TY - JOUR
T1 - Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media
AU - Pinto, José
AU - Aylwin, Ruben
AU - Jerez-Hanckes, Carlos
N1 - Publisher Copyright:
© The authors. Published by EDP Sciences, SMAI 2021.
PY - 2021/9/1
Y1 - 2021/9/1
N2 - 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.
AB - 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.
KW - Boundary integral equations
KW - Gratings
KW - Multi-layered domain
KW - Quasi-periodic scattering
KW - Spectral elements
UR - http://www.scopus.com/inward/record.url?scp=85118276523&partnerID=8YFLogxK
U2 - 10.1051/m2an/2021053
DO - 10.1051/m2an/2021053
M3 - Article
AN - SCOPUS:85118276523
SN - 0764-583X
VL - 55
SP - 2445
EP - 2472
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
IS - 5
ER -