nbody6++gpu: ready for the gravitational million-body problem

Abstract

Accurate direct <it>N</it>-body simulations help to obtain detailed information about the dynamical evolution of star clusters. They also enable comparisons with analytical models and Fokker-Planck or Monte Carlo methods. <scp>nbody6</scp> is a well-known direct <it>N</it>-body code for star clusters, and <scp>nbody6++</scp> is the extended version designed for large particle number simulations by supercomputers. We present <scp>nbody6++gpu</scp>, an optimized version of <scp>nbody6++</scp> with hybrid parallelization methods (MPI, GPU, OpenMP, and AVX/SSE) to accelerate large direct <it>N</it>-body simulations, and in particular to solve the million-body problem. We discuss the new features of the <scp>nbody6++gpu</scp> code, benchmarks, as well as the first results from a simulation of a realistic globular cluster initially containing a million particles. For million-body simulations, <scp>nbody6++gpu</scp> is 400–2000 times faster than <scp>nbody6</scp> with 320 CPU cores and 32 NVIDIA K20X GPUs. With this computing cluster specification, the simulations of million-body globular clusters including 5 per cent primordial binaries require about an hour per half-mass crossing time.