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

Document Type

Article

Publication Date

1-1-2019

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.

Identifier

85071856411 (Scopus)

Publication Title

Communications in Computational Physics

External Full Text Location

https://doi.org/10.4208/cicp.OA-2018-0021

e-ISSN

19917120

ISSN

18152406

First Page

265

Last Page

310

Issue

1

Volume

26

Grant

0807325

Fund Ref

National Science Foundation

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