TY - JOUR
T1 - Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies
AU - Carlos Pérez-Arancibia, Stephen P. Shipman, Catalin Turc & Stephanos Venakides
JO - Communications in Computational Physics
VL - 1
SP - 265
EP - 310
PY - 2019
DA - 2019/02
SN - 26
DO - http://doi.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 - <p style="text-align: justify;">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.</p>