Detection of a piecewise linear crack with one incident wave
Numerical Analysis
2024-05-09 v1 Numerical Analysis
Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.2405.05179,
title = {Detection of a piecewise linear crack with one incident wave},
author = {Xiaoxu Xu and Guanqiu Ma and Guanghui Hu},
journal= {arXiv preprint arXiv:2405.05179},
year = {2024}
}