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

Thomas Strauszer, Luiz M. Faria, Agustin Fernandez-Lado, Carlos Perez-Arancibia*

*Corresponding author for this work

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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.
Original languageEnglish
Article number12540
Pages (from-to)277-315
Number of pages39
JournalStudies in Applied Mathematics
Issue number1
Early online date5 Nov 2022
Publication statusPublished - Jan 2023


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