Factorization method with one plane wave: from model-driven and data-driven perspectives
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866908497491263488 |
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| author | Ma, Guanqiu Hu, Guanghui |
| author_facet | Ma, Guanqiu Hu, Guanghui |
| contents | The factorization method by Kirsch (1998) provides a necessary and sufficient condition for characterizing the shape and position of an unknown scatterer by using far-field patterns of infinitely many time-harmonic plane waves at a fixed frequency. This paper is concerned with the factorization method with a single far-field pattern to recover a convex polygonal scatterer/source. Its one-wave version relies on the absence of analytical continuation of the scattered/radiated wave-fields in corner domains. It can be regarded as a domain-defined sampling method and does not require forward solvers. In this paper we provide a rigorous mathematical justification of the one-wave factorization method and present some preliminary numerical examples. In particular, the proposed scheme can be interpreted as a model-driven and data-driven method, because it essentially depends on the scattering model and a priori given \emph{sample data}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_09664 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Factorization method with one plane wave: from model-driven and data-driven perspectives Ma, Guanqiu Hu, Guanghui Numerical Analysis The factorization method by Kirsch (1998) provides a necessary and sufficient condition for characterizing the shape and position of an unknown scatterer by using far-field patterns of infinitely many time-harmonic plane waves at a fixed frequency. This paper is concerned with the factorization method with a single far-field pattern to recover a convex polygonal scatterer/source. Its one-wave version relies on the absence of analytical continuation of the scattered/radiated wave-fields in corner domains. It can be regarded as a domain-defined sampling method and does not require forward solvers. In this paper we provide a rigorous mathematical justification of the one-wave factorization method and present some preliminary numerical examples. In particular, the proposed scheme can be interpreted as a model-driven and data-driven method, because it essentially depends on the scattering model and a priori given \emph{sample data}. |
| title | Factorization method with one plane wave: from model-driven and data-driven perspectives |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2101.09664 |