Fast multipole solvers for three-dimensional radiation and fluid flow problems

Abstract

A number of physics problems can be modeled by a set of N elements, which have pair-wise interactions with one another. The use of such elements for the evolution of vorticity in fluid flows and the calculation of the velocity field from the evolving vorticity field is well known. Fast multipole methods for fluid flow problems have been developed in the past to reduce computational effort to something less than O(N 2). In this paper we develop a fast multipole solver with application to both 3-D radiation problems (calculation of the heat flux from the evolving temperature field in an absorbing medium) and 3-D fluid flow. This is accomplished by using a more general kernel for the associated volume integrals. This kernel also encompasses other applications such as gravitational fields, electrostatics, scattering, etc. The present algorithm has been designed to have a very high efficiency when used on massively parallel computers. This feature comes at the expense of computational effort, which is less than O(N 2) but greater than O(N) or O(NlnN).