Multilevel techniques in solving electromagnetic scattering problems

Abstract

Recently, there has been renewed interest on solving integral equations due to the advent of various fast multilevel techniques in solving these equations. These fast solvers explore the special structure of the matrices that arise from the numerical approximation of the integral equation. The kernel of the integral equations is usually related to the Green's function which is translationally invariant. This property manifests itself in the numerical approximations of the Green's operator. As a result, an otherwise dense-matrix vector multiply can be performed in O(N log N) operations. These methods are reviewed and related to communication of N telephones, group theory, and fast Fourier transforms of nonuniformly spaced data.