Comptes Rendus
no. 5
Some applications of substructuring and domain decomposition techniques to radiation and scattering of time-harmonic electromagnetic waves
[Quelques applications de techniques de sous-structuration et de décomposition de domaine au rayonnement et à la diffraction des ondes électromagnétiques en régime harmonique]
Nolwenn Balin1, 2 ; Abderrahmane Bendali1, 3  ; M'Barek Fares1 ; Florence Millot1 ; Nicolas Zerbib1, 4
1 CERFACS, 42, avenue Gaspard-Coriolis, 31057 Toulouse cedex 1, France
2 MBDA-France, 2, rue Béranger, 92323 Châtillon cedex, France
3 UMR 5640, laboratoire MIP, INSA–CNRS–UPS, 135, avenue de Rangueil, 31077 Toulouse cedex 4, France
4 CNES, Centre spatial de Toulouse, 18, avenue Édouard-Belin, 31401 Toulouse cedex 9, France
Comptes Rendus. Physique, Volume 7 (2006) no. 5, pp. 474-485.

Après une revue rapide des méthodes de décomposition de domaine, et, plus particulièment de leur application aux problèmes relatifs au rayonnement et à la diffraction des ondes électromagnétiques en régime harmonique, nous décrivons deux contributions des auteurs dans ce contexte. Les deux contributions sont liées à la diffraction d'une onde électromagnétique en régime harmonique par une structure parfaitement conductrice de grande taille comportant une cavité profonde. La première contribution est une technique de sous-structuration. Elle est utilisée pour accroître la vitesse de convergence de l'algorithme itératif dans le cadre d'une résolution par la méthode multipôle rapide multi-niveaux. Des expérimentations numériques illustrent l'efficacité de l'approche en ce que la méthode itérative de Krylov afférente converge en un nombre d'itérations qui reste quasiment constant lorsqu'on augmente une longueur caractéristique dans le problème. La seconde contribution propose une adaptation de la méthode de décomposition de domaine par recouvrement pour une formulation par équations intégrales de frontière. Elle est utilisée ici pour effectuer une hybridation d'une formulation exacte, utilisée à l'ouverture de la cavitée, avec une méthode asymptotique haute fréquence, employée pour le reste de la frontière extérieure de la structure. Des résultats numériques prouvent la fiabilité et l'efficacité de la méthode.

After a quick review of the domain decomposition methods, and, more particularly on their application to large size problems relative to radiation and scattering of time-harmonic waves, we describe two contributions of the authors in this context. The two contributions are related to the scattering of a time-harmonic electromagnetic wave by a large perfectly conducting structure including a deep cavity. The first contribution is a substructuring technique. It is used to increase the speed of the convergence of the iterative algorithm in a Multi-Level Fast Multipol Method (MLFMM) solution. Numerical experiments illustrate the effectiveness of the approach since the number of iterations of the underlying Krylov iterative method remains almost constant while increasing a characteristic length in the problem. The second contribution proposes an adaptation of the overlapping domain decomposition techniques for a boundary integral formulation. It is used here to perform a hybridization of an exact formulation, used at the opening of the cavity, with an asymptotic high-frequency method employed for the rest of the exterior boundary of the structure. Numerical results demonstrate the reliability and the efficiency of the method.

Publié le :
DOI : 10.1016/j.crhy.2006.04.001
Keywords: Domain decomposition methods, Time-harmonic waves
Mot clés : Méthodes de décomposition de domaine, Régime harmonique
Nolwenn Balin 1, 2 ; Abderrahmane Bendali 1, 3 ; M'Barek Fares 1 ; Florence Millot 1 ; Nicolas Zerbib 1, 4

1 CERFACS, 42, avenue Gaspard-Coriolis, 31057 Toulouse cedex 1, France
2 MBDA-France, 2, rue Béranger, 92323 Châtillon cedex, France
3 UMR 5640, laboratoire MIP, INSA–CNRS–UPS, 135, avenue de Rangueil, 31077 Toulouse cedex 4, France
4 CNES, Centre spatial de Toulouse, 18, avenue Édouard-Belin, 31401 Toulouse cedex 9, France 
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Nolwenn Balin; Abderrahmane Bendali; M'Barek Fares; Florence Millot; Nicolas Zerbib. Some applications of substructuring and domain decomposition techniques to radiation and scattering of time-harmonic electromagnetic waves. Comptes Rendus. Physique, Volume 7 (2006) no. 5, pp. 474-485. doi : 10.1016/j.crhy.2006.04.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.04.001/

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