A fast multipole method for stellar dynamics

IF 16.281
Walter Dehnen
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引用次数: 53

Abstract

The approximate computation of all gravitational forces between N interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than O(N) operations. FMM groups particles into spatially bounded cells and uses cell-cell interactions to approximate the force at any position within the sink cell by a Taylor expansion obtained from the multipole expansion of the source cell. By employing a novel estimate for the errors incurred in this process, I minimise the computational effort required for a given accuracy and obtain a well-behaved distribution of force errors. For relative force errors of ~10?7, the computational costs exhibit an empirical scaling of N 0.87 . My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for N? 10 5 .

Abstract Image

恒星动力学的快速多极方法
用快速多极法(FMM)近似计算N个相互作用粒子之间的所有引力,可以达到直接求和的精度,但需要的操作少于O(N)次。FMM将粒子分组到空间有界的单元中,并利用单元间的相互作用,通过从源单元的多极展开得到的泰勒展开来近似吸收单元内任何位置的力。通过对这一过程中产生的误差采用新的估计,我最大限度地减少了给定精度所需的计算工作量,并获得了良好的力误差分布。相对力误差为~10?7、计算成本的经验标度为∝N 0.87。我的实现(在16核节点上运行)优于基于gpu的直接求和,对于N?5 . b。
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期刊介绍: Computational Astrophysics and Cosmology (CompAC) is now closed and no longer accepting submissions. However, we would like to assure you that Springer will maintain an archive of all articles published in CompAC, ensuring their accessibility through SpringerLink's comprehensive search functionality.
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