A grid-robust higher-order multilevel fast multipole algorithm for analysis of 3-D scatterers

Recently, a set of novel, grid-robust, higher-order vector basis functions were proposed for the method-of-moments (MoM) solution of integral equations of scattering. The evaluation of integrals in the MoM is greatly simplified due to the unique properties associated with these basis functions. Moreover, these basis functions do not require the edge of a given patch to be completely shared by another patch; thus, the resultant MoM is applicable even for defective meshes. In this article, these new basis functions are employed to solve integral equations for three-dimensional (3-D) mixed dielectric/conducting scatterers. The multilevel fast multipole algorithm (MLFMA) is incorporated to speed up the solution of the resultant matrix system, thereby leading to a grid-robust, higher-order MLFMA solution having an O(N log N) computational complexity, where N denotes the total number of unknowns. Numerical examples are presented to demonstrate the accuracy of the proposed method.