Publications [#341952] of Stephanos Venakides
Papers Published
- 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, vol. 26 no. 1
(January, 2019),
pp. 265-310, Global Science Press [doi]
(last updated on 2024/04/17)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.