Multibody multipole methods

doi:10.1016/j.jcp.2012.06.027

Multibody multipole methods

2012-08-01

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DOI：10.1016/j.jcp.2012.06.027

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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 algorithm uses two approximation schemes: (1) a deterministic series expansion-based method; (2) a Monte Carlo-based approximation based on the central limit theorem. Our approach guarantees a user-specified bound on the absolute or relative error in the computed potential with an asymptotic probability guarantee. We provide speedup results on a three-body dispersion potential, the Axilrod-Teller potential. (C) 2012 Elsevier Inc. All rights reserved.

Keyword:

Fast multipole methods

Data structures

kd-trees

Axilrod-Teller potential

Multi-tree algorithms

Multibody multipole methods

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