TY - JOUR

T1 - An O(n) time hierarchical tree algorithm for computing force field in n-body simulations

AU - Xue, Guoliang

N1 - Funding Information:
This researchw as supportedi n part by a Research Initiation Award of the National Science Foundation under Grant ASC-9409285.

PY - 1998/5/15

Y1 - 1998/5/15

N2 - We consider the following force field computation problem: given a cluster of n particles in three-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. In both cases, the force between two particles vanishes as the distance between them approaches to infinity. Since there are n(n - 1)/2 pairs, direct method requires (-)(n2) time for force-evaluation, which is very expensive for astronomical simulations. In 1985 and 1986, two famous O(n log n) time hierarchical tree algorithms were published by Appel (1985) and by Barnes and Hut (1986), respectively. In this paper, we show that Appel's algorithm can be implemented in O(n) time.

AB - We consider the following force field computation problem: given a cluster of n particles in three-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. In both cases, the force between two particles vanishes as the distance between them approaches to infinity. Since there are n(n - 1)/2 pairs, direct method requires (-)(n2) time for force-evaluation, which is very expensive for astronomical simulations. In 1985 and 1986, two famous O(n log n) time hierarchical tree algorithms were published by Appel (1985) and by Barnes and Hut (1986), respectively. In this paper, we show that Appel's algorithm can be implemented in O(n) time.

KW - Force field evaluation

KW - Spatial tree algorithms

KW - n-body simulations

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U2 - 10.1016/S0304-3975(97)00232-6

DO - 10.1016/S0304-3975(97)00232-6

M3 - Article

AN - SCOPUS:0001701198

VL - 197

SP - 157

EP - 169

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-2

ER -