Physics – Computational Physics
Scientific paper
2011-05-13
Physics
Computational Physics
Submitted to Journal of Computational Physics
Scientific paper
A three-body potential function can account for interactions among triples of particles which are uncaptured by pairwise interaction functions such as Coulombic or Lennard-Jones potentials. Likewise, a multibody potential of order $n$ can account for interactions among $n$-tuples of particles uncaptured by interaction functions of lower orders. To date, the computation of multibody potential functions for a large number of particles has not been possible due to its $O(N^n)$ scaling cost. In this paper we describe a fast tree-code for efficiently approximating multibody potentials that can be factorized as products of functions of pairwise distances. For the first time, we show how to derive a Barnes-Hut type algorithm for handling interactions among more than two particles. Our approach guarantees a user-specified bound on the absolute or relative error in the computed potential. We provide speedup results on a three-body dispersion potential, the Axilrod-Teller potential.
Gray Alexander G.
Lee Dongryeol
Ozakin Arkadas
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