Integral Equation Method for Inverse Scattering Problem from the Far-Field Data

Abstract

Consider the inverse scattering problem in terms of Helmholtz equation. We study a simply connected domain with oblique derivative boundary condition. In the case of constant $\lambda$, given a finite number of incident wave, the shape of the scatterer is reconstructed from the measured far-field data. We propose a Newton method which is based on the nonlinear boundary integral equation. After computing the Fréchet derivatives with respect to the unknown boundary, the nonlinear equation is transformed to its linear form, then we show the iteration scheme for the inverse problem. We conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.