Parallel N log N N-body algorithms and applications to astrophysics

A parallel version of the Barnes-Hut N-body algorithm is described. The algorithm first assembles a tree data structure which represents the distribution of bodies at all length scales. A domain decomposition is used to assign regions of space and hence bodies to processors. An adaptive load balancing technique is used to insure that processors are assigned equal amounts of work. A tree is built in each processor, and after log/sub 2/ N/sub proc/ exchanges of data, each processor has a restricted version of the tree which is sufficient for force calculations on bodies which lie within its spatial domain. A speedup of over 380 was obtained on a 512-processor Ncube system. Overhead is primarily due to redundant calculation and processor waiting, i.e., the time spent idle waiting for another processor to provide necessary data.<>