NBODY6++GPU: ready for the gravitational million-body problem

Accurate direct N-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. NBODY6 is a well-known direct N-body code for star clusters, and NBODY6++ is the extended version designed for large particle number simulations by supercomputers. We present NBODY6++ GPU, an optimized version of NBODY6++ with hybrid parallelization methods (MPI, GPU, OpenMP, and AVX/SSE) to accelerate large direct N-body simulations, and in particular to solve the million-body problem. We discuss the new features of the NBODY6++ GPU 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, NBODY6++ GPU is 400-2000 times faster than NBODY6 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.