Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media

José Pinto, Ruben Aylwin, Carlos Jerez-Hanckes

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2445-2472
Number of pages28
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number5
StatePublished - 1 Sep 2021


  • Boundary integral equations
  • Gratings
  • Multi-layered domain
  • Quasi-periodic scattering
  • Spectral elements


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