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Resilient asynchronous primal Schur method

Guillaume Gbikpi-Benissan;  Frédéric Magoulès — 2022

Applications of Mathematics

This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's...

Analysis of patch substructuring methods

Martin Gander;  Laurence Halpern;  Frédéric Magoulès;  Francois Roux — 2007

International Journal of Applied Mathematics and Computer Science

Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains condensated, on the interfaces to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one...

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