Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies

Carlos Pérez-Arancibia, Stephen P. Shipman, Catalin Turc, Stephanos Venakides

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We develop a non-overlapping domain decomposition method (DDM) for scalar wave scattering by periodic layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout the frequency spectrum, including cutoff (or Wood) frequencies. We overcome the obstacle of non-convergent quasi-periodic Green functions at these frequencies by incorporating newly introduced shifted Green functions. Using the latter in the definition of quasi-periodic boundary-integral operators leads to rigorously stable computations of RtR operators. We develop Nyström discretizations of the RtR maps that rely on trigonometric interpolation, singularity resolution, and fast convergent windowed quasi-periodic Green functions. We solve the tridiagonal DDM system via recursive Schur complements and establish rigorously that this procedure is always completed successfully. We present a variety of numerical results concerning Wood frequencies in two and three dimensions as well as large numbers of layers.

Original languageEnglish (US)
Pages (from-to)265-310
Number of pages46
JournalCommunications in Computational Physics
Volume26
Issue number1
DOIs
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Keywords

  • Domain decomposition
  • Helmholtz transmission problem
  • Lattice sum
  • Periodic layered media

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