A hierarchical O(N log N) forcecalculation algorithm
Abstract
Until recently the gravitational Nbody problem has been modelled numerically either by direct integration, in which the computation needed increases as N^{2}, or by an iterative potential method in which the number of operations grows as N log N. Here we describe a novel method of directly calculating the force on N bodies that grows only as N log N. The technique uses a treestructured hierarchical subdivision of space into cubic cells, each of which is recursively divided into eight subcells whenever more than one particle is found to occupy the same cell. This tree is constructed anew at every time step, avoiding ambiguity and tangling. Advantages over potentialsolving codes are: accurate local interactions; freedom from geometrical assumptions and restrictions; and applicability to a wide class of systems, including (proto)planetary, stellar, galactic and cosmological ones. Advantages over previous hierarchical treecodes include simplicity and the possibility of rigorous analysis of error. Although we concentrate here on stellar dynamical applications, our techniques of efficiently handling a large number of longrange interactions and concentrating computational effort where most needed have potential applications in other areas of astrophysics as well.
 Publication:

Nature
 Pub Date:
 December 1986
 DOI:
 10.1038/324446a0
 Bibcode:
 1986Natur.324..446B
 Keywords:

 Computational Astrophysics;
 Many Body Problem;
 Numerical Integration;
 Stellar Motions;
 Algorithms;
 Hierarchies;
 Physics (General)