An O(NlogN) hypercube N-body integrator

Abstract

The gravitational N-body algorithm of Barnes and Hut [1] has been successfully implemented on a hypercube concurrent processor. The novel approach of their sequential algorithm has demonstrated itself to be well suited to hypercube architectures. The sequential code achieves O (NlogN) speed by recursively dividing space into subcells, thereby creating a hierarchical grouping of particles. Computing interactions between these groups dramatically reduces the amount of communication between processors, as well as the number of force calculations. Parallelism is achieved through an irregular spatial grid decomposition. Since the decomposition topology is not simple, a general loosely synchronous communication routine has been developed. Operations are simplified if the conventional grey code decomposition is modified so that the bits are taken alternately from each Cartesian dimension. A speedup of 180 has been achieved for a 500,000 particle two-dimensional calculation on 256 processors. A speedup of 65 has been obtained for a 64,000 particle three-dimensional calculation on 256 processors.