An efficient iterative method for solving multiple scattering in locally inhomogeneous media

Abstract

In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then apply purely outgoing wave decomposition for the scattering field outside the enclosed region. As a result, the original multiple scattering problem can be decomposed into a finite number of single scattering problems, where each of them communicates with the other scattering problems only through its surrounding artificial boundary. Accordingly, they can be solved in a parallel manner at each iteration. This framework enjoys a great flexibility in using different combinations of iterative algorithms and single scattering problem solvers. The spectral element method seamlessly integrated with the non-reflecting boundary condition and the GMRES iteration is advocated and implemented in this work. The convergence of the proposed method is proved by using the compactness of involved integral operators.Ample numerical examples are presented to show its high accuracy and efficiency. key word: Multiple scattering, inhomogeneous media, iterative method, spectral element method, non-reflecting boundary condition, GMRES iteration arXiv:1908.10527v1 [math.NA]

An Efficient Cartesian Grid-Based Method for Scattering Problems with Inhomogeneous Media

“…Remark 4.1. In this work, evaluation of a boundary integral is implemented by solving an equivalent problem with Dirichlet boundary condition in a bounded domain B, while evaluating of boundary integrals in [59] is equivalent to solving an exterior problem using non-reflecting boundary condition (NRBC) and a spectral element solver.…”