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| Autors principals: | , , , |
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| Format: | Preprint |
| Publicat: |
2026
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2603.14708 |
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| _version_ | 1866915865158483968 |
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| author | Gong, Bo Sato, Takumi Sun, Jiguang Wu, Xinming |
| author_facet | Gong, Bo Sato, Takumi Sun, Jiguang Wu, Xinming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Edge element DtN method for electromagnetic scattering poles of perfectly conducting obstacles Gong, Bo Sato, Takumi Sun, Jiguang Wu, Xinming Numerical Analysis 35P25, 78M10, 35P30 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. |
| title | Edge element DtN method for electromagnetic scattering poles of perfectly conducting obstacles |
| topic | Numerical Analysis 35P25, 78M10, 35P30 |
| url | https://arxiv.org/abs/2603.14708 |