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Méthodes asynchrones de décomposition de domaine pour le calcul massivement parallèle

Abstract : An important class of numerical methods features a scalability property well known as the Amdahl’s law, which constitutes the main limiting drawback of parallel computing, as it establishes an upper bound on the number of parallel processing units that can be used to speed a computation up. Extensive research activities are therefore conducted on both mathematical and computer science aspects to increase this bound, in order to be able to squeeze the most out of parallel machines. Domain decomposition methods introduce a natural and optimal approach to solve large numerical problems in a distributed way. They consist in dividing the geometrical domain on which an equation is defined, then iteratively processing each sub-domain separately, while ensuring the continuity of the solution and of its derivative across the junction interface between them. In the present work, we investigate the removal of the scalability bound by the application of the asynchronous iterations theory in various decomposition frameworks, both for space and time domains. We cover various aspects of the development of asynchronous iterative algorithms, from theoretical convergence analysis to effective parallel implementation. Efficient asynchronous domain decomposition methods are thus successfully designed, as well as a new communication library for the quick asynchronous experimentation of existing scientific applications.
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Tete Guillaume Gbikpi Benissan. Méthodes asynchrones de décomposition de domaine pour le calcul massivement parallèle. Autre. Université Paris Saclay (COmUE), 2017. Français. ⟨NNT : 2017SACLC071⟩. ⟨tel-02003395⟩

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