Fast complex source point expansion for accelerating the method of moments

In this paper a rigorous complex source point (CSP) beam expansion is used to accelerate the matrix-vector product (MVP) computation in the iterative solution of method of moments (MoM) integral equation problems. The scattering object in this CSP-MoM algorithm is partitioned into groups in a manner similar to the fast multipole method (FMM). However, unlike FMM, the interactions between well separated groups are computed by using the CSP beams as field basis functions. The directional properties of CSP beams allow a fast evaluation these interactions such that the overall MVP is computed very efficiently. The direct solution time and the storage requirement of the CSP-MoM method is numerically shown to be O(N^3/2) by optimally selecting the number of groups.