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arXiv · 2011.02905

Fast Solver for Quasi-Periodic 2D-Helmholtz Scattering in Layered Media

José Pinto·Rubén Aylwin·Carlos Jerez-Hanckes
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Abstract

We present a fast spectral Galerkin scheme for the discretization of boundary integral equations arising from two-dimensional Helmholtz transmission problems in multi-layered periodic structures or gratings. Employing suitably parametrized Fourier basis and excluding Rayleigh-Wood anomalies, we rigorously establish the well-posedness of both continuous and discrete problems, and prove super-algebraic error convergence rates for the proposed scheme. Through several numerical examples, we confirm our findings and show performances competitive to those attained via Nystr\"om methods.

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José Pinto, Rubén Aylwin, Carlos Jerez-Hanckes. 2020-11-05. Fast Solver for Quasi-Periodic 2D-Helmholtz Scattering in Layered Media. https://arxiv.org/abs/2011.02905

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