Corrections Ingrid

diff --git a/hpcc.tex b/hpcc.tex
index 284e177d8e035d4580e233d3ee46226ad636409e..62922bcbae3b99f759e7d8dc5a1acf1910b9c8f4 100644 (file)
--- a/hpcc.tex
+++ b/hpcc.tex
@@ -76,7 +76,7 @@
 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
 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
+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
 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


@@ -92,8 +92,8 @@ efficient than the GMRES one to solve a 3D Poisson problem.
 
 \section{Introduction}
 
 
 \section{Introduction}
 

-Parallel computing and high performance computing (HPC) are becoming  more and more imperative for solving various
-problems raised by  researchers on various scientific disciplines but also by industrial in  the field. Indeed, the
+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
 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


@@ -106,39 +106,37 @@ Parallelization of such algorithms generally involves the division of the proble
 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
 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 \emph{synchronous} mode where a
-new iteration  begins only  when all nodes  communications are completed,  or in
+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
 \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 iterations required
-before  the convergence  is generally  greater  than for  the synchronous  case,
+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).
 
 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
+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
 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 is very
+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
 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 sensible to
+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
 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.  In  this  way, the  use of  a
-simulation  environment  to execute  parallel  iterative  algorithms found  some
-interests in reducing the highly cost  of access to computing resources: (1) for
+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
 the  applications  development life  cycle  and in  code  debugging  (2) and  in
 production  to get  results  in a  reasonable  execution time  with a  simulated

-infrastructure not  accessible with physical  resources.  Indeed, the  launch of
-distributed  iterative asynchronous  algorithms to  solve a  given problem  on a
-large-scale  simulated  environment challenges  to  find optimal  configurations
-giving  the best  results  with  a lowest  residual  error and  in  the best  of
-execution time.
+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
 
 
 To our knowledge,  there is no existing work on the  large-scale simulation of a


@@ -146,16 +144,16 @@ 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
   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

-effectiveness  of the  asynchronous  multisplitting algorithm  by comparing  its
-performance   with  the   synchronous  GMRES   (Generalized   Minimal  Residual) method
+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
 \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
+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?}. 
 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  had  allowed us  to  launch the  application  from  a modest  computing
+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
 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


@@ -168,10 +166,10 @@ tool to run efficiently an  asynchronous iterative parallel algorithm in a grid
 
 
 This article is structured as follows: after this introduction, the next section
 
 
 This article is structured as follows: after this introduction, the next section

-will  give a  brief  description  of iterative  asynchronous  model.  Then,  the
+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
 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  of the  splitting. This  code 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.
 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.


@@ -188,7 +186,7 @@ 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.
 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 to partially  overlap communications by  computations but
+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
 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


@@ -225,17 +223,17 @@ computing context.
 %% \AG{Several works\dots{} what?\\
 %  Le paragraphe suivant se trouve déjà dans l'intro ?}
 In the context of asynchronous algorithms, the number of iterations to reach the
 %% \AG{Several works\dots{} what?\\
 %  Le paragraphe suivant se trouve déjà dans l'intro ?}
 In the context of asynchronous algorithms, the number of iterations to reach the

-convergence depends on  the delay of messages. With  synchronous iterations, 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
 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 it is necessary to run the algorithm
-with real data. In fact, from an execution to another the order of messages will
+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,
 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 of the same parameters. As it is difficult to have
+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.
 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.


@@ -249,9 +247,9 @@ asynchronous iterative algorithms before being able to run real experiments.
 
 SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid} is a simulation
 framework to study the behavior of large-scale distributed systems.  As its name
 
 SimGrid~\cite{SimGrid,casanova+legrand+quinson.2008.simgrid} is a simulation
 framework to study the behavior of large-scale distributed systems.  As its name

-says, it emanates from the grid computing community, but is nowadays used to
+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
 study grids, clouds, HPC or peer-to-peer systems.  The early versions of SimGrid

-date from 1999, but it is still actively developed and distributed as an open
+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.
 
 source software.  Today, it is one of the major generic tools in the field of
 simulation for large-scale distributed systems.
 


@@ -265,8 +263,8 @@ 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
 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 the communications are intercepted, and their running time is computed
+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
 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


@@ -277,16 +275,16 @@ 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
 
 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 to run relatively fast
+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
 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 have no importance for the simulation results, there is
-also the possibility to share dynamically allocated data structures between
+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.
 several simulated processes, and thus to reduce the whole memory consumption.

-These two techniques can help to run simulations at a very large scale.
+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
 
 The validity of simulations with SimGrid has been asserted by several studies.
 See, for example, \cite{velho+schnorr+casanova+al.2013.validity} and articles


@@ -380,7 +378,7 @@ used iterative method by many researchers.
 \label{algo:01}
 \end{figure}
 
 \label{algo:01}
 \end{figure}
 

-Algorithm on Figure~\ref{algo:01} shows the main key points of the
+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
 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


@@ -408,12 +406,12 @@ 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
 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 $\ell$
+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
 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 masters of other clusters. In this work,
+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*}
 the local convergence on each cluster $\ell$ is detected when the following
 condition is satisfied
 \begin{equation*}


@@ -425,7 +423,7 @@ $X_\ell^k$ and $X_\ell^{k+1}$.
 
 
 
 
 
 

-In this paper, we solve the 3D Poisson problem whose the mathematical model is 
+In this paper, we solve the 3D Poisson problem whose mathematical model is 

 \begin{equation}
 \left\{
 \begin{array}{l}
 \begin{equation}
 \left\{
 \begin{array}{l}


@@ -435,7 +433,7 @@ u =0 \text{~on~} \Gamma =\partial\Omega
 \right.
 \label{eq:02}
 \end{equation}
 \right.
 \label{eq:02}
 \end{equation}

-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 the general expression could be written as
+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),
 \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),


@@ -447,7 +445,7 @@ 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
 \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. 
 
 \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. 
 

-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 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. 
+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. 

 
 \begin{figure}[!t]
 \centering
 
 \begin{figure}[!t]
 \centering


@@ -468,8 +466,8 @@ and with the addition of the primitive \texttt{MPI\_Test} was needed to avoid a
 %\CER{On voulait en fait montrer la simplicité de l'adaptation de l'algo a SimGrid. Les problèmes rencontrés décrits dans ce paragraphe concerne surtout le mode async}\LZK{OK. J'aurais préféré avoir un peu plus de détails sur l'adaptation de la version async} 
 %\CER{Le problème majeur sur l'adaptation MPI vers SMPI pour la partie asynchrone de l'algorithme a été le plantage en SMPI de Waitall après un Isend et Irecv. J'avais proposé un workaround en utilisant un MPI\_wait séparé pour chaque échange a la place d'un waitall unique pour TOUTES les échanges, une instruction qui semble bien fonctionner en MPI. Ce workaround aussi fonctionne bien. Mais après, tu as modifié le programme avec l'ajout d'un MPI\_Test, au niveau de la routine de détection de la convergence et du coup, l'échange global avec waitall a aussi fonctionné.}
 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.
 %\CER{On voulait en fait montrer la simplicité de l'adaptation de l'algo a SimGrid. Les problèmes rencontrés décrits dans ce paragraphe concerne surtout le mode async}\LZK{OK. J'aurais préféré avoir un peu plus de détails sur l'adaptation de la version async} 
 %\CER{Le problème majeur sur l'adaptation MPI vers SMPI pour la partie asynchrone de l'algorithme a été le plantage en SMPI de Waitall après un Isend et Irecv. J'avais proposé un workaround en utilisant un MPI\_wait séparé pour chaque échange a la place d'un waitall unique pour TOUTES les échanges, une instruction qui semble bien fonctionner en MPI. Ce workaround aussi fonctionne bien. Mais après, tu as modifié le programme avec l'ajout d'un MPI\_Test, au niveau de la routine de détection de la convergence et du coup, l'échange global avec waitall a aussi fonctionné.}
 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 the real life in the simulated environment after the following minor changes. The scope of all declared 
-global variables have been moved to local to subroutine. Indeed, global variables generate side effects arising from the concurrent access of 
+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?}
 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?}


@@ -486,7 +484,7 @@ study that the results depend on the following parameters:
 \begin{itemize}
 \item At the network level, we found that the most critical values are the
   bandwidth and the network latency.
 \begin{itemize}
 \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 on the results.
+\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. 
 \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. 


@@ -501,14 +499,14 @@ 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
 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 network as in grid computing context.
+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, totaling 100 hosts. Various combinations of the above
+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} =
 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 in average 2.5 times faster than with the synchronous GMRES one. 
+\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 reformulé la phrase par la lecture du tableau. Plus de détails seront lus dans la partie Interprétations et commentaires}
 % use the same column width for the following three tables
 %\AG{Expliquer comment lire les tableaux.}
 %\CER{J'ai reformulé la phrase par la lecture du tableau. Plus de détails seront lus dans la partie Interprétations et commentaires}
 % use the same column width for the following three tables


@@ -673,17 +671,16 @@ Note that the program was run with the following parameters:
 \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
 \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 more than 2.5, showing the effectiveness of the
+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
 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 we vary the residual error precision from \np{E-5} to \np{E-9}. By
+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
 increasing the matrix size up to $100^3$ elements, it was necessary to increase the

-CPU power of \np[\%]{50} to \np[GFlops]{1.5} to get the algorithm convergence and the same order of asynchronous mode efficiency.  Maintaining such processor power but increasing network throughput inter cluster up to
-\np[Mbit/s]{50}, the result of efficiency with a relative gain of 2.5 is obtained with
+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.
 
 high external precision of \np{E-11} for a matrix size from $110^3$ to $150^3$ side
 elements.
 


@@ -708,7 +705,7 @@ elements.
 %\CER{Définitivement, les paramètres réseaux variables ici se rapportent au réseau INTER cluster.}
 \section{Conclusion}
 The simulation of the execution of parallel asynchronous iterative algorithms on large scale  clusters has been presented. 
 %\CER{Définitivement, les paramètres réseaux variables ici se rapportent au réseau 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 allows us to 
+In this work, we show that SimGrid is an efficient simulation tool that has enabled us to 

 reach the following two objectives: 
 
 \begin{enumerate}
 reach the following two objectives: 
 
 \begin{enumerate}


@@ -719,9 +716,8 @@ reach the following two objectives:
 
 \item To test the combination of the cluster and network specifications permitting to execute an asynchronous algorithm faster than a synchronous one.
 \end{enumerate}
 
 \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 to \np[\%]{40} compared to the synchronous GMRES method
-which is not negligible for solving complex practical problems with more 
-and more increasing size.
+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 
 
 Several studies have already addressed the performance execution time of 
 this class of algorithm. The work presented in this paper has