Fourier-Galerkin method for scattering poles of sound soft obstacles
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909825427832832 |
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| author | Ma, Yunyun Sun, Jiguang |
| author_facet | Ma, Yunyun Sun, Jiguang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier-Galerkin method for scattering poles of sound soft obstacles Ma, Yunyun Sun, Jiguang Numerical Analysis 65N30, 45C05 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. |
| title | Fourier-Galerkin method for scattering poles of sound soft obstacles |
| topic | Numerical Analysis 65N30, 45C05 |
| url | https://arxiv.org/abs/2510.03826 |