Numerical analysis of the Half-Space Matching method with Robin traces on a convex polygonal scatterer - Archive ouverte HAL Access content directly
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Numerical analysis of the Half-Space Matching method with Robin traces on a convex polygonal scatterer

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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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Dates and versions

hal-01793511 , version 1 (16-05-2018)
hal-01793511 , version 2 (23-11-2018)
hal-01793511 , version 3 (05-12-2019)

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  • HAL Id : hal-01793511 , version 3

Cite

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: Analysis and numerics, 24, De Gruyter, 2019, Radon Series on Computational and Applied Mathematics. ⟨hal-01793511v3⟩
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