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.
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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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