The Fourier–Bessel method for the inverse scattering problem of cavities

Abstract

In this paper, we study the inverse scattering problem and propose a new method to determine the shape of a cavity with Dirichlet boundary conditions from the knowledge of acoustic near-field measurements. The Fourier–Bessel method (FBM) is used to reconstruct the boundary of the cavity from scattered fields which are incited by point sources and measured on a closed curve inside the cavity. We not only analyze the stability but also present the numerical experiments to show the effectiveness of the FBM.

Keywords:

• Inverse scattering problem
• cavity
• Fourier–Bessel functions
• stability
• optimization

2020 Mathematics Subject Classifications:

• 78A46
• 35R30
• 65N21

Disclosure statement

No potential conflict of interest was reported by the author(s).