Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies (Communications in Computational Physics, 2019)
We develop a non-overlapping domain decomposition method (DDM) forscalar 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 relyon trigonometric interpolation, singularity resolution, and fast convergent windowedquasi-periodic Green functions. We solve the tridiagonal DDM system via recursiveSchur complements and establish rigorously that this procedure is always completedsuccessfully. We present a variety of numerical results concerning Wood frequenciesin two and three dimensions as well as large numbers of layers.