+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 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 iterative executed
+in a distributed environment. As their name suggests, these algorithm
+solves a given problem that might be NP- complete complex 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. Generally, to reduce the complexity and the
+execution time, the problem is divided into several "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 distributed parallel
+computations can be performed either in "synchronous" communication mode
+where a new iteration begin only when all nodes communications are
+completed, either "asynchronous" mode where processors can continue
+independently without or few synchronization points. 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 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 (Simulation 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.
