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.
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.
Mots-clés : Diffusion, Domaine de décomposition, Transmission (conditions), Potentiel de Riesz
Matthieu Lecouvez 1; Bruno Stupfel 1; Patrick Joly 2; Francis Collino 2
@article{CRPHYS_2014__15_5_403_0,
author = {Matthieu Lecouvez and Bruno Stupfel and Patrick Joly and Francis Collino},
title = {Quasi-local transmission conditions for non-overlapping domain decomposition methods for the {Helmholtz} equation},
journal = {Comptes Rendus. Physique},
pages = {403--414},
publisher = {Elsevier},
volume = {15},
number = {5},
year = {2014},
doi = {10.1016/j.crhy.2014.04.005},
language = {en},
}
TY - JOUR AU - Matthieu Lecouvez AU - Bruno Stupfel AU - Patrick Joly AU - Francis Collino TI - Quasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation JO - Comptes Rendus. Physique PY - 2014 SP - 403 EP - 414 VL - 15 IS - 5 PB - Elsevier DO - 10.1016/j.crhy.2014.04.005 LA - en ID - CRPHYS_2014__15_5_403_0 ER -
%0 Journal Article %A Matthieu Lecouvez %A Bruno Stupfel %A Patrick Joly %A Francis Collino %T Quasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation %J Comptes Rendus. Physique %D 2014 %P 403-414 %V 15 %N 5 %I Elsevier %R 10.1016/j.crhy.2014.04.005 %G en %F CRPHYS_2014__15_5_403_0
Matthieu Lecouvez; Bruno Stupfel; Patrick Joly; Francis Collino. Quasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation. Comptes Rendus. Physique, Electromagnetism / Électromagnétisme, Volume 15 (2014) no. 5, pp. 403-414. doi : 10.1016/j.crhy.2014.04.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2014.04.005/
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