Numerical analysis of the Half-Space Matching method with Robin traces on a convex polygonal scatterer

Anne-Sophie Bonnet-Ben Dhia 1 Sonia Fliss 1 Yohanes Tjandrawidjaja 2, 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We consider the 2D Helmholtz equation with a complex wavenumber in the exterior of a convex polygonal obstacle, with a Robin type boundary condition. Using the principle of the Half-Space Matching method, the problem is formulated as a system of coupled Fourier-integral equations, the unknowns being the Robin traces on the infinite straight lines supported by the edges of the polygon. We prove that this system is a Fredholm equation of the second kind, in an $L^2$ functional framework. The truncation of the Fourier integrals and the finite element approximation of the corresponding numerical method are also analyzed. The theoretical results are supported by various numerical experiments.
Type de document :
Chapitre d'ouvrage
Maxwell's equations, De Gruyter, In press
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https://hal.inria.fr/hal-01793511
Contributeur : Sonia Fliss <>
Soumis le : vendredi 23 novembre 2018 - 15:07:45
Dernière modification le : vendredi 30 novembre 2018 - 09:10:35

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  • HAL Id : hal-01793511, version 2

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Anne-Sophie Bonnet-Ben Dhia, Sonia Fliss, Yohanes Tjandrawidjaja. Numerical analysis of the Half-Space Matching method with Robin traces on a convex polygonal scatterer. Maxwell's equations, De Gruyter, In press. 〈hal-01793511v2〉

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