Parallelization of such algorithms generally involved the division of the problem into several \emph{pieces} that will
be solved in parallel on multiple processing units. The latter will communicate each intermediate results before a new
-iteration starts until the approximate solution is reached. These parallel computations can be performed
-either in \emph{synchronous} communication mode where a new iteration begin only when all nodes communications are
-completed, either \emph{asynchronous} mode where processors can continue independently without or few synchronization
-points.
-
-% DL : reprendre correction ici
-Despite the effectiveness of iterative approach, a major drawback of the method is the requirement of huge
-resources in terms of computing capacity, storage and high speed communication network. Indeed, limited physical
-resources are blocking factors for large-scale deployment of parallel algorithms.
-
-In recent years, the use of a simulation environment to execute parallel iterative algorithms found some interests in
-reducing the highly cost of access to computing resources: (1) for the applications development life cycle and in code
-debugging (2) and in production to get results in a reasonable execution time with a simulated infrastructure not
-accessible with physical resources. Indeed, the launch of distributed iterative asynchronous algorithms to solve a
-given problem on a large-scale simulated environment challenges to find optimal configurations giving the best results
-with a lowest residual error and in the best of execution time. According our knowledge, no testing of large-scale
-simulation of the class of algorithm solving to achieve real results has been undertaken to date. We had in the scope
-of this work implemented a program for solving large non-symmetric linear system of equations by numerical method
-GMRES (Generalized Minimal Residual) in the simulation environment SimGrid. The simulated platform had allowed us to
-launch the application from a modest computing infrastructure by simulating different distributed architectures
-composed by clusters nodes interconnected by variable speed networks. In addition, it has been permitted to show the
-effectiveness of asynchronous mode algorithm by comparing its performance with the synchronous mode time. With selected
-parameters on the network platforms (bandwidth, latency of inter cluster network) and on the clusters architecture
-(number, capacity calculation power) in the simulated environment, the experimental results have demonstrated not only
-the algorithm convergence within a reasonable time compared with the physical environment performance, but also a time
-saving of up to \np[\%]{40} in asynchronous mode.
+iteration starts until the approximate solution is reached. These parallel computations can be performed either in
+\emph{synchronous} communication mode where a new iteration begin only when all nodes communications are completed,
+either \emph{asynchronous} mode where processors can continue independently without or few synchronization points. For
+instance in the \textit{Asynchronous Iterations - Asynchronous Communications (AIAC)} model \cite{bcvc06:ij}, 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, AIAC algorithms can significantly reduce overall execution times by suppressing idle times due to
+synchronizations especially in a grid computing context (see \cite{bcvc06:ij} for more details).
+
+Parallel numerical applications (synchronous or asynchronous) may have different configuration and deployment
+requirements. Quantifying their performance of resource allocation policies and application scheduling algorithms in
+grid computing environments under varying load, CPU power and network speeds is very costly, labor intensive and time
+consuming \cite{BuRaCa}. 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 bandwith (intra and inter- clusters), in the
+number and the power of nodes, in the number of clusters... can lead to very different number of iterations and so to
+very different execution times. In this context, it appears that the use of simulation tools to explore various platform
+scenarios and to run enormous 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 to give a first approach of the simulation of AIAC algorithms using the SimGrid toolkit \cite{SimGrid}. We had
+in the scope of this work implemented a program for solving large non-symmetric linear system of equations by numerical
+method GMRES (Generalized Minimal Residual). 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. The simulated results we obtained are in line with real results exposed in ?? In addition, it has been
+permitted to show the effectiveness of asynchronous mode algorithm by comparing its performance with the synchronous
+mode time. With selected parameters on the network platforms (bandwidth, latency of inter cluster network) and on the
+clusters architecture (number, capacity calculation power) in the simulated environment, the experimental results have
+demonstrated not only the algorithm convergence within a reasonable time compared with the physical environment
+performance, but also a time saving of up to \np[\%]{40} in asynchronous mode.
This article is structured as follows: after this introduction, the next section will give a brief description of
-iterative asynchronous model. Then, the simulation framework SimGrid will be presented with the settings to create
-various distributed architectures. The algorithm of the multi-splitting method used by GMRES written with MPI
-primitives and its adaptation to SimGrid with SMPI (Simulated MPI) will be in the next section. At last, the experiments
-results carried out will be presented before the conclusion which we will announce the opening of our future work after
-the results.
+iterative asynchronous model. Then, the simulation framework SimGrid is presented with the settings to create various
+distributed architectures. The algorithm of the multi-splitting method used by GMRES written with MPI primitives and
+its adaptation to SimGrid with SMPI (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.
\section{Motivations and scientific context}
