Treecode Guide

Hierarchical force calculation algorithms (e.g. Greengard 1990) provide fast, general, and reasonably accurate approximations for gravity and other inverse-square forces. They fill the gap between direct sum methods, which are accurate and general but require O(N2) operations for a complete force calculation, and field methods, which have limited generality and accuracy but require only O(N) operations. All hierarchical methods partition the mass distribution into a tree structure, where each node of the tree provides a concise description of the matter within some spatial volume. This tree structure is used to introduce explicit approximations into the force calculation. Hierarchical methods require either O(N) or O(N log N) operations per force calculation, depending on the representation employed. The algorithm described here improves on an earlier hierarchical O(N log N) method (Barnes & Hut 1986, hereafter BH86) which has been widely employed in astrophysical simulations.