Multilevel fast dipole method for electromagnetic scattering from perfect electric conducting targets

In this study, a multilevel fast dipole method (MLFDM) is proposed for the electromagnetic scattering from arbitrarily shaped three-dimensional (3D) perfect electric conducting targets to improve the equivalent dipole-moment method (EDM). The EDM views the basis functions as equivalent dipoles models and gives very extremely simplified forms for the impedance element. However, it is incapable of saving memory and matrix-vector multiplication (MVM) time. In the MLFDM, the multilevel grouping scheme is employed, and a simple Taylor-s series expansion of the distance between two interacting equivalent dipoles in far-group pair transforms the impedance element into an aggregation-translation-disaggregation form naturally at each level, which speeds up the MVM significantly. Further more, the memory requirement can be reduced to O(N), where N is the number of unknowns. Numerical results are presented to validate the merits of the MLFDM.