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Quasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation

Francis Collino 1 Patrick Joly 1 Matthieu Lecouvez 2 Bruno Stupfel 2 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this article, we present new transmission conditions for a domain decomposition method, applied to a scattering problem. Unlike other conditions used in the literature, the conditions developed here are non-local, but can be written as an integral operator (as a Riesz potential) on the interface between two domains. This operator, of order View the MathML source12, leads to an exponential convergence of the domain decomposition algorithm. A spectral analysis of the influence of the operator on simple cases is presented, as well as some numerical results and comparisons.
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https://hal.archives-ouvertes.fr/hal-01116028
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Submitted on : Thursday, February 12, 2015 - 2:00:53 PM
Last modification on : Saturday, June 25, 2022 - 9:09:24 PM

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Francis Collino, Patrick Joly, Matthieu Lecouvez, Bruno Stupfel. Quasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation. Comptes Rendus. Physique, Académie des sciences (Paris), 2014, 15 (5), pp.403-414. ⟨10.1016/j.crhy.2014.04.005⟩. ⟨hal-01116028⟩

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