Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies
This work provides a robust numerical method for wave scattering in periodic layered media, addressing a known bottleneck at Wood frequencies that previously caused instabilities.
The paper develops a domain decomposition method for quasi-periodic scattering by layered media that works robustly at all frequencies, including Wood frequencies, by using shifted Green functions. Numerical results demonstrate stable and accurate computations for 2D and 3D problems with many layers.
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.