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Comptes Rendus Physique
Volume 15, n° 5
pages 403-414 (mai 2014)
Doi : 10.1016/j.crhy.2014.04.005
Quasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation
Conditions de transmission quasi-locales pour des méthodes de décomposition de domaine appliquées à l'équation de Helmholtz

Matthieu Lecouvez a, , Bruno Stupfel a, Patrick Joly b, Francis Collino b
a Commissariat à l'énergie atomique (CEA), 15, avenue des Sablières, 33114 Le Barp, France 
b POEMS, UMR CNRS/ENSTA/INRIA, ENSTA ParisTech, 828, bd des Maréchaux, 91762 Palaiseau cedex, France 

Corresponding author.

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  , 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.

The full text of this article is available in PDF format.

Nous présentons dans cet article de nouvelles conditions de transmission pour une méthode de décomposition de domaine appliquée au problème de la diffraction. À l'inverse d'autres conditions décrites dans la littérature, celles développées ici ne sont pas locales, mais peuvent s'écrire sous la forme d'un opérateur intégral (tel qu'un potentiel de Riesz) à l'interface entre deux domaines. Cet opérateur, d'ordre  , conduit à une convergence exponentielle de l'algorithme de décomposition de domaine. Une analyse spectrale de l'influence de l'opérateur portant sur des cas simples est presentée, ainsi que quelques résultats numériques et comparaisons.

The full text of this article is available in PDF format.

Keywords : Scattering, Domain decomposition, Transmission conditions, Riesz potential

Mots-clés : Diffusion, Domaine de décomposition, Transmission (conditions), Potentiel de Riesz

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