A simple method of reconstructing a point-like scatterer according to time-dependent acoustic wave propagation. Issue 12 (2nd December 2021)

• Record Type: Journal Article
• Authors: Chen, Bo; Sun, Yao
• Is Part Of: Inverse problems in science and engineering. Volume 29:Issue 12(2021)
• Page Start: 1895
• Page End: 1911
• Publication Date: 2021-12-02
• Subjects: Point-like scatterer -- time-dependent -- acoustic -- inverse scattering problem -- sampling method; 35L05 -- 65M32 -- 65M80; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2021.1886290
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : This paper investigates the approximate solutions to the time-dependent acoustic scattering problem with a point-like scatterer under some basic assumptions and provides a simple method to reconstruct the location of the scatterer. The approximations of the solution to the forward scattering problem are analysed utilizing Green's function and the retarded single-layer potential. Then, based on the approximate solutions, a sampling method is proposed to solve the inverse scattering problem for the location of the scatterer. The proposed method is easy to implement since no equations or matrices have to be computed for the reconstruction. Numerical experiments are provided to show the effectiveness of the method.