<tt>frost</tt>: a momentum-conserving CUDA implementation of a hierarchical fourth-order forward symplectic integrator

ABSTRACT We present a novel hierarchical formulation of the fourth-order forward symplectic integrator and its numerical implementation in GPU-accelerated direct-summation N-body code frost. The new is especially suitable for simulations with large dynamical range due to nature. strictly positive sub-steps are made possible by computing an additional gradient term addition Newtonian accelerations. All force calculations kick operations synchronous so integration algorithm manifestly momentum-conserving. also employ time-step symmetrization procedure approximately restore time-reversibility adaptive individual time-steps. demonstrate series binary, few-body million-body that frost conserves energy level |ΔE/E| ∼ 10−10 while errors linear angular momentum practically negligible. For typical star cluster simulations, we find scales well up $N_\mathrm{GPU}^\mathrm{max}\sim 4\times N/10^5$ GPUs, making beyond N = 106 particles on systems several hundred more GPUs. Due nature integration, inclusion Kepler solver or regularized post-Newtonian corrections close encounters binaries straightforward.