Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912729869058048 |
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| author | Xu, Xiaoxu Hu, Guanghui |
| author_facet | Xu, Xiaoxu Hu, Guanghui |
| contents | This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from a single pair of Cauchy data. Uniqueness results are verified under some a priori assumptions and the one-wave factorization method has been adapted to recover the polygonal obstacle as well as the two coefficients. A modified factorization using the Dirichlet-to-Neumann operator is employed to overcome difficulties arising from possible eigenvalues. Intensive numerical examples indicate that our method is efficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21023 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation Xu, Xiaoxu Hu, Guanghui Analysis of PDEs 65N21, 35R30, 35R25, 35J25 This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from a single pair of Cauchy data. Uniqueness results are verified under some a priori assumptions and the one-wave factorization method has been adapted to recover the polygonal obstacle as well as the two coefficients. A modified factorization using the Dirichlet-to-Neumann operator is employed to overcome difficulties arising from possible eigenvalues. Intensive numerical examples indicate that our method is efficient. |
| title | Simultaneously recover two constant coefficients and a polygon with a single pair of Cauchy data for the Helmholtz equation |
| topic | Analysis of PDEs 65N21, 35R30, 35R25, 35J25 |
| url | https://arxiv.org/abs/2511.21023 |