Numerical method for solving electromagnetic wave scattering by one and many small perfectly conducting bodies

TL;DR

This paper develops a numerical method to solve electromagnetic wave scattering problems involving one or many small perfectly conducting bodies, accommodating arbitrary shapes and asymptotic conditions.

Contribution

It introduces a new numerical approach for EM scattering by small bodies, including asymptotic solutions for multiple bodies with error analysis.

Findings

Numerical results demonstrate the method's effectiveness.

Error estimates validate the accuracy of the approach.

Applicable to bodies of arbitrary shape under specified conditions.

Abstract

In this paper, we investigate the problem of electromagnetic (EM) wave scattering by one and many small perfectly conducting bodies and present a numerical method for solving it. For the case of one body, the problem is solved for a body of arbitrary shape, using the corresponding boundary integral equation. For the case of many bodies, the problem is solved asymptotically 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. Numerical results for the cases of one and many small bodies are presented. Error analysis for the numerical method are also provided.