Comptes Rendus
no. 5
A numerical strategy for a high frequency electromagnetic scattering problem in a mixed formulation
[Une stratégie de résolution d'un problème de diffraction électromagnétique à haute fréquence en formulation mixte]
Katherine Mer-Nkonga1  ; Michel Mandallena1 ; David Goudin1 ; Bruno Stupfel1 ; Francis Collino2
1 CEA/CESTA, BP 2, 33114 Le Barp, France
2 CERFACS, 42, avenue Gaspard-Coriolis, 31057 Toulouse cedex 1, France
Comptes Rendus. Physique, Volume 7 (2006) no. 5, pp. 509-517.

Notre but est de résoudre le problème de la diffraction électromagnétique par un obstacle hétérogène. La méthode que nous proposons couple une formulation volumique discrétisée par éléments finis avec une méthode intégrale surfacique. Ces deux formulations sont résolues numériquement par des méthodes efficaces et sont couplées à l'aide d'une méthode de décomposition de domaines. Les ingrédients principaux utilisés sont : la décomposition de domaines avec conditions de transmission de Després et des sous-domaines concentriques, les équations intégrales de Després, la méthode multipôle rapide, et enfin un solveur direct creux parallèle. Nous présentons des résultats obtenus pour différentes hétérogénéités sur des géométries complexes.

We consider the electromagnetic scattering problem of an inhomogeneous obstacle. The methodology applied combines a volume finite element method with a boundary integral method. Both are numerically solved in an efficient way and coupled with a domain decomposition method. The main ingredients are: domain decomposition method with Després's transmission conditions and concentric subdomains, Després's integral equations, fast multipole method, and a parallel sparse direct solver. Numerical results on different inhomogeneity and complex geometries are presented.

Publié le :
DOI : 10.1016/j.crhy.2006.03.003
Keywords: Electromagnetic scattering, Domain decomposition, Integral equations, Fast multipole method, Parallel sparse direct solver
Mot clés : Diffraction électromagnétique, Décomposition de domaines, Équations intégrales, Méthode multipôle rapide, Solveur direct creux parallèle
Katherine Mer-Nkonga 1 ; Michel Mandallena 1 ; David Goudin 1 ; Bruno Stupfel 1 ; Francis Collino 2

1 CEA/CESTA, BP 2, 33114 Le Barp, France
2 CERFACS, 42, avenue Gaspard-Coriolis, 31057 Toulouse cedex 1, France 
@article{CRPHYS_2006__7_5_509_0,
     author = {Katherine Mer-Nkonga and Michel Mandallena and David Goudin and Bruno Stupfel and Francis Collino},
     title = {A numerical strategy for a high frequency electromagnetic scattering problem in a mixed formulation},
     journal = {Comptes Rendus. Physique},
     pages = {509--517},
     publisher = {Elsevier},
     volume = {7},
     number = {5},
     year = {2006},
     doi = {10.1016/j.crhy.2006.03.003},
     language = {en},
}
TY  - JOUR
AU  - Katherine Mer-Nkonga
AU  - Michel Mandallena
AU  - David Goudin
AU  - Bruno Stupfel
AU  - Francis Collino
TI  - A numerical strategy for a high frequency electromagnetic scattering problem in a mixed formulation
JO  - Comptes Rendus. Physique
PY  - 2006
SP  - 509
EP  - 517
VL  - 7
IS  - 5
PB  - Elsevier
DO  - 10.1016/j.crhy.2006.03.003
LA  - en
ID  - CRPHYS_2006__7_5_509_0
ER  - 
%0 Journal Article
%A Katherine Mer-Nkonga
%A Michel Mandallena
%A David Goudin
%A Bruno Stupfel
%A Francis Collino
%T A numerical strategy for a high frequency electromagnetic scattering problem in a mixed formulation
%J Comptes Rendus. Physique
%D 2006
%P 509-517
%V 7
%N 5
%I Elsevier
%R 10.1016/j.crhy.2006.03.003
%G en
%F CRPHYS_2006__7_5_509_0
Katherine Mer-Nkonga; Michel Mandallena; David Goudin; Bruno Stupfel; Francis Collino. A numerical strategy for a high frequency electromagnetic scattering problem in a mixed formulation. Comptes Rendus. Physique, Volume 7 (2006) no. 5, pp. 509-517. doi : 10.1016/j.crhy.2006.03.003. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.03.003/

[1] A. Barka; P. Soudais; D. Volpert Scattering from 3-D cavities with a plug and play numerical scheme combining IE, PDE and modal techniques, IEEE Trans. Antennas Propagat., Volume AP-48 (2000), pp. 704-711

[2] B. Després; P. Joly; J.E. Roberts A domain decomposition method for the harmonic Maxwell equations, Iterative Meth. in Linear Algebra, Elsevier Science Publ., Amsterdam, 1992, pp. 475-484

[3] B. Stupfel A fast domain decomposition method for the solution of electromagnetic scattering by large objects, IEEE Trans. Antennas Propagat., Volume AP-44 (1996), pp. 1375-1385

[4] B. Stupfel A hybrid finite element and integral equation domain decomposition method for the solution of the 3D scattering problem, J. Comput. Phys., Volume 172 (2001), pp. 451-471

[5] B. Stupfel; B. Després A domain decomposition method for the solution of large electromagnetic scattering problems, J. Electromag. Waves and Appl., Volume 13 (1999), pp. 1553-1568

[6] B. Després Fonctionnelle quadratique et équations intégrales pour les équations de Maxwell harmoniques en domaine extérieur, C. R. Acad. Sci. Paris, Sér. I, Volume 323 (1996), pp. 1145-1163

[7] F. Collino; B. Després Integral equations via saddle point problems for time-harmonic Maxwell's equations, J. Comput. Appl. Math., Volume 150 (2003), pp. 157-192

[8] J.M. Song; W.C. Chew Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering, Micro. Opt. Tech. Lett., Volume 10 (1995) no. 1, pp. 14-19

[9] K. Mer-Nkonga, F. Collino, in: The Fast Multipole Method Applied to a Mixed Integral System for Time-Harmonic Maxwell's Equations, JEE'02, Toulouse, 2002, pp. 121–126

[10] A. Bachelot; E. Darrigrand; K. Mer-Nkonga Coupling of a multilevel fast multipole method and a microlocal discretization for the 3-D integral equations of electromagnetism, C. R. Acad. Sci. Paris, Sér. I, Volume 336 (2003), pp. 505-510

[11] P. Hénon; P. Ramet; J. Roman PaStix: a high-performance parallel direct solver for sparse symmetric definite systems, Parallel Comput., Volume 28 (2002) no. 2, pp. 301-321

[12] D. Goudin; P. Hénon; F. Pellegrini; P. Ramet; J. Roman; J.-J. Pesqué Parallel sparse linear algebra and application to structural mechanics, Numer. Alg., Baltzer Sci. Publ., Volume 24 (2000), pp. 371-391

[13] F. Collino; S. Ghanemi; P. Joly Domain decomposition method for harmonic wave propagation: a general presentation, Comput. Meth. Appl. Mech. Eng., Volume 184 (2000), pp. 171-211

[14] P. Soudais Iterative solution of a 3-D scattering problem from arbitrary shaped multidielectric and multiconducting bodies, IEEE Antennas and Propagation Magazine, Volume 42 (1994) no. 7, pp. 954-959

[15] Y. Saad A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Comput., Volume 14 (1993) no. 2, pp. 461-469

[16] A. Bendali; M'B. Fares; J. Gay A boundary-element solution of the Leontovitch problem, IEEE Tans. Antennas Propagat., Volume 47 (1999) no. 10

[17] V. Rokhlin Rapid solution of integral equations of scattering theory in two dimensions, J. Comput. Phys., Volume 86 (1990), pp. 414-439

[18] F. Collino, F. Millot, in: A 2-Components Algorithm for the Multilevel Fast Multipole Method for Solving Large scale Diffraction Problems, JEE'02, Toulouse, France, 2002, pp. 103–108

[19] G. Sylvand Performance of a parallel implementation of the FMM for CEM, Int. J. Numer. Meth. Fluids, Volume 43 (2003) no. 8, pp. 865-880

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Some applications of substructuring and domain decomposition techniques to radiation and scattering of time-harmonic electromagnetic waves

Nolwenn Balin; Abderrahmane Bendali; M'Barek Fares; ...

C. R. Phys (2006)

Coupling of a multilevel fast multipole method and a microlocal discretization for the 3-D integral equations of electromagnetism

Alain Bachelot; Eric Darrigrand; Katherine Mer-Nkonga

C. R. Math (2003)

State of the art in computational methods for the prediction of radar cross-sections and antenna–platform interactions

Frédéric Molinet; Hervé Stève; Jean-Pierre Adam

C. R. Phys (2005)