A Numerical Solution for the Inverse Scattering Problem in the Impedance Boundary from the Far Field Pattern

In the paper,the inverse scattering problem we are considering is to determine the shape of an impedance boundary obstacle from the time-harmonic incident field and the far field pattern of the scattered wave.We use the single-layer potential to approximate the scattered wave.Eventually the inverse scattering problem is transformed into an optimization problem which is solved by Levenberg -Marquardt algorithm.The numerical examples show that this method is feasible and effective。