Detection of a piecewise linear crack with one incident wave
<|reference_start|>Detection of a piecewise linear crack with one incident wave: This paper is concerned with inverse crack scattering problems for time-harmonic acoustic waves. We prove that a piecewise linear crack with the sound-soft boundary condition in two dimensions can be uniquely determined by the far-field data corresponding to a single incident plane wave or point source. We propose two non-iterative methods for imaging the location and shape of a crack. The first one is a contrast sampling method, while the second one is a variant of the classical factorization method but only with one incoming wave. Newton's iteration method is then employed for getting a more precise reconstruction result. Numerical examples are presented to show the effectiveness of the proposed hybrid method.<|reference_end|>
@article{xu2024detection,
    title={Detection of a piecewise linear crack with one incident wave},
    author={Xiaoxu Xu, Guanqiu Ma and Guanghui Hu},
    journal={arXiv preprint arXiv:2405.05179},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.05179},
    primaryClass={math.NA cs.NA math.AP}
}