Detection of a piecewise linear crack with one incident wave
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911870743478272 |
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| author | Xu, Xiaoxu Ma, Guanqiu Hu, Guanghui |
| author_facet | Xu, Xiaoxu Ma, Guanqiu Hu, Guanghui |
| contents | This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field data corresponding to a single incident plane wave or point source. We propose two non-iterative methods for imaging the location and shape of a crack. The first one is a contrast sampling method, while the second one is a variant of the classical factorization method but only with one incoming wave. Newton's iteration method is then employed for getting a more precise reconstruction result. Numerical examples are presented to show the effectiveness of the proposed hybrid method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Detection of a piecewise linear crack with one incident wave Xu, Xiaoxu Ma, Guanqiu Hu, Guanghui Numerical Analysis Analysis of PDEs This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field data corresponding to a single incident plane wave or point source. We propose two non-iterative methods for imaging the location and shape of a crack. The first one is a contrast sampling method, while the second one is a variant of the classical factorization method but only with one incoming wave. Newton's iteration method is then employed for getting a more precise reconstruction result. Numerical examples are presented to show the effectiveness of the proposed hybrid method. |
| title | Detection of a piecewise linear crack with one incident wave |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2405.05179 |