3 years ago

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

Carlos Pérez-Arancibia, Stephanos Venakides, Catalin Turc, Stephen Shipman

We develop a non-overlapping domain decomposition method (DDM) for the solution of quasi-periodic scalar transmission problems in layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout the frequency spectrum, including at Wood, or cutoff, frequencies. We overcome the obstacle of non-convergent quasi-periodic Green functions at these frequencies by incorporating newly introduced shifted quasi-periodic Green functions. Using the latter in the definition of our quasi-periodic boundary-integral operators leads to rigorously stable computations of RtR operators. We develop Nystr\"om 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 we 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.

Publisher URL: http://arxiv.org/abs/1801.09094

DOI: arXiv:1801.09094v1

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