of asynchronous iterative algorithms. For that, we compare the behaviour of a
synchronous GMRES algorithm with an asynchronous multisplitting one with
simulations in which we choose some parameters. Both codes are real MPI
-codes. Experiments allow us to see when the multisplitting algorithm can be more
+codes. Simulations allow us to see when the multisplitting algorithm can be more
efficient than the GMRES one to solve a 3D Poisson problem.
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{numerical iterative algorithms} executed in a distributed environment. As their name
+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}.
synchronous case, AIAC 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 numerical applications (synchronous or asynchronous) 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 costly,
-very labor intensive and very time
-consuming~\cite{Calheiros:2011:CTM:1951445.1951450}. The case of AIAC
-algorithms is even more problematic since they are very sensible to the
+Parallel (synchronous or asynchronous) applications 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 costly,
+very labor intensive and very time
+consuming~\cite{Calheiros:2011:CTM:1951445.1951450}. The case of AIAC
+algorithms is even more problematic since they are very sensible 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. 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 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
+(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 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.
-To our knowledge, there is no existing work on the large-scale simulation of a
-real AIAC application. The aim of this paper is twofold. First we give a first
-approach of the simulation of AIAC algorithms using a simulation tool (i.e. the
-SimGrid toolkit~\cite{SimGrid}). Second, we confirm the effectiveness of
-asynchronous mode algorithms by comparing their performance with the synchronous
-mode. More precisely, we had implemented a program for solving large
-linear system of equations by numerical method GMRES (Generalized
-Minimal Residual) \cite{ref1}. We show, that with minor modifications of the
-initial MPI code, the SimGrid toolkit allows us to perform a test campaign of a
-real AIAC 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
-infrastructure by simulating different distributed architectures composed by
-clusters nodes interconnected by variable speed networks. With selected
-parameters on the network platforms (bandwidth, latency of inter cluster
-network) and on the clusters architecture (number, capacity calculation power)
-in the simulated environment, the experimental results have demonstrated not
-only the algorithm convergence within a reasonable time compared with the
-physical environment performance, but also a time saving of up to \np[\%]{40} in
-asynchronous mode.
-\AG{Il faudrait revoir la phrase précédente (couper en deux?). Là, on peut
- avoir l'impression que le gain de \np[\%]{40} est entre une exécution réelle
- et une exécution simulée!}
-
-This article is structured as follows: after this introduction, the next section will give a brief description of
-iterative asynchronous model. Then, the simulation framework SimGrid is presented with the settings to create various
-distributed architectures. The algorithm of the multisplitting method used by GMRES \LZK{??? GMRES n'utilise pas la méthode de multisplitting! Sinon ne doit on pas expliquer le choix d'une méthode de multisplitting?} written with MPI primitives and
-its adaptation to SimGrid with SMPI (Simulated MPI) is detailed in the next section. At last, the experiments results
-carried out will be presented before some concluding remarks and future works.
+To our knowledge, there is no existing work on the large-scale simulation of a
+real AIAC application. {\bf The contribution of the present paper can be
+ summarised in two main points}. First we give a first approach of the
+simulation of AIAC 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) \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 AIAC
+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
+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.
+
+
+
+This article is structured as follows: after this introduction, the next section
+will give a brief description of iterative asynchronous model. Then, the
+simulation framework SimGrid 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
+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.
\section{Motivations and scientific context}
