mstar – a fast parallelized algorithmically regularized integrator with minimum spanning tree coordinates
Antti Rantala, Pauli Pihajoki, Matias Mannerkoski, Peter H. Johansson, Thorsten Naab
Abstract
ABSTRACT We present the novel algorithmically regularized integration method mstar for high-accuracy (|ΔE/E| ≳ 10−14) integrations of N-body systems using minimum spanning tree coordinates. The twofold parallelization of the $\mathcal {O}(N_\mathrm{part}^2)$ force loops and the substep divisions of the extrapolation method allow for a parallel scaling up to NCPU = 0.2 × Npart. The efficient parallel scaling of mstar makes the accurate integration of much larger particle numbers possible compared to the traditional algorithmic regularization chain (ar-chain) methods, e.g. Npart = 5000 particles on 400 CPUs for 1 Gyr in a few weeks of wall-clock time. We present applications of mstar on few particle systems, studying the Kozai mechanism and N-body systems like star clusters with up to Npart = 104 particles. Combined with a tree or fast multipole-based integrator, the high performance of mstar removes a major computational bottleneck in simulations with regularized subsystems. It will enable the next-generation galactic-scale simulations with up to 109 stellar particles (e.g. $m_\star = 100 \, \mathrm{M}_\odot$ for an $M_\star = 10^{11} \, \mathrm{M}_\odot$ galaxy), including accurate collisional dynamics in the vicinity of nuclear supermassive black holes.