\ell$ (sparse sub-matrix), $B_\ell$ (right-hand side sub-vector)
+\Output $X_\ell$ (solution sub-vector)\medskip
+
+\State Load $A_\ell$, $B_\ell$
+\State Set the initial guess $x^0$
+\For {$k=0,1,2,\ldots$ until the global convergence}
+\State Restart outer iteration with $x^0=x^k$
+\State Inner iteration: \Call{InnerSolver}{$x^0$, $k+1$}
+\State\label{algo:01:send} Send shared elements of $X_\ell^{k+1}$ to neighboring clusters
+\State\label{algo:01:recv} Receive shared elements in $\{X_m^{k+1}\}_{m\neq \ell}$
+\EndFor
+
+\Statex
+
+\Function {InnerSolver}{$x^0$, $k$}
+\State Compute local right-hand side $Y_\ell$:
+       \begin{equation*}
+         Y_\ell = B_\ell - \sum\nolimits^L_{\substack{m=1\\ m\neq \ell}}A_{\ell m}X_m^0
+       \end{equation*}
+\State Solving sub-system $A_{\ell\ell}X_\ell^k=Y_\ell$ with the parallel GMRES method
+\State \Return $X_\ell^k$
+\EndFunction
+\end{algorithmic}
+\caption{A multisplitting solver with GMRES method}
+\label{algo:01}
+\end{figure}
+
+The algorithm in Figure~\ref{algo:01} shows the main key points of the
+multisplitting method to solve a large sparse linear system. This algorithm is
+based on an outer-inner iteration method where the parallel synchronous GMRES
+method is used to solve the inner iteration. It is executed in parallel by each
+cluster of processors. For all $\ell,m\in\{1,\ldots,L\}$, the matrices and
+vectors with the subscript $\ell$ represent the local data for cluster $\ell$,
+while $\{A_{\ell m}\}_{m\neq \ell}$ are off-diagonal matrices of sparse matrix
+$A$ and $\{X_m\}_{m\neq \ell}$ contain vector elements of solution $x$ shared
+with neighboring clusters. At every outer iteration $k$, asynchronous
+communications are performed between processors of the local cluster and those
+of distant clusters (lines~\ref{algo:01:send} and~\ref{algo:01:recv} in
+Figure~\ref{algo:01}). The shared vector elements of the solution $x$ are
+exchanged by message passing using MPI non-blocking communication routines.
+
+\begin{figure}[!t]
+\centering
+  \includegraphics[width=60mm,keepaspectratio]{clustering}
+\caption{Example of three distant clusters of processors.}
+\label{fig:4.1}
+\end{figure}
+
+The global convergence of the asynchronous multisplitting solver is detected
+when the clusters of processors have all converged locally. We implemented the
+global convergence detection process as follows. On each cluster a master
+processor is designated (for example the processor with rank 1) and masters of
+all clusters are interconnected by a virtual unidirectional ring network (see
+Figure~\ref{fig:4.1}). During the resolution, a Boolean token circulates around
+the virtual ring from a master processor to another until the global convergence
+is achieved. So, starting from the cluster with rank 1, each master processor $\ell$
+sets the token to \textit{True} if the local convergence is achieved or to
+\textit{False} otherwise, and sends it to master processor $\ell+1$. Finally, the
+global convergence is detected when the master of cluster 1 receives from the
+master of cluster $L$ a token set to \textit{True}. In this case, the master of
+cluster 1 broadcasts a stop message to the masters of other clusters. In this work,
+the local convergence on each cluster $\ell$ is detected when the following
+condition is satisfied
+\begin{equation*}
+  (k\leq \MI) \text{ or } (\|X_\ell^k - X_\ell^{k+1}\|_{\infty}\leq\epsilon)
+\end{equation*}
+where $\MI$ is the maximum number of outer iterations and $\epsilon$ is the
+tolerance threshold of the error computed between two successive local solution
+$X_\ell^k$ and $X_\ell^{k+1}$.
+
+
+
+In this paper, we solve the 3D Poisson problem whose mathematical model is 
 \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,
+\nabla^2 u = f \text{~in~} \Omega \\
+u =0 \text{~on~} \Gamma =\partial\Omega
 \end{array}
 \right.
-\label{eq:4.1}
+\label{eq:02}
 \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. 
-%%%%%
-
-
-
-
-
-
-
-
-\section{Experimental results}
+where $\nabla^2$ is the Laplace operator, $f$ and $u$ are real-valued functions, and $\Omega=[0,1]^3$. The spatial discretization with a finite differences scheme reduces problem~(\ref{eq:02}) to a system of sparse linear equations. Our multisplitting method solves the 3D Poisson problem using a seven point stencil whose general expression could be written as
+\begin{equation}
+\begin{array}{l}
+u(x-1,y,z) + u(x,y-1,z) + u(x,y,z-1)\\+u(x+1,y,z)+u(x,y+1,z)+u(x,y,z+1) \\ -6u(x,y,z)=h^2f(x,y,z),
+%u(x,y,z)= & \frac{1}{6}\times [u(x-1,y,z) + u(x+1,y,z) + \\
+ %         & u(x,y-1,z) + u(x,y+1,z) + \\
+  %        & u(x,y,z-1) + u(x,y,z+1) - \\ & h^2f(x,y,z)],
+\end{array}
+\label{eq:03}
+\end{equation} 
+where $h$ is the distance between two adjacent elements in the spatial discretization scheme and the iteration matrix $A$ of size $N_x\times N_y\times N_z$ of the discretized linear system is sparse, symmetric and positive definite. 
 
-When the ``real'' application runs in the simulation environment and produces
-the expected results, varying the input parameters and the program arguments
-allows us to compare outputs from the code execution. We have noticed from this
-study that the results depend on the following parameters: (1) at the network
-level, we found that the most critical values are the bandwidth (bw) and the
-network latency (lat). (2) Hosts power (GFlops) can also influence on the
-results. And finally, (3) when submitting job batches for execution, the
-arguments values passed to the program like the maximum number of iterations or
-the ``external'' precision are critical to ensure not only the convergence of the
-algorithm but also to get the main objective of the experimentation of the
-simulation in having an execution time in asynchronous less than in synchronous
-mode, in others words, in having a ``speedup'' less than 1 (Speedup = Execution
-time in synchronous mode / Execution time in asynchronous mode).
+The parallel solving of the 3D Poisson problem with our multisplitting method requires a data partitioning of the problem between clusters and between processors within a cluster. We have chosen the 3D partitioning instead of the row-by-row partitioning one in order to reduce the data exchanges at sub-domain boundaries. Figure~\ref{fig:4.2} shows an example of the data partitioning of the 3D Poisson problem between two clusters of processors, where each sub-problem is assigned to a processor. In this context, a processor has at most six neighbors within a cluster or in distant clusters with which it shares data at sub-domain boundaries. 
 
-A priori, obtaining a speedup less than 1 would be difficult in a local area
-network configuration where the synchronous mode will take advantage on the rapid
-exchange of information on such high-speed links. Thus, the methodology adopted
-was to launch the application on clustered network. In this last configuration,
-degrading the inter-cluster network performance will "penalize" the synchronous
-mode allowing to get a speedup lower than 1. This action simulates the case of
-clusters linked with long distance network like Internet.
+\begin{figure}[!t]
+\centering
+  \includegraphics[width=80mm,keepaspectratio]{partition}
+\caption{Example of the 3D data partitioning between two clusters of processors.}
+\label{fig:4.2}
+\end{figure}
 
-As a first step, the algorithm was run on a network consisting of two clusters
-containing fifty hosts each, totaling one hundred hosts. Various combinations of
-the above factors have providing the results shown in Table~\ref{tab.cluster.2x50} with a matrix size
-ranging from Nx = Ny = Nz = 62 to 171 elements or from 62$^{3}$ = 238328 to
-171$^{3}$ = 5,211,000 entries.
 
-Then we have changed the network configuration using three clusters containing
-respectively 33, 33 and 34 hosts, or again by on hundred hosts for all the
-clusters. In the same way as above, a judicious choice of key parameters has
-permitted to get the results in Table~\ref{tab.cluster.3x33} which shows the speedups less than 1 with
-a matrix size from 62 to 100 elements.
+\subsection{Simulation of the multisplitting method using SimGrid and SMPI}
 
-In a final step, results of an execution attempt to scale up the three clustered
-configuration but increasing by two hundreds hosts has been recorded in Table~\ref{tab.cluster.3x67}.
 
-Note that the program was run with the following parameters:
 
-\paragraph*{SMPI parameters}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+We did not encounter major blocking problems when adapting the multisplitting algorithm previously described to a simulation environment like SimGrid unless some code 
+debugging. Indeed, apart from the review of the program sequence for asynchronous exchanges between processors within a cluster or between clusters, the algorithm was executed successfully with SMPI and provided identical outputs as those obtained with direct execution under MPI. For the synchronous GMRES method, the execution of the program raised no particular issue but in the asynchronous multisplitting method, the review of the sequence of \texttt{MPI\_Isend, MPI\_Irecv} and \texttt{MPI\_Waitall} instructions
+and with the addition of the primitive \texttt{MPI\_Test} was needed to avoid a memory fault due to an infinite loop resulting from the non-convergence of the algorithm.
+%\CER{On voulait en fait montrer la simplicitÃ© de l'adaptation de l'algo a SimGrid. Les problÃ¨mes rencontrÃ©s dÃ©crits dans ce paragraphe concerne surtout le mode async}\LZK{OK. J'aurais prÃ©fÃ©rÃ© avoir un peu plus de dÃ©tails sur l'adaptation de la version async} 
+%\CER{Le problÃ¨me majeur sur l'adaptation MPI vers SMPI pour la partie asynchrone de l'algorithme a Ã©tÃ© le plantage en SMPI de Waitall aprÃ¨s un Isend et Irecv. J'avais proposÃ© un workaround en utilisant un MPI\_wait sÃ©parÃ© pour chaque Ã©change a la place d'un waitall unique pour TOUTES les Ã©changes, une instruction qui semble bien fonctionner en MPI. Ce workaround aussi fonctionne bien. Mais aprÃ¨s, tu as modifiÃ© le programme avec l'ajout d'un MPI\_Test, au niveau de la routine de dÃ©tection de la convergence et du coup, l'Ã©change global avec waitall a aussi fonctionnÃ©.}
+Note here that the use of SMPI functions optimizer for memory footprint and CPU usage is not recommended knowing that one wants to get real results by simulation.
+As mentioned, upon this adaptation, the algorithm is executed as in real life in the simulated environment after the following minor changes. The scope of all declared 
+global variables have been moved to local subroutines. Indeed, global variables generate side effects arising from the concurrent access of 
+shared memory used by threads simulating each computing unit in the SimGrid architecture. 
+%Second, some compilation errors on MPI\_Waitall and MPI\_Finalize primitives have been fixed with the latest version of SimGrid.
+%\AG{compilation or run-time error?}
+In total, the initial MPI program running on the simulation environment SMPI gave after a very simple adaptation the same results as those obtained in a real 
+environment. We have successfully executed the code for the synchronous GMRES algorithm compared with our asynchronous multisplitting algorithm after few modifications. 
 
-\begin{itemize}
-	\item HOSTFILE : Hosts file description.
-	\item PLATFORM: file description of the platform architecture : clusters (CPU power,
-... ) , intra cluster network description, inter cluster network (bandwidth bw ,
-lat latency , ... ).
-\end{itemize}
 
 
-\paragraph*{Arguments of the program}
+\section{Simulation results}
 
+When the \textit{real} application runs in the simulation environment and produces the expected results, varying the input
+parameters and the program arguments allows us to compare outputs from the code execution. We have noticed from this
+study that the results depend on the following parameters:  
 \begin{itemize}
-	\item Description of the cluster architecture;
-	\item Maximum number of internal and external iterations;
-	\item Internal and external precisions;
-	\item Matrix size NX , NY and NZ;
-	\item Matrix diagonal value = 6.0;
-	\item Execution Mode: synchronous or asynchronous.
-\end{itemize}
-
-\begin{table}
+\item At the network level, we found that the most critical values are the
+  bandwidth and the network latency.
+\item Hosts processors power (GFlops) can also influence the results.
+\item Finally, when submitting job batches for execution, the arguments values
+  passed to the program like the maximum number of iterations or the precision are critical. They allow us to ensure not only the convergence of the
+  algorithm but also to get the main objective in getting an execution time with the asynchronous multisplitting  less than with synchronous GMRES. 
+  \end{itemize}
+
+The ratio between the simulated execution time of synchronous GMRES algorithm
+compared to the asynchronous multisplitting algorithm ($t_\text{GMRES} / t_\text{Multisplitting}$) is defined as the \emph{relative gain}. So,
+our objective running the algorithm in SimGrid is to obtain a relative gain greater than 1.
+A priori, obtaining a relative gain greater than 1 would be difficult in a local
+area network configuration where the synchronous GMRES method will take advantage on the
+rapid exchange of information on such high-speed links. Thus, the methodology
+adopted was to launch the application on a clustered network. In this
+configuration, degrading the inter-cluster network performance will penalize the
+synchronous mode allowing to get a relative gain greater than 1.  This action
+simulates the case of distant clusters linked with long distance networks as in grid computing context.
+
+
+
+Both codes were simulated on a two clusters based network with 50 hosts each, totalling 100 hosts. Various combinations of the above
+factors have provided the results shown in Table~\ref{tab.cluster.2x50}. The problem size of the 3D Poisson problem  ranges from $N=N_x = N_y = N_z = \text{62}$ to 150 elements (that is from
+$\text{62}^\text{3} = \text{\np{238328}}$ to $\text{150}^\text{3} =
+\text{\np{3375000}}$ entries). With the asynchronous multisplitting algorithm the simulated execution time is on average 2.5 times faster than with the synchronous GMRES one. 
+%\AG{Expliquer comment lire les tableaux.}
+%\CER{J'ai reformulÃ© la phrase par la lecture du tableau. Plus de dÃ©tails seront lus dans la partie InterprÃ©tations et commentaires}
+% use the same column width for the following three tables
+\newlength{\mytablew}\settowidth{\mytablew}{\footnotesize\np{E-11}}
+\newenvironment{mytable}[1]{% #1: number of columns for data
+  \renewcommand{\arraystretch}{1.3}%
+  \begin{tabular}{|>{\bfseries}r%
+                  |*{#1}{>{\centering\arraybackslash}p{\mytablew}|}}}{%
+    \end{tabular}}
+
+\begin{table}[!t]
   \centering
-  \caption{2 clusters X 50 nodes}
+  \caption{Relative gain  of the multisplitting algorithm compared  to GMRES for
+    different configurations with 2 clusters, each one composed of 50 nodes. Latency = $20$ms}
   \label{tab.cluster.2x50}
-  \includegraphics[width=209pt]{img-1.eps}
-\end{table}
-
-\begin{table}
-  \centering
-  \caption{3 clusters X 33 n\oe{}uds}
-  \label{tab.cluster.3x33}
-  \includegraphics[width=209pt]{img-1.eps}
-\end{table}
 
-\begin{table}
-  \centering
-  \caption{3 clusters X 67 noeuds}
-  \label{tab.cluster.3x67}
-  \includegraphics[width=128pt]{img-2.eps}
+  \begin{mytable}{5}
+    \hline
+    bandwidth (Mbit/s)
+    & 5         & 5         & 5         & 5         & 5         \\
+    \hline
+  %  latency (ms)
+   % & 20      &  20      & 20      & 20      & 20      \\
+    %\hline
+    power (GFlops)
+    & 1         & 1         & 1         & 1.5       & 1.5       \\
+    \hline
+    size $(N)$
+    & $62^3$        & $62^3$        & $62^3$        & $100^3$       & $100^3$       \\
+    \hline
+    Precision
+    & \np{E-5}  & \np{E-8}  & \np{E-9}  & \np{E-11} & \np{E-11} \\
+    \hline
+    \hline
+    Relative gain
+    & 2.52      & 2.55      & 2.52      & 2.57      & 2.54      \\
+    \hline
+  \end{mytable}
+
+  \bigskip
+
+  \begin{mytable}{5}
+    \hline
+    bandwidth (Mbit/s)
+    & 50        & 50        & 50        & 50        & 50 \\ %       & 10        & 10 \\
+    \hline
+    %latency (ms)
+    %& 20      & 20      & 20      & 20      & 20 \\ %      & 0.03      & 0.01 \\
+    %\hline
+    Power (GFlops)
+    & 1.5       & 1.5       & 1.5       & 1.5       & 1.5 \\ %      & 1         & 1.5 \\
+    \hline
+    size $(N)$
+    & $110^3$       & $120^3$       & $130^3$       & $140^3$       & $150^3$  \\ %     & 171       & 171 \\
+    \hline
+    Precision
+    & \np{E-11} & \np{E-11} & \np{E-11} & \np{E-11} & \np{E-11} \\ % & \np{E-5}  & \np{E-5} \\
+    \hline
+    \hline
+    Relative gain
+    & 2.53      & 2.51     & 2.58     & 2.55     & 2.54   \\ %  & 1.59      & 1.29 \\
+    \hline
+  \end{mytable}
 \end{table}
+  
+%\RC{Du coup la latence est toujours la mÃªme, pourquoi la mettre dans la table?}
 
-\paragraph*{Interpretations and comments}
-
-After analyzing the outputs, generally, for the configuration with two or three
-clusters including one hundred hosts (Tables~\ref{tab.cluster.2x50} and~\ref{tab.cluster.3x33}), some combinations of the
-used parameters affecting the results have given a speedup less than 1, showing
-the effectiveness of the asynchronous performance compared to the synchronous
-mode.
-
-In the case of a two clusters configuration, Table~\ref{tab.cluster.2x50} shows that with a
-deterioration of inter cluster network set with 5 Mbits/s of bandwidth, a latency
-in order of a hundredth of a millisecond and a system power of one GFlops, an
-efficiency of about 40\% in asynchronous mode is obtained for a matrix size of 62
-elements . It is noticed that the result remains stable even if we vary the
-external precision from E -05 to E-09. By increasing the problem size up to 100
-elements, it was necessary to increase the CPU power of 50 \% to 1.5 GFlops for a
-convergence of the algorithm with the same order of asynchronous mode efficiency.
-Maintaining such a system power but this time, increasing network throughput
-inter cluster up to 50 Mbits /s, the result of efficiency of about 40\% is
-obtained with high external  precision of E-11 for a matrix size from 110 to 150
-side elements .
-
-For the 3 clusters architecture including a total of 100 hosts, Table~\ref{tab.cluster.3x33} shows
-that it was difficult to have a combination which gives an efficiency of
-asynchronous below 80 \%. Indeed, for a matrix size of 62 elements, equality
-between the performance of the two modes (synchronous and asynchronous) is
-achieved with an inter cluster of 10 Mbits/s and a latency of E- 01 ms. To
-challenge an efficiency by 78\% with a matrix size of 100 points, it was
-necessary to degrade the inter cluster network bandwidth from 5 to 2 Mbit/s.
-
-A last attempt was made for a configuration of three clusters but more power
-with 200 nodes in total. The convergence with a speedup of 90 \% was obtained
-with a bandwidth of 1 Mbits/s as shown in Table~\ref{tab.cluster.3x67}.
-
-\section{Conclusion}
-
+%Then we have changed the network configuration using three clusters containing
+%respectively 33, 33 and 34 hosts, or again by on hundred hosts for all the
+%clusters. In the same way as above, a judicious choice of key parameters has
+%permitted to get the results in Table~\ref{tab.cluster.3x33} which shows the
+%relative gains greater than 1 with a matrix size from 62 to 100 elements.
 
-% 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*}
+%\CER{En accord avec RC, on a pour le moment enlevÃ© les tableaux 2 et 3 sachant que les rÃ©sultats obtenus sont limites. De mÃªme, on a enlevÃ© aussi les deux derniÃ¨res colonnes du tableau I en attendant une meilleure performance et une meilleure precision}
+%\begin{table}[!t]
+%  \centering
+%  \caption{3 clusters, each with 33 nodes}
+%  \label{tab.cluster.3x33}
 %
-% 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.
+%  \begin{mytable}{6}
+%    \hline
+%    bandwidth 
+%    & 10       & 5        & 4        & 3        & 2        & 6 \\
+%    \hline
+%    latency
+%    & 0.01     & 0.02     & 0.02     & 0.02     & 0.02     & 0.02 \\
+%    \hline
+%    power
+%    & 1        & 1        & 1        & 1        & 1        & 1 \\
+%    \hline
+%    size
+%    & 62       & 100      & 100      & 100      & 100      & 171 \\
+%    \hline
+%    Prec/Eprec
+%    & \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} & \np{E-5} \\
+%    \hline
+%    \hline
+%    Relative gain
+%    & 1.003    & 1.01     & 1.08     & 1.19     & 1.28     & 1.01 \\
+%    \hline
+%  \end{mytable}
+%\end{table}
 
+%In a final step, results of an execution attempt to scale up the three clustered
+%configuration but increasing by two hundreds hosts has been recorded in
+%Table~\ref{tab.cluster.3x67}.
 
-% 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}
+%  \centering
+%  \caption{3 clusters, each with 66 nodes}
+%  \label{tab.cluster.3x67}
+%
+%  \begin{mytable}{1}
+%    \hline
+%    bandwidth  & 1 \\
+%    \hline
+%    latency    & 0.02 \\
+%    \hline
+%    power      & 1 \\
+%    \hline
+%    size       & 62 \\
+%    \hline
+%    Prec/Eprec & \np{E-5} \\
+%    \hline
+%    \hline
+%    Relative gain    & 1.11 \\
+%    \hline
+%  \end{mytable}
 %\end{table}
 
+Note that the program was run with the following parameters:
 
-% 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.
-
-
+\paragraph*{SMPI parameters}
 
+\begin{itemize}
+\item HOSTFILE: Text file containing the list of the processors units name. Here 100 hosts;
+\item PLATFORM: XML file description of the platform architecture with the
+  following characteristics:
+  % two clusters (cluster1 and cluster2) with the following characteristics:
+  \begin{itemize}
+  \item 2 clusters of 50 hosts each;
+  \item Processor unit power: \np[GFlops]{1} or \np[GFlops]{1.5};
+  \item Intra-cluster network bandwidth: \np[Gbit/s]{1.25} and latency: \np[$\mu$s]{50};
+  \item Inter-cluster network bandwidth: \np[Mbit/s]{5} or \np[Mbit/s]{50} and latency: \np[ms]{20};
+  \end{itemize}
+\end{itemize}
 
 
+\paragraph*{Arguments of the program}
 
+\begin{itemize}
+\item Description of the cluster architecture matching the format <Number of
+  clusters> <Number of hosts in cluster1> <Number of hosts in cluster2>;
+\item Maximum numbers of outer and inner iterations;
+\item Outer and inner precisions on the residual error;
+\item Matrix size $N_x$, $N_y$ and $N_z$;
+\item Matrix diagonal value: $6$ (see Equation~(\ref{eq:03}));
+\item Matrix off-diagonal values: $-1$;
+\item Communication mode: asynchronous.
+\end{itemize}
 
-% conference papers do not normally have an appendix
+\paragraph*{Interpretations and comments}
 
+After analyzing the outputs, generally, for the two clusters including one hundred hosts configuration (Tables~\ref{tab.cluster.2x50}), some combinations of parameters affecting
+the results, have given a relative gain of more than 2.5, showing the effectiveness of the
+asynchronous multisplitting  compared to GMRES with two distant clusters.
+
+With these settings, Table~\ref{tab.cluster.2x50} shows
+that after setting the bandwidth of the  inter cluster network to  \np[Mbit/s]{5}, the latency to $20$ millisecond and the processor power
+to one GFlops, an efficiency of about \np[\%]{40} is
+obtained in asynchronous mode for a matrix size of $62^3$ elements. It is noticed that the result remains
+stable even if the residual error precision varies from \np{E-5} to \np{E-9}. By
+increasing the matrix size up to $100^3$ elements, it was necessary to increase the
+CPU power by \np[\%]{50} to \np[GFlops]{1.5} to get the algorithm convergence and the same order of asynchronous mode efficiency.  Maintaining  a relative gain of $2.5$ and such processor power but increasing network throughput inter cluster up to \np[Mbit/s]{50},  is obtained with
+high external precision of \np{E-11} for a matrix size from $110^3$ to $150^3$ side
+elements.
+
+%For the 3 clusters architecture including a total of 100 hosts,
+%Table~\ref{tab.cluster.3x33} shows that it was difficult to have a combination
+%which gives a relative gain of asynchronous mode more than 1.2. Indeed, for a
+%matrix size of 62 elements, equality between the performance of the two modes
+%(synchronous and asynchronous) is achieved with an inter cluster of
+%\np[Mbit/s]{10} and a latency of \np[ms]{E-1}. To challenge an efficiency greater than 1.2 with a matrix %size of 100 points, it was necessary to degrade the
+%inter cluster network bandwidth from 5 to \np[Mbit/s]{2}.
+%\AG{Conclusion, on prend une plateforme pourrie pour avoir un bon ratio sync/async ???
+  %Quelle est la perte de perfs en faisant Ã§a ?}
+
+%A last attempt was made for a configuration of three clusters but more powerful
+%with 200 nodes in total. The convergence with a relative gain around 1.1 was
+%obtained with a bandwidth of \np[Mbit/s]{1} as shown in
+%Table~\ref{tab.cluster.3x67}.
+
+%\RC{Est ce qu'on sait expliquer pourquoi il y a une telle diffÃ©rence entre les rÃ©sultats avec 2 et 3 clusters... Avec 3 clusters, ils sont pas trÃ¨s bons... Je me demande s'il ne faut pas les enlever...}
+%\RC{En fait je pense avoir la rÃ©ponse Ã  ma remarque... On voit avec les 2 clusters que le gain est d'autant plus grand qu'on choisit une bonne prÃ©cision. Donc, plusieurs solutions, lancer rapidement un long test pour confirmer ca, ou enlever des tests... ou on ne change rien :-)}
+%\LZK{Ma question est: le bandwidth et latency sont ceux inter-clusters ou pour les deux inter et intra cluster??}
+%\CER{DÃ©finitivement, les paramÃ¨tres rÃ©seaux variables ici se rapportent au rÃ©seau INTER cluster.}
+\section{Conclusion}
+The simulation of the execution of parallel asynchronous iterative algorithms on large scale  clusters has been presented. 
+In this work, we show that SimGrid is an efficient simulation tool that has enabled us to 
+reach the following two objectives: 
+
+\begin{enumerate}
+\item  To have  a flexible  configurable execution  platform that  allows  us to
+  simulate algorithms for  which execution of all parts of
+  the  code is  necessary. Using  simulations before  real executions  is  a nice
+  solution to detect potential scalability problems.
+
+\item To test the combination of the cluster and network specifications permitting to execute an asynchronous algorithm faster than a synchronous one.
+\end{enumerate}
+Our results have shown that with two distant clusters, the asynchronous multisplitting method is faster by \np[\%]{40} compared to the synchronous GMRES method
+which is not negligible for solving complex practical problems with ever increasing size.
+
+Several studies have already addressed the performance execution time of 
+this class of algorithm. The work presented in this paper has 
+demonstrated an original solution to optimize the use of a simulation 
+tool to run efficiently an iterative parallel algorithm in asynchronous 
+mode in a grid architecture. 
+
+In future works, we plan to extend our experimentations to larger scale platforms by increasing the number of computing cores and the number of clusters. 
+We will also have to increase the size of the input problem which will require the use of a more powerful simulation platform. At last, we expect to compare our simulation results to real execution results on real architectures in order to better experimentally validate our study. Finally, we also plan to study other problems with the multisplitting method and other asynchronous iterative methods.
 
-% use section* for acknowledgement
 \section*{Acknowledgment}
 
-
-The authors would like to thank...
-
-
-
-
+This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
+%\todo[inline]{The authors would like to thank\dots{}}
 
 % 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{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{IEEEabrv,hpccBib}
 
 
 
-
-% that's all folks
 \end{document}
 
-
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% fill-column: 80
+%%% ispell-local-dictionary: "american"
+%%% End:
+
+% LocalWords:  Ramamonjisoa Laiymani Arnaud Giersch Ziane Khodja RaphaÃ«l Femto
+% LocalWords:  UniversitÃ© Franche ComtÃ© IUT MontbÃ©liard MarÃ©chal Juin Inria Sud
+% LocalWords:  Ouest Vieille Talence cedex scalability experimentations HPC MPI
+% LocalWords:  Parallelization AIAC GMRES multi SMPI SISC SIAC SimDAG DAGs Lua
+% LocalWords:  Fortran GFlops priori Mbit de du fcomte multisplitting scalable
+% LocalWords:  SimGrid Belfort parallelize Labex ANR LABX IEEEabrv hpccBib Gbit
+% LocalWords:  intra durations nonsingular Waitall discretization discretized
+% LocalWords:  InnerSolver Isend Irecv parallelization
