Mstar – a fast parallelized algorithmically regularized integrator with minimum spanning tree coordinates. Issue 3 (15th January 2020)

• Record Type: Journal Article
• Authors: Rantala, Antti; Pihajoki, Pauli; Mannerkoski, Matias; Johansson, Peter H; Naab, Thorsten
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 492:Issue 3(2020)
• Page Start: 4131
• Page End: 4148
• Publication Date: 2020-01-15
• Subjects: gravitation -- methods: numerical -- quasars: supermassive black holes -- galaxies: star clusters: general; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/staa084
• Languages: English
• ISSNs: 0035-8711

Abstract

ABSTRACT: We present the novel algorithmically regularized integration method mstar for high-accuracy (|Δ E/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 N CPU = 0.2 × N part . 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. N part = 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 N part = 10 4 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 10 9 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.