Full Paper: http://arxiv.org/abs/1105.2769

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. For the first time, we show how to extend the series-expansion-based approach of Fast Multipole Method-like algorithms to handle 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.   ...   http://arxiv.org/abs/1105.2769

 

 

 

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