Fast algorithms for large 3-D electromagnetic scattering and radiation problems

Abstract

Some interesting real-life radiation and scattering problems are electrically very large and cannot be solved using traditional solution algorithms. Despite the difficulties involved, the solution of these problems usually offer valuable results that are immediately useful in real-life applications. The fast multipole method (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^) complexity by a faster equivalent of complexity in each iteration of an iterative scheme. Fast Far-Field Algorithm(FAFFA) further reduces 0{N^) complexity to 0{N^·^). A direct solution would require 0{N^) operations.