Numerical method for solving electromagnetic scattering problem by many small impedance bodies

TL;DR

This paper introduces a numerical method for efficiently solving electromagnetic scattering problems involving many small impedance bodies, validated through simulations with up to 1000 bodies and supported by error estimates.

Contribution

The paper presents a novel asymptotic numerical approach for EM scattering by numerous small bodies, including error analysis and practical simulations.

Findings

Successfully modeled scattering with 125 and 1000 bodies

Provided error estimates for the asymptotic solutions

Demonstrated the method's effectiveness through numerical results

Abstract

In this paper, we study the problem of electromagnetic (EM) wave scattering by many small impedance bodies. A numerical method for solving this problem is presented. The problem is solved under the physical assumptions $a\ll d \ll \lambda$, where $a$ is the characteristic size of the bodies, $d$ is the minimal distance between neighboring bodies, $\lambda=2\pi/k$ is the wave length and $k$ is the wave number. This problem is solved asymptotically and numerical results for the cases of 125 and 1000 small bodies are presented to illustrate the method. Error estimates for the asymptotic solutions are also provided.