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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021053
Keywords: Boundary integral equations, quasi-periodic scattering, spectral elements, gratings, multi-layered domain
@article{M2AN_2021__55_5_2445_0,
author = {Pinto, Jos\'e and Aylwin, Ruben and Jerez-Hanckes, Carlos},
title = {Fast solver for quasi-periodic {2D-Helmholtz} scattering in layered media},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2445--2472},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021053},
mrnumber = {4329968},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021053/}
}
TY - JOUR AU - Pinto, José AU - Aylwin, Ruben AU - Jerez-Hanckes, Carlos TI - Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2445 EP - 2472 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021053/ DO - 10.1051/m2an/2021053 LA - en ID - M2AN_2021__55_5_2445_0 ER -
%0 Journal Article %A Pinto, José %A Aylwin, Ruben %A Jerez-Hanckes, Carlos %T Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2445-2472 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021053/ %R 10.1051/m2an/2021053 %G en %F M2AN_2021__55_5_2445_0
Pinto, José; Aylwin, Ruben; Jerez-Hanckes, Carlos. Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2445-2472. doi: 10.1051/m2an/2021053
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