DL : conclu. Manque les futurs works

[rce2015.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 0df781f114c3964a53bda90e85659d749f7a2955..fa447f65dda929248e60d8372c2057d50db6ad9a 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -21,7 +21,6 @@
 \usepackage{algpseudocode}
 %\usepackage{amsthm}
 \usepackage{graphicx}
 \usepackage{algpseudocode}
 %\usepackage{amsthm}
 \usepackage{graphicx}

-\usepackage[american]{babel}

 % Extension pour les liens intra-documents (tagged PDF)
 % et l'affichage correct des URL (commande \url{http://example.com})
 %\usepackage{hyperref}
 % Extension pour les liens intra-documents (tagged PDF)
 % et l'affichage correct des URL (commande \url{http://example.com})
 %\usepackage{hyperref}


@@ -71,27 +70,30 @@
 
 
 
 
 
 

-\begin{document} \RCE{Titre a confirmer.} \title{Comparative performance
-analysis of simulated grid-enabled numerical iterative algorithms}
+\begin{document}
+\title{Grid-enabled simulation of large-scale linear iterative solvers}

 %\itshape{\journalnamelc}\footnotemark[2]}
 
 %\itshape{\journalnamelc}\footnotemark[2]}
 

-\author{    Charles Emile Ramamonjisoa and
-    David Laiymani and
-    Arnaud Giersch and
-    Lilia Ziane Khodja and
-    Raphaël Couturier
+\author{Charles Emile Ramamonjisoa\affil{1},
+    David Laiymani\affil{1},
+    Arnaud Giersch\affil{1},
+    Lilia Ziane Khodja\affil{2} and
+    Raphaël Couturier\affil{1}

 }
 
 \address{
 }
 
 \address{

-       \centering
-    Femto-ST Institute - DISC Department\\
-    Université de Franche-Comté\\
-    Belfort\\
-    Email: \email{{raphael.couturier,arnaud.giersch,david.laiymani,charles.ramamonjisoa}@univ-fcomte.fr}
+  \affilnum{1}%
+  Femto-ST Institute, DISC Department,
+  University of Franche-Comté,
+  Belfort, France.
+  Email:~\email{{charles.ramamonjisoa,david.laiymani,arnaud.giersch,raphael.couturier}@univ-fcomte.fr}\break
+  \affilnum{2}
+  Department of Aerospace \& Mechanical Engineering,
+  Non Linear Computational Mechanics,
+  University of Liege, Liege, Belgium.
+  Email:~\email{l.zianekhodja@ulg.ac.be}

 }
 
 }
 

-%% Lilia Ziane Khodja: Department of Aerospace \& Mechanical Engineering\\ Non Linear Computational Mechanics\\ University of Liege\\ Liege, Belgium. Email: l.zianekhodja@ulg.ac.be
-

 \begin{abstract}   The behavior of multi-core applications is always a challenge
 to predict, especially with a new architecture for which no experiment has been
 performed. With some applications, it is difficult, if not impossible, to build
 \begin{abstract}   The behavior of multi-core applications is always a challenge
 to predict, especially with a new architecture for which no experiment has been
 performed. With some applications, it is difficult, if not impossible, to build


@@ -134,7 +136,7 @@ are often very important. So, in this context it is difficult to optimize a
 given application for a given  architecture. In this way and in order to reduce
 the access cost to these computing resources it seems very interesting to use a
 simulation environment.  The advantages are numerous: development life cycle,
 given application for a given  architecture. In this way and in order to reduce
 the access cost to these computing resources it seems very interesting to use a
 simulation environment.  The advantages are numerous: development life cycle,

-code debugging, ability to obtain results quickly~\ldots. In counterpart, the simulation results need to be consistent with the real ones.
+code debugging, ability to obtain results quickly\dots{} In counterpart, the simulation results need to be consistent with the real ones.

 
 In this paper we focus on a class of highly efficient parallel algorithms called
 \emph{iterative algorithms}. The parallel scheme of iterative methods is quite
 
 In this paper we focus on a class of highly efficient parallel algorithms called
 \emph{iterative algorithms}. The parallel scheme of iterative methods is quite


@@ -163,34 +165,30 @@ application  on   a  given   multi-core  architecture.  Finding   good  resource
 allocations policies under  varying CPU power, network speeds and  loads is very
 challenging and  labor intensive~\cite{Calheiros:2011:CTM:1951445.1951450}. This
 problematic is  even more difficult  for the  asynchronous scheme where  a small
 allocations policies under  varying CPU power, network speeds and  loads is very
 challenging and  labor intensive~\cite{Calheiros:2011:CTM:1951445.1951450}. This
 problematic is  even more difficult  for the  asynchronous scheme where  a small

-parameter variation of the execution platform can lead to very different numbers
-of iterations to reach the converge and so to very different execution times. In
-this challenging context we think that the  use of a simulation tool can greatly
-leverage the possibility of testing various platform scenarios.
-
-The main contribution of this paper is to show that the use of a simulation tool
-(i.e. the SimGrid toolkit~\cite{SimGrid}) in the context of real  parallel
-applications (i.e. large linear system solvers) can help developers to better
-tune their application for a given multi-core architecture. To show the validity
-of this approach we first compare the simulated execution of the multisplitting
-algorithm  with  the  GMRES   (Generalized   Minimal  Residual)
-solver~\cite{saad86} in synchronous mode. 
-
-\LZK{Pas trop convainquant comme argument pour valider l'approche de simulation. \\On peut dire par exemple: on a pu simuler différents algos itératifs à large échelle (le plus connu GMRES et deux variantes de multisplitting) et la simulation nous a permis (sans avoir le vrai matériel) de déterminer quelle serait la meilleure solution pour une telle configuration de l'archi ou vice versa.\\A revoir...}
-
-The obtained results on different
-simulated multi-core architectures confirm the real results previously obtained
-on non simulated architectures.  
-
-\LZK{Il n y a pas dans la partie expé cette comparaison et confirmation des résultats entre la simulation et l'exécution réelle des algos sur les vrais clusters.\\ Sinon on pourrait ajouter dans la partie expé une référence vers le journal supercomput de krylov multi pour confirmer que cette méthode est meilleure que GMRES sur les clusters large échelle.}
-
-We also confirm  the efficiency  of the
-asynchronous  multisplitting algorithm  compared to the synchronous  GMRES. 
-
-\LZK{P.S.: Pour tout le papier, le principal objectif n'est pas de faire des comparaisons entre des méthodes itératives!!\\Sinon, les deux algorithmes Krylov multisplitting synchrone et multisplitting asynchrone sont plus efficaces que GMRES sur des clusters à large échelle.\\Et préciser, si c'est vraiment le cas, que le multisplitting asynchrone est plus efficace et adapté aux clusters distants par rapport aux deux autres algos (je n'ai pas encore lu la partie expé)}
-
-In
-this way and with a simple computing architecture (a laptop) SimGrid allows us
+parameter variation of the execution platform and of the application data can
+lead to very different numbers of iterations to reach the converge and so to
+very different execution times. In this challenging context we think that the
+use of a simulation tool can greatly leverage the possibility of testing various
+platform scenarios.
+
+The  {\bf main  contribution  of  this paper}  is  to show  that  the  use of  a
+simulation tool (i.e. the SimGrid toolkit~\cite{SimGrid}) in the context of real
+parallel applications (i.e. large linear  system solvers) can help developers to
+better tune their  application for a given multi-core architecture.  To show the
+validity of this approach we first compare the simulated execution of the Krylov
+multisplitting  algorithm   with  the   GMRES  (Generalized   Minimal  Residual)
+solver~\cite{saad86} in  synchronous mode.  The simulation  results allow  us to
+determine  which method  to choose  given a  specified multi-core  architecture.
+Moreover the  obtained results  on different simulated  multi-core architectures
+confirm the  real results  previously obtained  on non  simulated architectures.
+More precisely the simulated results are in accordance (i.e. with the same order
+of magnitude)  with the works  presented in~\cite{couturier15}, which  show that
+the synchronous  multisplitting method  is more efficient  than GMRES  for large
+scale  clusters.   Simulated   results  also  confirm  the   efficiency  of  the
+asynchronous  multisplitting   algorithm  compared  to  the   synchronous  GMRES
+especially in case of geographically distant clusters.
+
+In this way and with a simple computing architecture (a laptop) SimGrid allows us

 to run a test campaign  of  a  real parallel iterative  applications on
 different simulated multi-core architectures.  To our knowledge, there is no
 related work on the large-scale multi-core simulation of a real synchronous and
 to run a test campaign  of  a  real parallel iterative  applications on
 different simulated multi-core architectures.  To our knowledge, there is no
 related work on the large-scale multi-core simulation of a real synchronous and


@@ -203,8 +201,6 @@ Section~\ref{sec:04} details the different solvers that we use.  Finally our
 experimental results are presented in section~\ref{sec:expe} followed by some
 concluding remarks and perspectives.
 
 experimental results are presented in section~\ref{sec:expe} followed by some
 concluding remarks and perspectives.
 

-\LZK{Proposition d'un titre pour le papier: Grid-enabled simulation of large-scale linear iterative solvers.}
-

 
 \section{The asynchronous iteration model and the motivations of our work}
 \label{sec:asynchro}
 
 \section{The asynchronous iteration model and the motivations of our work}
 \label{sec:asynchro}


@@ -235,7 +231,7 @@ for the asynchronous scheme (this number depends depends on  the delay of the
 messages). Note that, it is not the case in the synchronous mode where the
 number of iterations is the same than in the sequential mode. In this way, the
 set of the parameters  of the  platform (number  of nodes,  power of nodes,
 messages). Note that, it is not the case in the synchronous mode where the
 number of iterations is the same than in the sequential mode. In this way, the
 set of the parameters  of the  platform (number  of nodes,  power of nodes,

-inter and  intra clusters  bandwidth  and  latency \ldots) and  of  the
+inter and  intra clusters  bandwidth  and  latency, \ldots) and  of  the

 application can drastically change the number of iterations required to get the
 convergence. It follows that asynchronous iterative algorithms are difficult to
 optimize since the financial and deployment costs on large scale multi-core
 application can drastically change the number of iterations required to get the
 convergence. It follows that asynchronous iterative algorithms are difficult to
 optimize since the financial and deployment costs on large scale multi-core


@@ -246,9 +242,61 @@ by simulation are in accordance with reality i.e. of the same order of
 magnitude. To our knowledge, there is no study on this problematic.
 
 \section{SimGrid}
 magnitude. To our knowledge, there is no study on this problematic.
 
 \section{SimGrid}

- \label{sec:simgrid}
+\label{sec:simgrid}
+SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid,casanova+giersch+legrand+al.2014.versatile} is a discrete event simulation framework to study the behavior of large-scale distributed computing platforms as Grids, Peer-to-Peer systems, Clouds and High Performance Computation systems. It is widely used to simulate and evaluate heuristics, prototype applications or even assess legacy MPI applications. It is still actively developed by the scientific community and distributed as an open source software.

 
 %%%%%%%%%%%%%%%%%%%%%%%%%
 
 %%%%%%%%%%%%%%%%%%%%%%%%%

+% SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid,casanova+giersch+legrand+al.2014.versatile}
+% 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 described 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 (cf Section IV - paragraph B).
+
+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
+means 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{Two-stage multisplitting methods}
 %%%%%%%%%%%%%%%%%%%%%%%%%
 
 \section{Two-stage multisplitting methods}


@@ -386,8 +434,6 @@ In addition, the following arguments are given to the programs at runtime:
         \item maximum number of restarts for the Arnorldi process in GMRES method,
        \item execution mode: synchronous or asynchronous.
 \end{itemize}
         \item maximum number of restarts for the Arnorldi process in GMRES method,
        \item execution mode: synchronous or asynchronous.
 \end{itemize}

-\LZK{CE pourrais tu vérifier et confirmer les valeurs des éléments diag et off-diag de la matrice?}
-\RCE{oui, les valeurs de diag et off-diag donnees sont ok}

 
 It should also be noticed that both solvers have been executed with the Simgrid selector \texttt{-cfg=smpi/running\_power} which determines the computational power (here 19GFlops) of the simulator host machine.
 
 
 It should also be noticed that both solvers have been executed with the Simgrid selector \texttt{-cfg=smpi/running\_power} which determines the computational power (here 19GFlops) of the simulator host machine.
 


@@ -496,7 +542,7 @@ and  between distant  clusters.  This parameter is application dependent.
 
 In the scope  of this paper, our  first objective is to analyze  when the Krylov
 Multisplitting  method   has  better  performance  than   the  classical  GMRES
 
 In the scope  of this paper, our  first objective is to analyze  when the Krylov
 Multisplitting  method   has  better  performance  than   the  classical  GMRES

-method. With a synchronous  iterative method, better performance mean a
+method. With a synchronous  iterative method, better performance means a

 smaller number of iterations and execution time before reaching the convergence.
 For a systematic study,  the experiments  should figure  out  that, for  various
 grid  parameters values, the simulator will confirm  the targeted outcomes,
 smaller number of iterations and execution time before reaching the convergence.
 For a systematic study,  the experiments  should figure  out  that, for  various
 grid  parameters values, the simulator will confirm  the targeted outcomes,


@@ -521,7 +567,8 @@ architectures and scaling up the input matrix size}
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ %\hline
  - &  N$_{x}$ x N$_{y}$ x N$_{z}$  =170 x 170 x 170    \\ \hline
  \end{tabular}
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ %\hline
  - &  N$_{x}$ x N$_{y}$ x N$_{z}$  =170 x 170 x 170    \\ \hline
  \end{tabular}

-\caption{Test conditions: Various grid configurations with the input matix size N$_{x}$=150 or N$_{x}$=170 \RC{je ne comprends pas la légende... Ca ne serait pas plutot Characteristics of cluster (mais il faudrait lui donner un nom)}}
+\caption{Test conditions: various grid configurations with the input matix size N$_{x}$=150 or N$_{x}$=170 \RC{N2 n'est pas défini..}\RC{Nx est défini, Ny? Nz?}
+\AG{La lettre 'x' n'est pas le symbole de la multiplication. Utiliser \texttt{\textbackslash times}.  Idem dans le texte, les figures, etc.}}

 \label{tab:01}
 \end{center}
 \end{table}
 \label{tab:01}
 \end{center}
 \end{table}


@@ -529,8 +576,6 @@ architectures and scaling up the input matrix size}
 
 
 
 
 
 

-%\RCE{J'ai voulu mettre les tableaux des données mais je pense que c'est inutile et ça va surcharger}
-

 
 In this  section, we analyze the  performance of algorithms running  on various
 grid configurations  (2x16, 4x8, 4x16  and 8x8). First,  the results in  Figure~\ref{fig:01}
 
 In this  section, we analyze the  performance of algorithms running  on various
 grid configurations  (2x16, 4x8, 4x16  and 8x8). First,  the results in  Figure~\ref{fig:01}


@@ -546,7 +591,8 @@ multisplitting method.
   \begin{center}
     \includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
   \end{center}
   \begin{center}
     \includegraphics[width=100mm]{cluster_x_nodes_nx_150_and_nx_170.pdf}
   \end{center}

-  \caption{Various grid configurations with the input matrix size N$_{x}$=150 and N$_{x}$=170}
+  \caption{Various grid configurations with the input matrix size N$_{x}$=150 and N$_{x}$=170\RC{idem}
+\AG{Utiliser le point comme séparateur décimal et non la virgule.  Idem dans les autres figures.}}

   \label{fig:01}
 \end{figure}
 
   \label{fig:01}
 \end{figure}
 


@@ -556,7 +602,7 @@ grid architectures, even  with the same number of processors  (for example, 2x16
 and  4x8). We  can  observ  the low  sensitivity  of  the Krylov multisplitting  method
 (compared with the classical GMRES) when scaling up the number of the processors
 in the  grid: in  average, the GMRES  (resp. Multisplitting)  algorithm performs
 and  4x8). We  can  observ  the low  sensitivity  of  the Krylov multisplitting  method
 (compared with the classical GMRES) when scaling up the number of the processors
 in the  grid: in  average, the GMRES  (resp. Multisplitting)  algorithm performs

-$40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors.
+$40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors. \RC{pas très clair, c'est pas précis de dire qu'un algo perform mieux qu'un autre, selon quel critère?}

 
 \subsubsection{Running on two different inter-clusters network speeds \\}
 
 
 \subsubsection{Running on two different inter-clusters network speeds \\}
 


@@ -569,27 +615,25 @@ $40\%$ better (resp. $48\%$) when running from 2x16=32 to 8x8=64 processors.
  - & N2 : bw=1Gbs-lat=5.10$^{-5}$ \\
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline
  \end{tabular}
  - & N2 : bw=1Gbs-lat=5.10$^{-5}$ \\
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline
  \end{tabular}

-\caption{Test conditions: Grid 2x16 and 4x8 - Networks N1 vs N2}
+\caption{Test conditions: grid 2x16 and 4x8 with  networks N1 vs N2}

 \label{tab:02}
 \end{center}
 \end{table}
 
 These experiments  compare the  behavior of  the algorithms  running first  on a
 \label{tab:02}
 \end{center}
 \end{table}
 
 These experiments  compare the  behavior of  the algorithms  running first  on a

-speed inter-cluster  network (N1) and  also on  a less performant  network (N2).
-Figure~\ref{fig:02} shows that end users will  gain to reduce the execution time
-for  both  algorithms  in using  a  grid  architecture  like  4x16 or  8x8:  the
-performance was increased  by a factor of  $2$. The results depict  also that when
+speed inter-cluster  network (N1) and  also on  a less performant  network (N2). \RC{Il faut définir cela avant...}
+Figure~\ref{fig:02} shows that end users will reduce the execution time
+for  both  algorithms when using  a  grid  architecture  like  4x16 or  8x8: the reduction is about $2$. The results depict  also that when

 the  network speed  drops down (variation of 12.5\%), the  difference between  the two Multisplitting algorithms execution times can reach more than 25\%.
 the  network speed  drops down (variation of 12.5\%), the  difference between  the two Multisplitting algorithms execution times can reach more than 25\%.

-%\RC{c'est pas clair : la différence entre quoi et quoi?}
-%\DL{pas clair}
-%\RCE{Modifie}
+

 
 
 %\begin{wrapfigure}{l}{100mm}
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}
 
 
 %\begin{wrapfigure}{l}{100mm}
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{cluster_x_nodes_n1_x_n2.pdf}

-\caption{Grid 2x16 and 4x8 - Networks N1 vs N2}
+\caption{Grid 2x16 and 4x8 with networks N1 vs N2
+\AG{\np{8E-6}, \np{5E-6} au lieu de 8E-6, 5E-6}}

 \label{fig:02}
 \end{figure}
 %\end{wrapfigure}
 \label{fig:02}
 \end{figure}
 %\end{wrapfigure}


@@ -605,7 +649,7 @@ the  network speed  drops down (variation of 12.5\%), the  difference between  t
  Network & N1 : bw=1Gbs \\ %\hline
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline
  \end{tabular}
  Network & N1 : bw=1Gbs \\ %\hline
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline
  \end{tabular}

-\caption{Test conditions: Network latency impacts}
+\caption{Test conditions: network latency impacts}

 \label{tab:03}
 \end{table}
 
 \label{tab:03}
 \end{table}
 


@@ -614,20 +658,22 @@ the  network speed  drops down (variation of 12.5\%), the  difference between  t
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf}
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_latency_impact_on_execution_time.pdf}

-\caption{Network latency impacts on execution time}
+\caption{Network latency impacts on execution time
+\AG{\np{E-6}}}

 \label{fig:03}
 \end{figure}
 
 
 \label{fig:03}
 \end{figure}
 
 

-According to the results  of  Figure~\ref{fig:03}, a  degradation  of the  network
-latency from $8.10^{-6}$  to $6.10^{-5}$ implies an absolute  time increase of more
-than $75\%$  (resp. $82\%$) of the  execution for the classical  GMRES (resp. Krylov
-multisplitting)   algorithm.   In   addition,   it  appears   that  the   Krylov
-multisplitting method tolerates  more the network latency variation  with a less
-rate  increase  of  the  execution   time.   Consequently,  in  the  worst  case
-($lat=6.10^{-5 }$), the  execution time for GMRES is almost  the double than the
-time of the Krylov multisplitting, even  though, the performance was on the same
-order of magnitude with a latency of $8.10^{-6}$.
+According to  the results of  Figure~\ref{fig:03}, a degradation of  the network
+latency from  $8.10^{-6}$ to  $6.10^{-5}$ implies an  absolute time  increase of
+more  than $75\%$  (resp.  $82\%$)  of the  execution  for  the classical  GMRES
+(resp.  Krylov multisplitting)  algorithm.   In addition,  it  appears that  the
+Krylov multisplitting method tolerates more the network latency variation with a
+less  rate increase  of  the  execution time.\RC{Les  2  précédentes phrases  me
+  semblent en contradiction....}  Consequently, in the worst case ($lat=6.10^{-5
+}$), the  execution time for  GMRES is  almost the double  than the time  of the
+Krylov multisplitting,  even though, the  performance was  on the same  order of
+magnitude with a latency of $8.10^{-6}$.

 
 \subsubsection{Network bandwidth impacts on performance}
 \ \\
 
 \subsubsection{Network bandwidth impacts on performance}
 \ \\


@@ -639,7 +685,7 @@ order of magnitude with a latency of $8.10^{-6}$.
  Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \\
  \end{tabular}
  Network & N1 : bw=1Gbs - lat=5.10$^{-5}$ \\ %\hline
  Input matrix size & N$_{x}$ x N$_{y}$ x N$_{z}$ =150 x 150 x 150\\ \hline \\
  \end{tabular}

-\caption{Test conditions: Network bandwidth impacts}
+\caption{Test conditions: Network bandwidth impacts\RC{Qu'est ce qui varie ici? Il n'y a pas de variation dans le tableau}}

 \label{tab:04}
 \end{table}
 
 \label{tab:04}
 \end{table}
 


@@ -647,7 +693,8 @@ order of magnitude with a latency of $8.10^{-6}$.
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf}
 \begin{figure} [ht!]
 \centering
 \includegraphics[width=100mm]{network_bandwith_impact_on_execution_time.pdf}

-\caption{Network bandwith impacts on execution time}
+\caption{Network bandwith impacts on execution time
+\AG{``Execution time'' avec un 't' minuscule}. Idem autres figures.}

 \label{fig:04}
 \end{figure}
 
 \label{fig:04}
 \end{figure}
 


@@ -685,9 +732,9 @@ In these experiments, the input matrix size  has been set from $N_{x} = N_{y}
 time for  both algorithms increases when  the input matrix size  also increases.
 But the interesting results are:
 \begin{enumerate}
 time for  both algorithms increases when  the input matrix size  also increases.
 But the interesting results are:
 \begin{enumerate}

-  \item the drastic increase ($10$ times) \RC{Je ne vois pas cela sur la figure}
-\RCE{Corrige} of the  number of  iterations needed  to reach the  convergence for  the classical
-GMRES algorithm when  the matrix size go beyond $N_{x}=150$;
+  \item the drastic increase ($10$ times)  of the number of iterations needed to
+    reach the convergence for the classical GMRES algorithm when the matrix size
+    go beyond $N_{x}=150$; \RC{C'est toujours pas clair... ok le nommbre d'itérations est 10 fois plus long mais la suite de la phrase ne veut rien dire}

 \item the  classical GMRES execution time  is almost the double  for $N_{x}=140$
   compared with the Krylov multisplitting method.
 \end{enumerate}
 \item the  classical GMRES execution time  is almost the double  for $N_{x}=140$
   compared with the Krylov multisplitting method.
 \end{enumerate}


@@ -723,10 +770,16 @@ on the  algorithms performance in  varying the CPU  power of the  clusters nodes
 from $1$ to $19$ GFlops.  The outputs  depicted in Figure~\ref{fig:06}  confirm the
 performance gain,  around $95\%$ for  both of the  two methods, after  adding more
 powerful CPU.
 from $1$ to $19$ GFlops.  The outputs  depicted in Figure~\ref{fig:06}  confirm the
 performance gain,  around $95\%$ for  both of the  two methods, after  adding more
 powerful CPU.

+\ \\
+%\DL{il faut une conclusion sur ces tests : ils confirment les résultats déjà
+%obtenus en grandeur réelle. Donc c'est une aide précieuse pour les dev. Pas
+%besoin de déployer sur une archi réelle}

 
 

-\DL{il faut une conclusion sur ces tests : ils confirment les résultats déjà
-obtenus en grandeur réelle. Donc c'est une aide précieuse pour les dev. Pas
-besoin de déployer sur une archi réelle}
+To conclude these series of experiments, with  SimGrid we have been able to make
+many simulations  with many parameters  variations. Doing all  these experiments
+with a real platform is most of  the time not possible. Moreover the behavior of
+both GMRES and  Krylov multisplitting methods is in accordance  with larger real
+executions on large scale supercomputer~\cite{couturier15}.

 
 
 \subsection{Comparing GMRES in native synchronous mode and the multisplitting algorithm in asynchronous mode}
 
 
 \subsection{Comparing GMRES in native synchronous mode and the multisplitting algorithm in asynchronous mode}


@@ -815,23 +868,46 @@ geographically distant clusters through the internet.
     \hline
   \end{mytable}
 %\end{table}
     \hline
   \end{mytable}
 %\end{table}

- \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES}
+ \caption{Relative gain of the multisplitting algorithm compared with the classical GMRES
+\AG{C'est un tableau, pas une figure}}

  \label{fig:07}
 \end{figure}
 
 
 \section{Conclusion}
  \label{fig:07}
 \end{figure}
 
 
 \section{Conclusion}

-CONCLUSION

 
 

+In this paper we have presented the simulation of the execution of three
+different parallel solvers on some multi-core architectures. We have show that
+the SimGrid toolkit is an interesting simulation tool that has allowed us to
+determine  which method  to choose  given a  specified multi-core  architecture.
+Moreover the simulated results are in accordance (i.e. with the same order of
+magnitude)  with the works  presented in~\cite{couturier15}. Simulated   results
+also  confirm  the   efficiency  of  the asynchronous  multisplitting
+algorithm  compared  to  the   synchronous  GMRES especially in case of
+geographically distant clusters.

 
 

-\section*{Acknowledgment}
+These results are important since it is very  time consuming to find optimal
+configuration  and deployment requirements for a given application  on   a given
+multi-core  architecture. Finding   good  resource allocations policies under
+varying CPU power, network speeds and  loads is very challenging and  labor
+intensive. This problematic is  even more difficult  for the  asynchronous
+scheme where  a small parameter variation of the execution platform and of the
+application data can lead to very different numbers of iterations to reach the
+converge and so to very different execution times.

 
 

-This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
+
+Our future works...

 
 
 
 

+
+%\section*{Acknowledgment}
+\ack
+This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
+

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 \bibliography{biblio}
 
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 \bibliography{biblio}
 

+

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