East Asian J. Appl. Math., 12 (2022), pp. 96-110.
Published online: 2021-10
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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} }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.