Edge element DtN method for electromagnetic scattering poles of perfectly conducting obstacles

TL;DR

This paper introduces a novel finite element DtN method using edge elements to accurately compute electromagnetic scattering poles of perfectly conducting obstacles, with proven convergence and demonstrated effectiveness through numerical examples.

Contribution

The paper develops a new numerical approach combining DtN mapping and edge elements to compute scattering poles, ensuring convergence and eliminating non-physical poles.

Findings

Method accurately computes electromagnetic poles.

Convergence of the method is theoretically proven.

Numerical examples confirm the method's effectiveness.

Abstract

Meromorphic continuation of the scattering operator leads to scattering poles (resonances) in the complex plane. Despite their significance, numerical investigation of scattering poles remains limited. In this paper, we propose and analyze a numerical method to compute electromagnetic poles of perfectly conducting obstacles. The unbounded domain for the scattering problem is truncated using the DtN mapping and the poles are shown to be the eigenvalues of a holomorphic Fredholm operator function related to Maxwell's equations. Edge elements are used for discretization. The convergence is proved using the abstract approximation theory for eigenvalue problems of holomorphic Fredholm operator functions. The proposed finite element DtN approach is free of non-physical poles. A spectral indicator method is then employed to compute the resulting nonlinear matrix eigenvalue problem. Numerical examples are presented to demonstrate the effectiveness of the method.