Volume 55, Number 5, September-October 2021
|Page(s)||2445 - 2472|
|Published online||25 October 2021|
Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media
Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Santiago, Chile
* Corresponding author: email@example.com
Accepted: 30 August 2020
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 cut-off frequencies (also known as Rayleigh-Wood frequencies), 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 Nyström methods.
Mathematics Subject Classification: 65N35 / 65N38 / 45M15 / 78A45
Key words: Boundary integral equations / quasi-periodic scattering / spectral elements / gratings / multi-layered domain
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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