Edge element DtN method for electromagnetic scattering poles of perfectly conducting obstacles
This work addresses a limited area in computational electromagnetics for researchers, but it is incremental as it builds on existing methods for scattering pole computation.
The paper tackles the problem of numerically computing electromagnetic scattering poles for perfectly conducting obstacles, proposing a finite element DtN method that avoids non-physical poles and demonstrates effectiveness through numerical examples.
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.