mstar – a fast parallelized algorithmically regularized integrator with minimum spanning tree coordinates

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.