  We describe the implementation and performance of the ${\rm P^3T}$
(Particle-Particle Particle-Tree) scheme for simulating dense stellar systems.
In ${\rm P^3T}$, 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.
