MSTAR -- a fast parallelised algorithmically regularised integrator with
  minimum spanning tree coordinates
  We present the novel algorithmically regularised integration method MSTAR for
high accuracy ($|\Delta E/E| \gtrsim 10^{-14}$) integrations of N-body systems
using minimum spanning tree coordinates. The two-fold parallelisation of the
$\mathcal{O}(N_\mathrm{part}^2)$ force loops and the substep divisions of the
extrapolation method allows for a parallel scaling up to $N_\mathrm{CPU} = 0.2
\times N_\mathrm{part}$. The efficient parallel scaling of MSTAR makes the
accurate integration of much larger particle numbers possible compared to the
traditional algorithmic regularisation chain (AR-CHAIN) methods, e.g.
$N_\mathrm{part} = 5000$ 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
$N_\mathrm{part} =10^4$ particles. Combined with a tree or a fast multipole
based integrator the high performance of MSTAR removes a major computational
bottleneck in simulations with regularised subsystems. It will enable the next
generation galactic-scale simulations with up to $10^9$ stellar particles (e.g.
$m_\star = 100 M_\odot$ for a $M_\star = 10^{11} M_\odot$ galaxy) including
accurate collisional dynamics in the vicinity of nuclear supermassive black
holes.
