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.
Domains
Mathematics [math]
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Stud Appl Math - 2022 - Strauszer%E2%80%90Caussade - Windowed Green function method for wave scattering by periodic arrays of 2D.pdf (2.04 Mo)
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