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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.04242 |
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| _version_ | 1866911041503363072 |
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| author | Liu, Xiaodong Sun, Jiguang Zhang, Lei |
| author_facet | Liu, Xiaodong Sun, Jiguang Zhang, Lei |
| contents | Scattering poles correspond to non-trivial scattered fields in the absence of incident waves and play a crucial role in the study of wave phenomena. These poles are complex wavenumbers with negative imaginary parts. In this paper, we prove two generalized Rellich's lemmas for scattered fields associated with complex wavenumbers. These lemmas are then used to establish uniqueness results for inverse scattering problems. We further explore the inside-out duality, which characterizes scattering poles through the linear sampling method applied to interior scattering problems. Notably, we demonstrate that exterior Dirichlet/Neumann poles can be identified without prior knowledge of the actual sound-soft or sound-hard obstacles. Numerical examples are provided to validate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles Liu, Xiaodong Sun, Jiguang Zhang, Lei Numerical Analysis Scattering poles correspond to non-trivial scattered fields in the absence of incident waves and play a crucial role in the study of wave phenomena. These poles are complex wavenumbers with negative imaginary parts. In this paper, we prove two generalized Rellich's lemmas for scattered fields associated with complex wavenumbers. These lemmas are then used to establish uniqueness results for inverse scattering problems. We further explore the inside-out duality, which characterizes scattering poles through the linear sampling method applied to interior scattering problems. Notably, we demonstrate that exterior Dirichlet/Neumann poles can be identified without prior knowledge of the actual sound-soft or sound-hard obstacles. Numerical examples are provided to validate the theoretical results. |
| title | Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.04242 |