paper

A Hierarchical O(N) Force Calculation Algorithm

arXiv:astro-ph/0202512 · doi:10.1006/jcph.2002.7026

Abstract

A novel code for the approximate computation of long-range forces between N mutually interacting bodies is presented. The code is based on a hierarchical tree of cubic cells and features mutual cell-cell interactions which are calculated via a Cartesian Taylor expansion in a symmetric way, such that total momentum is conserved. The code benefits from an improved and simple multipole acceptance criterion that reduces the force error and the computational effort. For N>10^4, the computational costs are found empirically to rise sub-linear with N. For applications in stellar dynamics, this is the first competitive code with complexity O(N), it is faster than the standard tree code by a factor ten or more.

16 pages, 4 figures, accepted for publication: Journal of Computaional Physics

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