Windowed Green function method for wave scattering by periodic arrays of 2D obstacles - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Studies in Applied Mathematics Year : 2022

Windowed Green function method for wave scattering by periodic arrays of 2D obstacles

Abstract

This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free-space Green function but in turn entails evaluation of integrals over the unit-cell boundaries. Such integrals are here treated via the window Green function method. The windowing approximation together with a finite-rank operator correction—used to properly impose the Rayleigh radiation condition—yield a robust second-kind BIE that produces superalgebraically convergent solutions throughout the spectrum, including at the challenging Rayleigh–Wood anomalies. The corrected windowed BIE can be discretized by means of off-the-shelf Nyström and boundary element methods, and it leads to linear systems suitable for iterative linear algebra solvers as well as standard fast matrix–vector product algorithms. A variety of numerical examples demonstrate the accuracy and robustness of the proposed methodology.
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Dates and versions

hal-03940468 , version 1 (16-01-2023)

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Thomas Strauszer-Caussade, Luiz M Faria, Agustín Fernandez-Lado, Carlos Pérez‐arancibia. Windowed Green function method for wave scattering by periodic arrays of 2D obstacles. Studies in Applied Mathematics, 2022, 150 (1), pp.277-315. ⟨10.1111/sapm.12540⟩. ⟨hal-03940468⟩
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