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.
|Number of pages||28|
|Journal||ESAIM: Mathematical Modelling and Numerical Analysis|
|State||Published - 1 Sep 2021|
- Boundary integral equations
- Multi-layered domain
- Quasi-periodic scattering
- Spectral elements