Detection of a piecewise linear crack with one incident wave
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.
Fields of Study & Subjects
Ultrasonics and Acoustic Wave Propagation
Non-Destructive Testing Techniques
Structural Health Monitoring Techniques
Publication details
- Journal / source
- Inverse Problems and Imaging
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 0
- Issue
- 0
- Publication date
- 1 January 2026
- Language
- EN