×

Schwarz method justification of a coupling between finite elements and integral representation for Maxwell exterior problem. (Justification par la méthode de Schwarz du couplage entre éléments finis et représentation intégrale pour le problème de Maxwell en domaine extérieur.) (English. Abridged French version) Zbl 1293.78011

Summary: We are interested in the resolution of an exterior Maxwell problem in 3D using a coupling between finite elements and integral representation. This strategy is interpreted as a Schwarz method which suggests a preconditioner for Krylov solvers. Numerical results confirm the relevance of the resolution scheme.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
78A45 Diffraction, scattering
PDFBibTeX XMLCite
Full Text: DOI HAL

References:

[1] Ben Belgacem, F.; Fournié, M.; Gmati, N.; Jelassi, F., On the Schwarz algorithms for the elliptic exterior boundary value problems, ESAIM: M2AN, 39, 4, 693-714 (2005) · Zbl 1089.65126
[2] Gmati, N.; Philippe, B., Comments on the GMRES convergence for preconditioned systems, (Large-Scale Scientific Computing. Large-Scale Scientific Computing, Lecture Notes in Computer Science, vol. 4818 (2008)), 40-51 · Zbl 1229.65063
[3] Hazard, C.; Lenoir, M., On the solution of time-harmonic scattering problems for Maxwell’s equations, SIAM J. Math. Anal., 27, 6, 1597-1630 (1996) · Zbl 0860.35129
[4] Jin, J.-M.; Liu, J., A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems, IEEE Trans. Antennas Propag., 49, 12, 1794-1806 (2001) · Zbl 1001.78021
[5] Martin, D., Université Rennes-1, November 2013
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.