Performance and accuracy of a GRAPE‐3 system for collisionless N‐body simulations
Performance and accuracy of a GRAPE‐3 system for collisionless N‐body simulations
复制标题
用于无碰撞 N 体模拟的 GRAPE-3 系统的性能和精度
DOI：
10.1046/j.1365-8711.1998.01102.x
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发表时间：
1997
影响因子：
4.8
通讯作者：
Accepted Received
中科院分区：
文献类型：
--
作者：
E. Athanassoula;A. Bosma;J. Lambert;J. Makino;Accepted Received
讨论了用于无碰撞 N 体模拟的 GRAPE-3 系统的性能和精度。在对马赛可用的硬件配置以及在线分析的有用性进行初步描述之后，我们将重点放在直接求和和树代码软件的实际性能和准确性上。对于前者，我们讨论舍入误差的来源。标准 Barnes–Hut 树代码不能在 GRAPE-3 系统上使用。相反，粒子被分成块，并且对整个块执行树遍历，而不是单独对块中的每个粒子执行树遍历。然后通过对整个交互列表进行直接求和来计算力。树代码的性能取决于块中粒子的数量，最佳数量取决于前端的速度和板的数量。我们发现代码的规模为 O(N) 并解释了这种行为。随着容差的增加，每步的时间会减少，但依赖性比标准树代码弱得多。最后，我们发现，与标准版本的预期相反，树代码的速度随着配置的聚类而增加。我们讨论了前端的效果，并将 GRAPE-3 上的直接求和和树代码的性能与通用计算机上的其他软件的性能进行了比较。 直接求和和树代码的准确性被讨论为粒子数量和软化的函数。为此，我们考虑力计算的准确性以及模拟过程中的能量守恒。由于直接求和在力计算中的作用增强，我们的树代码比标准树代码准确得多。最后，我们使用不同的硬件和软件跟踪孤立的棒状星系的演化，以评估我们结果的可靠性和可重复性。我们发现在高精度 GRAPE-4 机器上运行的直接求和模拟中的条形速度与在我们的 GRAPE-3 系统上运行的直接求和模拟中的条形速度非常一致。只要容差值小于 1.0 左右，与树代码的一致性也非常好。 我们得出的结论是，GRAPE-3 系统非常适合无碰撞模拟，特别是星系的模拟。这是由于它们具有良好的精度和高速度，从而允许使用大量粒子。
The performance and accuracy of a GRAPE-3 system for collisionless N-body simulations is discussed. After an initial description of the hardware configurations available to us at Marseille, and the usefulness of on-line analysis, we concentrate on the actual performance and accuracy of direct summation and of tree code software. For the former we discuss the sources of round-off errors. The standard Barnes–Hut tree code cannot be used as such on a GRAPE-3 system. Instead particles are divided into blocks and the tree traversal is performed for the whole block, instead of for each particle in the block separately. The forces are then calculated by direct summation over the whole interaction list. The performance of the tree code depends on the number of particles in the block, the optimum number depending on the speed of the front end and the number of boards. We find that the code scales as O(N) and explain this behaviour. The time per step decreases as the tolerance increases, but the dependence is much weaker than for the standard tree code. Finally, we find that, contrary to what is expected for the standard version, the speed of our tree code increases with the clustering of the configuration. We discuss the effect of the front end and compare the performance of direct summation and of tree code on GRAPE-3 with that of other software on general purpose computers. The accuracy of both direct summation and the tree code is discussed as a function of number of particles and softening. For this we consider the accuracy of the force calculation as well as the energy conservation during a simulation. Because of the increased role of the direct summation in the force calculation, our tree code is much more accurate than the standard one. Finally, we follow the evolution of an isolated barred galaxy using different hardware and software in order to assess the reliability and reproducibility of our results. We find excellent agreement between the pattern speed of the bar in direct summation simulations run on the high-precision GRAPE-4 machines and that in direct summation simulations run on our GRAPE-3 system. The agreement with the tree code is also very good provided the tolerance values are smaller than about 1.0. We conclude that GRAPE-3 systems are well suited for collisionless simulations and in particular for those of galaxies. This is due to their good accuracy and their high speed, which allows the use of a large number of particles.