MSTAR --一种快速并行的最小生成树坐标正则化积分算法
MSTAR -- a fast parallelised algorithmically regularised integrator with minimum spanning tree coordinates
摘要：
我们提出了一种新的算法正则化的集成方法MSTAR的高精度（$|ΔE/E| \gtrsim 10^{-14}$）集成的N体系统使用最小生成树坐标。$\mathcal{O}(N_\mathrm{part}^2)$力环的双重并行化和外推法的子步划分允许并行缩放到$N_\mathrm{CPU} = 0.2 \times N_\mathrm{part}$。与传统的算法正则化链（AR-CHAIN）方法相比，MSTAR的高效并行缩放使得更大数量的粒子的精确积分成为可能，例如，用于$1$ Gyr的$400$ CPU上的$N_\mathrm{part} = 5000$粒子在几周的挂钟时间内。我们目前的应用程序MSTAR的几个粒子系统，研究Kozai机制和N体系统，如星团与$N_\mathrm{part} =10^4$粒子。结合树或快速多极子为基础的积分器的高性能的MSTAR消除了一个主要的计算瓶颈，在模拟与正规化的子系统。它将使下一代银河系规模的模拟高达$10^9$恒星粒子（例如，$m_\star = 100 M_\odot$的$M_\star = 10^{11} M_\odot$星系），包括准确的碰撞动力学在核超大质量黑洞附近。
英文摘要：
We present the novel algorithmically regularised integration method MSTAR for high accuracy ($|ΔE/E| \gtrsim 10^{-14}$) 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.
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