The Parallel Multipole Method on the Connection Machine

This paper reports on a fast implementation of the three-dimensional nonadaptive Parallel Multipole Method (PMM) on the Connection Machine system model CM—2. The data interactions within the decomposition tree are modeled by a hierarchy of three-dimensional grids forming a pyramid in which parent nodes have degree eight. The base of the pyramid is embedded in the Connection Machine as a three-dimensional grid. The standard grid embedding feature is used. For 10 or more particles per processor the communication time is insignificant. The evaluation of the potential field for a system with 128k particles takes 5 seconds, and a system of a million particles about 3 minutes. The maximum number of particles that can be represented in 2G bytes of primary storage is —‘ 50 million. The execution rate of this implementation of the PMM is at about 1.7 Gflops/sec for a particle-processor-ratio of 10 or greater. A further speed improvement is possible by an improved use of the memory hierarchy associated with each floating-point unit in the system.