TY - JOUR
T1 - Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies
AU - Pérez-Arancibia, Carlos
AU - Shipman, Stephen P.
AU - Turc, Catalin
AU - Venakides, Stephanos
N1 - Funding Information:
Stephen Shipman acknowledges support from NSF through contract DMS-0807325. Catalin Turc acknowledges support from NSF through contract DMS-1614270. Stephanos Venakides acknowledges support from NSF through contract DMS-1211638.
Publisher Copyright:
© 2019 Global-Science Press
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
KW - Domain decomposition
KW - Helmholtz transmission problem
KW - Lattice sum
KW - Periodic layered media
UR - http://www.scopus.com/inward/record.url?scp=85071856411&partnerID=8YFLogxK
U2 - 10.4208/cicp.OA-2018-0021
DO - 10.4208/cicp.OA-2018-0021
M3 - Article
SN - 1815-2406
VL - 26
SP - 265
EP - 310
JO - Communications in computational physics
JF - Communications in computational physics
IS - 1
ER -