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

Publication ,  Journal Article
Pérez-Arancibia, C; Shipman, SP; Turc, C; Venakides, S
Published in: Communications in Computational Physics
January 1, 2019

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.

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Published In

Communications in Computational Physics

DOI

EISSN

1991-7120

ISSN

1815-2406

Publication Date

January 1, 2019

Volume

26

Issue

1

Start / End Page

265 / 310

Related Subject Headings

  • Applied Mathematics
  • 4601 Applied computing
 

Citation

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Pérez-Arancibia, C., Shipman, S. P., Turc, C., & Venakides, S. (2019). Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies. Communications in Computational Physics, 26(1), 265–310. https://doi.org/10.4208/cicp.OA-2018-0021
Pérez-Arancibia, C., S. P. Shipman, C. Turc, and S. Venakides. “Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies.” Communications in Computational Physics 26, no. 1 (January 1, 2019): 265–310. https://doi.org/10.4208/cicp.OA-2018-0021.
Pérez-Arancibia C, Shipman SP, Turc C, Venakides S. Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies. Communications in Computational Physics. 2019 Jan 1;26(1):265–310.
Pérez-Arancibia, C., et al. “Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies.” Communications in Computational Physics, vol. 26, no. 1, Jan. 2019, pp. 265–310. Scopus, doi:10.4208/cicp.OA-2018-0021.
Pérez-Arancibia C, Shipman SP, Turc C, Venakides S. Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies. Communications in Computational Physics. 2019 Jan 1;26(1):265–310.
Journal cover image

Published In

Communications in Computational Physics

DOI

EISSN

1991-7120

ISSN

1815-2406

Publication Date

January 1, 2019

Volume

26

Issue

1

Start / End Page

265 / 310

Related Subject Headings

  • Applied Mathematics
  • 4601 Applied computing