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Volume 12, Issue 1
Time Domain Linear Sampling Method for Inverse Scattering Problems with Cracks

Yang Yue, Fuming Ma & Bo Chen

East Asian J. Appl. Math., 12 (2022), pp. 96-110.

Published online: 2021-10

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  • Abstract

The paper analyses time-dependent scattering and inverse scattering problems with cracks. The well-posedness of the forward scattering problem is proved and a modified retarded potential boundary integral equation method is utilised to solve the forward problem. Besides, the inverse scattering problem of finding the cracks by using measured scattered data is considered. A time domain linear sampling method for inverse problems is developed and the blow-up property is proved. The computation scheme is relatively simple and easy to implement. Numerical examples demonstrate the effectiveness of the methods.

  • AMS Subject Headings

35L20, 65M32

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-96, author = {Yue , YangMa , Fuming and Chen , Bo}, title = {Time Domain Linear Sampling Method for Inverse Scattering Problems with Cracks}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {12}, number = {1}, pages = {96--110}, abstract = {

The paper analyses time-dependent scattering and inverse scattering problems with cracks. The well-posedness of the forward scattering problem is proved and a modified retarded potential boundary integral equation method is utilised to solve the forward problem. Besides, the inverse scattering problem of finding the cracks by using measured scattered data is considered. A time domain linear sampling method for inverse problems is developed and the blow-up property is proved. The computation scheme is relatively simple and easy to implement. Numerical examples demonstrate the effectiveness of the methods.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.120421.190721 }, url = {http://global-sci.org/intro/article_detail/eajam/19922.html} }
TY - JOUR T1 - Time Domain Linear Sampling Method for Inverse Scattering Problems with Cracks AU - Yue , Yang AU - Ma , Fuming AU - Chen , Bo JO - East Asian Journal on Applied Mathematics VL - 1 SP - 96 EP - 110 PY - 2021 DA - 2021/10 SN - 12 DO - http://doi.org/10.4208/eajam.120421.190721 UR - https://global-sci.org/intro/article_detail/eajam/19922.html KW - Time domain, inverse scattering problem, cracks, boundary integral equation, linear sampling method. AB -

The paper analyses time-dependent scattering and inverse scattering problems with cracks. The well-posedness of the forward scattering problem is proved and a modified retarded potential boundary integral equation method is utilised to solve the forward problem. Besides, the inverse scattering problem of finding the cracks by using measured scattered data is considered. A time domain linear sampling method for inverse problems is developed and the blow-up property is proved. The computation scheme is relatively simple and easy to implement. Numerical examples demonstrate the effectiveness of the methods.

Yang Yue, Fuming Ma & Bo Chen. (2021). Time Domain Linear Sampling Method for Inverse Scattering Problems with Cracks. East Asian Journal on Applied Mathematics. 12 (1). 96-110. doi:10.4208/eajam.120421.190721
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