Acceleration Method of Neighbor Search with GRAPE and Morton-ordering

We describe a new method to accelerate neighbor searches on GRAPE, i.e. a special purpose hardware that efficiently calculates gravitational forces and potentials in $N$-body simulations. In addition to the gravitational calculations, GRAPE simultaneously constructs the lists of neighbor particles that are necessary for Smoothed Particle Hydrodynamics (SPH). However, data transfer of the neighbor lists from GRAPE to the host computer is time consuming, and can be a bottleneck. In fact, the data transfer can take about the same time as the calculations of forces themselves. Making use of GRAPE's special treatment of neighbor lists, we can reduce the amount of data transfer if we search neighbors in the order that the neighbor lists, constructed in a single GRAPE run, overlap each other. We find that the Morton-ordering requires very low additional calculation and programming costs, and results in successful speed-up on data transfer. We show some benchmark results in the case of GRAPE-5. Typical reduction in transferred data becomes as much as 90%. This method is suitable not only for GRAPE-5, but also GRAPE-3 and the other versions of GRAPE.