Performance analysis of direct N-body calculations

A theoretical framework for analyzing the computational cost of gravitational N-body codes is introduced and applied to three different types of direct-summation codes, including the type of Aarseth code which has found most general use. The method of analysis, based on the probability distribution of nearest-neighbor distances, is described. The number of time steps required for a variety of different versions of the Aarseth scheme and a variety of physical models of spherical star clusters is estimated in order to measure the effects of different degrees of central concentration. Analytical estimates of computer time required are compared with actual measurements, and the validity of the scaling outside the range actually tested is discussed. A practical result for planning star cluster simulations on the next generation of supercomputers is derived. It is found that the consumption of computer time can be very centrally concentrated.