Fast Dipole Method for Electromagnetic Scattering From Perfect Electric Conducting Targets

A new fast dipole method (FDM) is proposed for the electromagnetic scattering from arbitrarily shaped three-dimensional (3D), electrically large, perfect electric conducting (PEC) targets in free space based on the concept of equivalent dipole-moment method (EDM) and the fast multipole method (FMM). The electric-field, magnetic-field and combined-field integral equations (CFIE) for this algorithm have been developed and implemented. Although the basic acceleration idea in the FDM has been borrowed from the FMM, the specific implementation of these two algorithms is completely different. In the FDM, a simple Taylor's series expansion of the distance between two interacting equivalent dipoles is used, which transforms the impedance element into another aggregation-translation-disaggregation form naturally. Furthermore, this algorithm is very simple for numerical implementation for it does not involve the calculation of a number of Bessel functions, Legendre functions for the addition theorem and complex integral operators. The FDM can achieve O(
N
^1.5
) computational complexity and memory requirement, where
N
is the number of unknowns. Numerical results are presented to validate the efficiency and accuracy of this method through comparison with other rigorous solutions.