From the summary: We develop a fast multipole solver with application to both three-dimensional radiation problems (calculation of the heat flux from evolving temperature field in an absorbing medium) and three-dimensional fluid flows. 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 “parallel 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 \(O(N\ln N)\).