Grape-4: A massively parallel special-purpose computer for collisional N-body simulations

In this paper, we describe the architecture and performance of the GRAPE-4 system, a massively parallel special-purpose computer for N-body simulation of gravitational collisional systems. The calculation cost of N-body simulation of collisional self-gravitating system is O(N-3). Thus, even with present-day supercomputers, the number of particles one can handle is still around 10,000. In N-body simulations, almost all computing time is spent calculating the force between particles, since the number of interactions is proportional to the square of the number of particles. Computational cost of the rest of the simulation, such as the time integration and the reduction of the result, is generally proportional to the number of particles. The calculation of the force between particles call be greatly accelerated by means of a dedicated special-purpose hardware. We have developed a series of hardware systems, the GRAPE (GRAvity PipE) systems, which perform the force calculation. They are used with a general-purpose host computer which performs the rest of the calculation. The GRAPE-4 system is our newest hardware, completed in 1995 summer. Its peak speed is 1.08 TFLOPS. This speed is achieved by running 1692 pipeline large-scale integrated circuits (LSIs), each providing 640 MFLOPS, in parallel.