Solution of radiation problems using the fast multipole method

EM radiation problems involving electrically large radiators and reflectors are to be solved using the fast multipole method (FMM). Structures that are intentional radiators, such as antennas, have to be designed to optimize the required radiation characteristics. On the other hand, unintentional radiators, such as electronic systems, have to be designed to suppress the radiation mechanisms. Computational simulation of both types of radiators can be used to improve the design in a shorter time spending less resources. However, some interesting real-life radiation problems are electrically very large and thus cannot be solved using traditional solution algorithms due to the limitations on the computational resources. The FMM enables the solution of larger problems with existing computational resources by reducing the computational complexity and the memory requirement of the solution without sacrificing the accuracy. This is achieved by replacing the matrix-vector multiplications of O(N/sup 2/) complexity by a faster equivalent of O(N/sup 1.5/) complexity in each iteration of an iterative scheme. Some versions of the FMM have complexities that are even lower than O(N/sup 1.5/) per iteration. In contrast, a direct solution would require O(N/sup 3/) operations. 3D radiation problems involving complicated geometries are modelled using arbitrary surface triangulations. Piecewise linear basis functions defined on triangular domains due to Rao, Wilton, and Glisson (RWG) (1982) and referred to as RWG basis functions are used to approximate the induced currents.