A hybrid method for the interior inverse scattering problem

In this paper, the interior inverse scattering problem of a cavity is considered. By use of a general boundary condition, we can reconstruct the shape of the cavity without a priori information of the boundary condition type. The method of fundamental solutions (MFS) with regularization is formulated for solving the scattered field and its normal derivative on the cavity boundary. Newton's method is employed to reconstruct the cavity boundary by satisfying the general boundary condition. This hybrid method copes with the ill-posedness of the inverse problem in the MFS step and deals with the nonlinearity in the Newton's step. Some computational examples are presented to demonstrate the effectiveness of our method.