| Issue |
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
|
|
|---|---|---|
| Page(s) | 2445 - 2472 | |
| DOI | https://doi.org/10.1051/m2an/2021053 | |
| 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: carlos.jerez@uai.cl
Received:
30
September
2021
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
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