High Accuracy Iterative Algorithm For Multiple Scattering Problems

In this paper,an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous me-dia.The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then apply purely outgo-ing 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 prob-lems 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,specially,to solve the scatter-ing problem with slender scatterer,we present a semi-analytic ap-proach to enhance the integration of elliptic Dirichlet-to-Neumann(DtN)boundary condition and high order spectral element method in solving scattering problem with slender scatterer.By using ap-propriate elemental mapping in the spectral element discretization,semi-analytic formulas are obtained for the computation of Math-ieu expansion coefficients involved in the global DtN operator.Fur-ther,a semi-analytic approach is proposed for the computation of global boundary integral terms in the spectral element discretiza-tion.The proposed semi-analytic formulas can also be used to calculate Mathieu expansion coefficients for functions given values on spectral element grids.Numerical examples show that spec-tral element method with the proposed semi-analytic approach can produce high order numerical solution for scattering problem with slender scatterer.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.The algorithm can be expanded to the case of penetrable scatterers.