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 1, 2
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, for a general family of Robin type boundary conditions. Using the principle of the Half-Space Matching method, the problem is formulated as a system of coupled Fourier-integral equations: the unknowns are 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 corresponding numerical method is also analyzed, including the effect of truncation of the Fourier integrals and of the finite element approximation. The theoretical results are supported by various numerical experiments.
Type de document :
Pré-publication, Document de travail
2018
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Soumis le : mercredi 16 mai 2018 - 16:07:17
Dernière modification le : vendredi 18 mai 2018 - 01:14:43

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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. 2018. 〈hal-01793511〉

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