A fast solver for multi-particle scattering in a layered medium

TL;DR

This paper introduces a fast computational method for simulating acoustic or electromagnetic scattering in layered media with numerous particles, combining advanced mathematical techniques for efficiency.

Contribution

The paper presents a novel algorithm that integrates Sommerfeld integrals, high-order discretization, the fast multipole method, and multiple scattering theory for layered media.

Findings

Efficiently handles thousands of particles in layered media.

Demonstrates high accuracy and speed through numerical experiments.

Applicable to microstructured composite material design.

Abstract

In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of microstructured composite materials, and the evaluation of the scattered field requires a suitable fast solver for either a single configuration or for a sequence of configurations as part of a design or optimization process. We have developed an algorithm for problems of this type by combining the Sommerfeld integral representation, high order integral equation discretization, the fast multipole method and classical multiple scattering theory. The efficiency of the solver is illustrated with several numerical experiments.