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 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.
Funder
Fondo Nacional de Desarrollo Científico y Tecnológico
ANID - Beca Doctorado Nacional
Subject
Applied Mathematics,Modeling and Simulation,Numerical Analysis,Analysis,Computational Mathematics