The numerical realization of the probe method for the inverse scattering problems from the near-field data

In this paper, we present some results on the numerical realization of the probe method for the inverse scattering problem of determining an obstacle with impedance boundary condition from the near-field data. The keys are how to construct the Runge approximate function for the fundamental solutions and compute the indicator function for the boundary of an obstacle. We test the performance of the probe method for a 2D obstacle by taking the simulated Dirichlet-to-Neumann map as inversion input data.