A Very Fast and Momentumconserving Tree Code
Abstract
The tree code for the approximate evaluation of gravitational forces is extended and substantially accelerated by including mutual cellcell interactions. These are computed by a Taylor series in Cartesian coordinates and in a completely symmetric fashion, such that Newton's third law is satisfied by construction and that therefore momentum is exactly conserved. The computational effort is further reduced by exploiting the mutual symmetry of the interactions. For typical astrophysical problems with N=10^{5} and at the same level of accuracy, the new code is about 4 times faster than the tree code. For large N, the computational costs are found to scale almost linearly with N, which can also be supported by a theoretical argument, and the advantage over the tree code increases with ever larger N.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 2000
 DOI:
 10.1086/312724
 arXiv:
 arXiv:astroph/0003209
 Bibcode:
 2000ApJ...536L..39D
 Keywords:

 Celestial Mechanics;
 Stellar Dynamics;
 Methods: nBody Simulations;
 Methods: Numerical;
 Astrophysics
 EPrint:
 revised version (accepted by ApJ Letters), 5 pages LaTeX, 3 figures