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

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.

References in corpus (6)

• Notes on Perfectly Matched Layers (PMLs)
• A fast and robust solver for the scattering from a layered periodic structure containing multi-particle inclusions
• Windowed Green Function method for the Helmholtz equation in presence of multiply layered media
• Rapidly convergent quasi-periodic Green functions for scattering by arrays of cylinders---including Wood anomalies
• Three-dimensional quasi-periodic shifted Green function throughout the spectrum--including Wood anomalies
• Multitrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

Cited by in corpus (1)

• Windowed Green function method for wave scattering by periodic arrays of 2D obstacles