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


Journal Article

© 2019 Global-Science Press 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.

Full Text

Duke Authors

Cited Authors

  • Pérez-Arancibia, C; Shipman, SP; Turc, C; Venakides, S

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 26 / 1

Start / End Page

  • 265 - 310

Electronic International Standard Serial Number (EISSN)

  • 1991-7120

International Standard Serial Number (ISSN)

  • 1815-2406

Digital Object Identifier (DOI)

  • 10.4208/cicp.OA-2018-0021

Citation Source

  • Scopus