Adaptation and Evaluation of the Multisplitting-Newton and Waveform Relaxation Methods Over Distributed Volatile Environments

International audienceThis paper presents new adaptations of two methods that solve large differential equations systems, to the grid context. The first method isbased on the Multisplitting concept and the second on the Waveform Relaxation concept. Their adaptations are implemented according to the asynchronous iteration model which is well suited to volatile architectures that suffer from high latency networks. Many experiments were conducted to evaluate and compare the accuracy and performance of both methods while solving the advection-diffusion problem over heterogeneous, distributed and volatile architectures. The JACEP2P-V2 middleware provided the fault tolerant asynchronous environment, required for these experiments

Parallel multisplitting explicit AOR methods for numerical solutions of semilinear elliptic boundary value problems

AbstractA class of parallel multisplitting explicit AOR methods for a large scale system of nonlinear algebraic equations, which is a finite difference approximation of a semilinear elliptic boundary value problem, are presented. This class of methods avoid the inner iteration and are shown to converge monotonically either from above or from below to a solution of the system without the monotonicity property of nonlinearity. Moreover, this class of methods are applicable to the pure Neumann boundary value problems. A sufficient condition for the uniqueness of the solutions is provided. The global convergence of the methods and the influence of the acceleration factor on the convergence rate are considered. The applications and numerical results are given

Parallelization of direct algorithms using multisplitting methods in grid environments

The goal of this paper is to introduce a new approach to the building of efficient distributed linear system solvers. The starting point of the results of this paper lies in the fact that the parallelization of direct algorithms requires frequent synchronizations in order to obtain the solution for a linear problem. In a grid computing environment, communication times are significant and the bandwidth is variable, therefore frequent synchronizations slow down performances. Thus it is desirable to reduce the number of synchronizations in a parallel direct algorithm. Inspired from multisplitting techniques, the method we present consists in solving several linear problems obtained by splitting the original one. Each linear system is solved independently on a cluster by using the direct method. This paper uses the theoretical results of \cite{BMR97} in order to build coarse grained algorithms designed for solving linear systems in the grid computing context