Time Domain Linear Sampling Method for Inverse Scattering Problems with Cracks

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.