×

A hybrid finite element and integral equation domain decomposition method for the solution of the 3-D scattering problem. (English) Zbl 0992.78014

Author’s abstract: A domain decomposition method (DDM) is presented for the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous 3-D objects. The computational domain is partitioned into concentric subdomains on the interfaces of which Robin-type transmission conditions are prescribed. On the outer boundary terminating the computational domain, the radiation condition is accounted for by employing an integral equation (IE) formulation. The DDM decouples the interior problems, that correspond to the solution of Maxwell’s equations inside each subdomain and are formulated by using a finite element method, from the exterior problem solved by employing the IE. It has been shown that the solutions of this DDM algorithm converge to those of the original problem. A particular IE is used that allows the implementation of a very simple and fully iterative solver. The main advantage offered by this technique is a reduction in memory requirements. Various numerical examples are presented that illustrate its potential.

MSC:

78A45 Diffraction, scattering
78M25 Numerical methods in optics (MSC2010)
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yuan, X., Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method, IEEE Trans. Microwave Theory Tech., MTT-38, 1053 (1990)
[2] Boyse, W. E.; Seidl, A. A., A hybrid finite element method for near bodies of revolution, IEEE Trans. Mag., 27, 3833 (1991)
[3] Stupfel, B.; Le Martret, R.; Bonnemason, P.; Scheurer, B., Combined boundary-element and finite-element method for the scattering problem by axisymmetrical penetrable objects, Proceedings of the international Symposium on Mathematical and Numerical Aspects of Wave Propagation Phenomena, 332 (1991)
[4] Soudais, P., Computation of the electromagnetic scattering from complex 3D objects by a hybrid FEM/BEM method, J. Electromag. Waves Appl., 9, 871 (1995)
[5] Sheng, X. Q.; Jin, J. M.; Song, J.; Lu, C. C.; Chew, W. C., On the formulation of hybrid finite-element and boundary-integrals method for 3-D scattering, IEEE Trans. Antennas Prop., AP-46, 303 (1998)
[6] Lee, R.; Chupongstimun, V., A partitioning technique for the finite element solution of electromagnetic scattering from electrically large dielectric cylinders, IEEE Trans. Antennas Prop., AP-42, 737 (1994)
[7] Spring, C. T.; Cangellaris, A. C., Parallel implementation of domain decomposition methods for the electromagnetic analysis of guided wave systems, J. Electromag. Waves Appl., 9, 175 (1995)
[8] Barka, A.; Soudais, P.; Volpert, D., Scattering from 3-D cavities with a plug and play numerical scheme combining IE, PDE and modal techniques, IEEE Trans. Antennas Prop., AP-48, 704 (2000) · Zbl 1113.78306
[9] Wolfe, C. T.; Navsariwala, U.; Gedney, S. D., A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium, IEEE Trans. Antennas Prop., AP-48, 278 (2000)
[10] B. Després, Ph.D. dissertation, Université Paris IX Dauphine, France, 1991.; B. Després, Ph.D. dissertation, Université Paris IX Dauphine, France, 1991.
[11] B. Després, P. Joly, and, J. E. Roberts, A domain decomposition method for the harmonic Maxwell equations, in, Iterative methods in Linear Algebra, edited by, R. Beauwens and P. de Groen, Elsevier, Amsterdam/New York, 1992, p, 475.; B. Després, P. Joly, and, J. E. Roberts, A domain decomposition method for the harmonic Maxwell equations, in, Iterative methods in Linear Algebra, edited by, R. Beauwens and P. de Groen, Elsevier, Amsterdam/New York, 1992, p, 475.
[12] Collino, P.; Ghanemi, S.; Joly, P., Domain decomposition method for harmonic wave propagation: A general presentation, Comput. Meth. Appl. Mech. Eng., 184, 171 (2000) · Zbl 0965.65134
[13] Stupfel, B., A fast domain decomposition method for the solution of electromagnetic scattering by large objects, IEEE Trans. Antennas Prop., AP-44, 1375 (1996)
[14] Stupfel, B.; Mognot, M., A domain decomposition method for the vector wave equation, IEEE Trans. Antennas Prop., AP-48, 653 (2000) · Zbl 1113.78320
[15] Stupfel, B.; Despres, B., A domain decomposition method for the solution of large electromagnetic scattering problems, J. Electromag. Waves Appl., 13, 1553 (1999) · Zbl 1066.78512
[16] Stupfel, B.; Mognot, M., Implementation and derivation of conformal absorbing boundary conditions for the vector wave equation, J. Electromag. Waves Appl., 12, 1653 (1998) · Zbl 0990.78016
[17] Després, B., Fonctionnelle quadratique et équations intégrales pour les équations de Maxwell harmoniques en domaine extérieur, C. R. Acad. Sci. Paris, 323, 1145 (1996)
[18] Collino, F.; Després, B., Integral Equations via Saddle Point Problems for Time-Harmonic Maxwell’s Equations (2000) · Zbl 1034.35134
[19] Rao, S. M.; Wilton, D. R.; Glisson, A. W., Electromagnetic scattering by surfaces of arbitrary shape, IEEE Trans. Antennas Prop., AP-30, 409 (1982)
[20] Bonnemason, P., Résolution par formulations intégrales du problème de la diffraction d’une onde électromagnétique par des objets 3D conducteurs recouverts ou non de matériaux, Proceedings of the Journées Européennes sur les méthodes numériques en électromagnétisme, 185 (Nov. 1993)
[21] Weston, V. H., Theory of absorbers in scattering, IEEE Trans. Antennas Prop., AP-11, 578 (1963)
[22] Bonnemason, P.; Stupfel, B., Modeling high frequency scattering by axisymmetric perfectly or imperfectly conducting scatterers, Electromagnetics, 13, 111 (1993)
[23] M. Mandallena, Modélisation d’antennes plaquées par méthodes intégrales, in, Proceedings of Atelier de travail CNES: Méthodes numériques pour la modélisation d’antennes, October 1996, Toulouse, France.; M. Mandallena, Modélisation d’antennes plaquées par méthodes intégrales, in, Proceedings of Atelier de travail CNES: Méthodes numériques pour la modélisation d’antennes, October 1996, Toulouse, France.
[24] Stupfel, B., Absorbing boundary conditions on arbitrary boundaries for the scalar and vector wave equations, IEEE Trans. Antennas Prop., AP-42, 773 (1994) · Zbl 0953.78500
[25] Liu, J.; Jin, J. M., A special higher-order finite-element method for scattering by deep cavities, IEEE Trans. Antennas Prop., AP-48, 694 (2000) · Zbl 1113.78316
[26] Song, J. M.; Lu, C. C.; Chew, W. C.; Lee, S. W., Fast Illinois solver code (FISC), IEEE Trans. Antennas Prop. Mag., 40, 27 (1998)
[27] Mer, K., The fast multipole method applied to a mixed integral system for time-harmonic Maxwell’s equations, Proceedings of the Second International Conference on Boundary Integral Methods: Theory and Applications (September 2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.