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Résolution de grands systèmes linéaires issus de la méthode des éléments finis sur des calculateurs massivement parallèles

Abstract : This study is devoted to the resolution of large sparse linear systems on massively parallel computers. The computational effort for these linear systems, often encountered in the numerical simulation of structural mechanics problems by finite element codes, is very significant in terms of runtime and memory requirements. In this work, we develop a two-level parallelism and integrate it into domain decomposition methods like FETI. The approach is organized around three main chapters. We first implement a direct solver for sparse linear systems which can be symmetric or non-symmetric, real or complex, with single or multiple right-hand sides. The implementation, based on a nested dissection technique, is completed by a useful point in many domain decomposition methods (building a preconditioner or formulation of the FETI operator) : handling of zero-energy modes of singular systems. As a second step, we parallelize the sparse direct solver through a model of shared memory parallelism (multi-threading) to take advantage of the recent multi-core processors. In a third step, we integrate this multi-threads version in FETI methods to solve local problems in parallel. The results of this study highlight the usefulness of the work and interest to use as local solver in FETI methods a parallel direct solver which is robust and efficient. This can give access to new ranges of complex problems in structural mechanics. It would be interesting to review the coarse-grained parallelism between subdomains in FETI methods. This could be to use the multiple right-hand sides version of the direct solver to improve the processing of the interface problem.
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Contributor : Ibrahima Gueye <>
Submitted on : Thursday, April 29, 2010 - 5:37:04 PM
Last modification on : Wednesday, October 14, 2020 - 3:52:48 AM
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  • HAL Id : tel-00477653, version 1

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Ibrahima Gueye. Résolution de grands systèmes linéaires issus de la méthode des éléments finis sur des calculateurs massivement parallèles. Modélisation et simulation. École Nationale Supérieure des Mines de Paris, 2009. Français. ⟨NNT : 2009ENMP1658⟩. ⟨tel-00477653⟩

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