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

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8 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)157-169
Number of pages13
JournalTheoretical Computer Science
Volume197
Issue number1-2
DOIs
StatePublished - May 15 1998
Externally publishedYes

Keywords

  • Force field evaluation
  • Spatial tree algorithms
  • n-body simulations

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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