Volume 26, Issue 1
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

Commun. Comput. Phys., 26 (2019), pp. 265-310.

Published online: 2019-02

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  • 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.

  • Keywords

Helmholtz transmission problem, domain decomposition, periodic layered media, lattice sum.

  • AMS Subject Headings

65N38, 35J05, 65T40, 65F08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-265, author = {}, title = {Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {1}, pages = {265--310}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0021}, url = {http://global-sci.org/intro/article_detail/cicp/13034.html} }
TY - JOUR T1 - Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies JO - Communications in Computational Physics VL - 1 SP - 265 EP - 310 PY - 2019 DA - 2019/02 SN - 26 DO - http://dor.org/10.4208/cicp.OA-2018-0021 UR - https://global-sci.org/intro/article_detail/cicp/13034.html KW - Helmholtz transmission problem, domain decomposition, periodic layered media, lattice sum. AB -

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.

Carlos Pérez-Arancibia, Stephen P. Shipman, Catalin Turc & Stephanos Venakides. (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. doi:10.4208/cicp.OA-2018-0021
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