A ray propagation approach for accelerating the fast multipole method

Abstract

Recently, many researchers have been investigating the use of radiation beam ideas to extend classical integral equation techniques for solution of wave scattering problems into the high frequency regime. Here, we use a propagation approach to accelerate the fast multipole method (FMM) of Rokhlin. The FMM allows the rapid solution of surface integral equations arising in electromagnetics. In this approach, the integral equation is discretized using, for example, the method of moments (MOM), then solved using an iterative method, such as conjugate gradient. The main bottleneck in the computation is the cost of computing a matrix-vector multiply. A standard matrix-vector multiply for a problem with N unknowns has a cost of O(N/sup 2/). A straight-forward application of the FMM reduces this cost to O(N/sup 3/2/). A two-level nested application further reduces the cost to O(N/sup 4/3/). Here we present a non-nested method, using a ray propagation approach, to reduce the cost of a FMM matrix vector multiply to O(N/sup 4/3/). >