Domain Decomposition for Quasi-Periodic Scattering by Layered Media via Robust Boundary-Integral Equations at All Frequencies  

作　　者：Carlos Perez-Arancibia Stephen P.Shipman Catalin Turc Stephanos Venakides 

机构地区：[1]Institute for Mathematical and Computational Engineering,School of Engineering and Faculty of Mathematics,Pontificia Universidad Catlica de Chile,Santiago,Chile [2]Department of Mathematics,Louisiana State University,Baton Rouge,LA 70803,USA [3]Department of Mathematical Sciences,New Jersey Institute of Technology,Newark,NJ 07102,USA [4]Department of Mathematics,Duke University,Durham,NC 27708,USA

出　　处：《Communications in Computational Physics》2019年第6期265-310,共46页计算物理通讯（英文）

摘　　要：We develop a non-overlapping domain decomposition method(DDM)for scalar wave scattering by periodic layered media.Our approach relies on robust boun-dary-integral equation formulations of Robin-to-Robin(RtR)maps throughout the frequency spectrum,including cutoff(or Wood)frequencies.We overcome the obsta-cle of non-convergent quasi-periodic Green functions at these frequencies by incor-porating newly introduced shifted Green functions.Using the latter in the defini-tion of quasi-periodic boundary-integral operators leads to rigorously stable computations of RtR operators.We develop Nystr̈om 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.

关 键 词：Helmholtz transmission problem domain decomposition periodic layered media lattice sum 

分 类 号：O17[理学—数学]