An iterative decomposition method for scatterer reconstruction in R3R3

In this paper we investigate an iterative method to reconstruct the unknown scatter in R3R3, with only the far-field pattern for just one incident wave. We introduce a general boundary condition and prove its Fréchet derivative. Then this iterative method is able to implement without the boundary condition of the scatterer provided. In practical, one can obtain a better reconstruction without a forward solver at each step. The numerical experiments show the feasibility of this method.