GPU-enabled particle-particle particle-tree scheme for simulating dense stellar cluster system

We describe the implementation and performance of the \(\mathrm {P}^{3}\mathrm{T}\) (Particle-Particle Particle-Tree) scheme for simulating dense stellar systems. In \(\mathrm{P}^{3}\mathrm{T}\), the force experienced by a particle is split into short-range and long-range contributions. Short-range forces are evaluated by direct summation and integrated with the fourth order Hermite predictor-corrector method with the block timesteps. For long-range forces, we use a combination of the Barnes-Hut tree code and the leapfrog integrator. The tree part of our simulation environment is accelerated using graphical processing units (GPU), whereas the direct summation is carried out on the host CPU. Our code gives excellent performance and accuracy for star cluster simulations with a large number of particles even when the core size of the star cluster is small.