Treecode with a Special-Purpose Processor
Junichiro Makino · Publications of the Astronomical Society of Japan · 1991
Abstract We describe an implementation of the modified Barnes-Hut tree algorithm for a gravitational N-body calculation on a GRAPE (GRAvity PipE) backend processor. GRAPE is a special-purpose computer for N-body calculations. It receives the positions and masses of particles from a host computer and then calculates the gravitational force at each coordinate specified by the host. To use this GRAPE processor with the hierarchical tree algorithm, the host computer must maintain a list of all nodes that exert force on a particle. If we create this list for each particle of the system at each timestep, the number of floating-point operations on the host and that on GRAPE would become comparable, and the increased speed obtained by using GRAPE would be small. In our modified algorithm, we create a list of nodes for many particles. Thus, the amount of the work required of the host is significantly reduced. This algorithm was originally developed by Barnes in order to vectorize the force calculation on a Cyber 205. With this algorithm, the computing time of the force calculation becomes comparable to that of the tree construction, if the GRAPE backend processor is sufficiently fast. The obtained speed-up factor is 30 to 50 for a RISC-based host computer and GRAPE-lA with a peak speed of 240 Mflops.