ANALYSES AVANCÉES DE LA MÉTHODE HYBRIDE GMRES/LS-ARNOLDI ASYNCHRONE PARALLÈLE ET DISTRIBUÉE POUR LES GRILLES DE CALCUL ET LES SUPERCALCULATEURS

Haiwu He 1, 2
2 GRAND-LARGE - Global parallel and distributed computing
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LIFL - Laboratoire d'Informatique Fondamentale de Lille, LRI - Laboratoire de Recherche en Informatique
Abstract : Many scientific and industrial problems need the resolution of nonsymmetric linear systems of large scale, which are described by sparse matrices of very large size. We frequently use the iterative numerical methods and benefit from parallelism for a fast and effective resolution. The GMRES(m) algorithm is an iterative method which gives good results in most cases. Nevertheless we observe the limitation of its parallelization because of much provoked communications, in some case convergence is reached very slowly even never. We present in this thesis a hybrid method GMRES(m)/LS-Arnoldi which accelerates the convergence thanks to the knowledge of the eigenvalues calculated in parallel by the method of Arnoldi for the real cases with its implementation on the supercomputers. Furthermore we study an extension of complex cases. The latest tendency of global computing, the GRID computing proposes the massive exploitation of the vacant resources on the local area networks and on world wide Internet for the execution of parallel applications. The XtremWeb environment is a secured, light GRID system, with the failures tolerance mechanism for the execution of parallel applications. It is a high-performance computing environment, a software GRID platform of experimentation for academic or industrial organisation. We present in this thesis the implementation of the GMRES(m) method on this GRID system XtremWeb as well as a distributed computing environment LAM-MPI. We made numerous tests on GRID and supercomputer. From performances which we obtained, we note the advantages and the disadvantages for these different computing
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Haiwu He. ANALYSES AVANCÉES DE LA MÉTHODE HYBRIDE GMRES/LS-ARNOLDI ASYNCHRONE PARALLÈLE ET DISTRIBUÉE POUR LES GRILLES DE CALCUL ET LES SUPERCALCULATEURS. Informatique [cs]. Université des Sciences et Technologie de Lille - Lille I, 2005. Français. ⟨tel-00431124⟩

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