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arXiv · 1801.09094

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

Carlos Pérez-Arancibia·Stephen Shipman·Catalin Turc·Stephanos Venakides
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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.

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Carlos Pérez-Arancibia, Stephen Shipman, Catalin Turc, Stephanos Venakides. 2018-05-25. Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies. https://doi.org/10.4208/cicp.oa-2018-0021

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