An Efficient Iterative Method for Solving Multiple Scattering in Locally Inhomogeneous Media

TL;DR

This paper introduces an efficient iterative approach for solving multiple scattering problems in locally inhomogeneous media by decomposing the problem into single scattering problems and solving them in parallel, demonstrating high accuracy and efficiency.

Contribution

It proposes a novel iterative framework that decomposes complex scattering problems into manageable single scattering problems with flexible algorithms.

Findings

High accuracy demonstrated through numerical examples

Efficient parallel solution of multiple scattering problems

Convergence proved using integral operator compactness

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.