Integrating the probe and singular sources methods
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915455835308032 |
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| author | Ikehata, Masaru |
| author_facet | Ikehata, Masaru |
| contents | The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by the Laplace equation in a bounded domain as a prototype case, an integrated theory of the probe and singular sources methods is proposed. The theory consists of three parts: (i) introducing the singular sources method combined with the notion of the probe method; (ii) finding a third indicator function whose two ways decomposition yields the indicator functions in the probe and singular sources methods; (iii) finding the completely integrated version of the probe and singular sources methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_08133 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Integrating the probe and singular sources methods Ikehata, Masaru Analysis of PDEs Numerical Analysis 35R30, 35J05, 78A46 The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this paper, by considering an inverse obstacle problem governed by the Laplace equation in a bounded domain as a prototype case, an integrated theory of the probe and singular sources methods is proposed. The theory consists of three parts: (i) introducing the singular sources method combined with the notion of the probe method; (ii) finding a third indicator function whose two ways decomposition yields the indicator functions in the probe and singular sources methods; (iii) finding the completely integrated version of the probe and singular sources methods. |
| title | Integrating the probe and singular sources methods |
| topic | Analysis of PDEs Numerical Analysis 35R30, 35J05, 78A46 |
| url | https://arxiv.org/abs/2308.08133 |