  In this paper, an efficient iterative method is proposed for solving multiple
scattering problem in locally inhomogeneous media. The key idea is to enclose
the inhomogeneity of the media by well separated artificial boundaries and then
apply purely outgoing wave decomposition for the scattering field outside the
enclosed region. As a result, the original multiple scattering problem can be
decomposed into a finite number of single scattering problems, where each of
them communicates with the other scattering problems only through its
surrounding artificial boundary. Accordingly, they can be solved in a parallel
manner at each iteration. This framework enjoys a great flexibility in using
different combinations of iterative algorithms and single scattering problem
solvers. The spectral element method seamlessly integrated with the
non-reflecting boundary condition and the GMRES iteration is advocated and
implemented in this work. The convergence of the proposed method is proved by
using the compactness of involved integral operators. Ample numerical examples
are presented to show its high accuracy and efficiency.
