A provably optimal, distribution-independent parallel fast multipole method

The Fast Multipole Method (FMM) is a robust technique for the rapid evaluation of the combined effect of pairwise interactions of n data sources. Parallel computation of the FMM is considered a challenging problem due to the dependence of the computation on the distribution of the data sources, usually resulting in dynamic data decomposition and load balancing problems. In this paper, we present the first provably efficient and distribution-independent parallel algorithm for the FMM on distributed memory parallel computers. Our algorithm does not require any dynamic data decomposition or load balancing step. We present our algorithm in terms of a few basic and well understood primitive operations such as sorting and parallel prefix.