Fourier-Galerkin method for scattering poles of sound soft obstacles
Numerical Analysis
2025-10-07 v1 Numerical Analysis
Abstract
The computation of scattering poles for a sound-soft obstacle is investigated. These poles correspond to the eigenvalues of two boundary integral operators. We construct novel decompositions of these operators and show that they are Fredholm. Then a Fourier-Galerkin method is proposed for discretization. By establishing the regular convergence of the discrete operators, an error estimate is established using the abstract approximation theory for eigenvalue problems of holomorphic Fredholm operator functions. We give details of the numerical implementation. Several examples are presented to validate the theory and demonstrate the effectiveness of the proposed method.
Keywords
Cite
@article{arxiv.2510.03826,
title = {Fourier-Galerkin method for scattering poles of sound soft obstacles},
author = {Yunyun Ma and Jiguang Sun},
journal= {arXiv preprint arXiv:2510.03826},
year = {2025}
}