### Abstract

We consider the following force field computation problem: given a cluster of n particles in 3-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. Since there are n(n - 1)/2 pairs, direct method requires Θ(n^{2}) time. In this paper, we report our computational experiences with a new O(n log n) time algorithm for fast evaluation of potential and force field in large Lennard-Jones clusters. This algorithm is based on a fair-split tree which guarantees O(n log n) worst-case time complexity without any restriction on particle distributions. For randomly generated particle systems, our implementation outperforms the direct method when the number of particles is 500 or larger. This is the lowest cross over point ever reported in the literature.

Original language | English (US) |
---|---|

Pages (from-to) | 245-265 |

Number of pages | 21 |

Journal | Optimization Methods and Software |

Volume | 14 |

Issue number | 4 |

State | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Fair-split tree
- Force field evaluation
- Particle systems

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Management Science and Operations Research
- Applied Mathematics
- Control and Optimization

### Cite this

*Optimization Methods and Software*,

*14*(4), 245-265.

**Fast evaluation of potential and force field in particle systems using a fair-split tree spatial structure.** / Xue, Guoliang; Lasher, M. R.

Research output: Contribution to journal › Article

*Optimization Methods and Software*, vol. 14, no. 4, pp. 245-265.

}

TY - JOUR

T1 - Fast evaluation of potential and force field in particle systems using a fair-split tree spatial structure

AU - Xue, Guoliang

AU - Lasher, M. R.

PY - 2001

Y1 - 2001

N2 - We consider the following force field computation problem: given a cluster of n particles in 3-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. Since there are n(n - 1)/2 pairs, direct method requires Θ(n2) time. In this paper, we report our computational experiences with a new O(n log n) time algorithm for fast evaluation of potential and force field in large Lennard-Jones clusters. This algorithm is based on a fair-split tree which guarantees O(n log n) worst-case time complexity without any restriction on particle distributions. For randomly generated particle systems, our implementation outperforms the direct method when the number of particles is 500 or larger. This is the lowest cross over point ever reported in the literature.

AB - We consider the following force field computation problem: given a cluster of n particles in 3-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard-Jones. Since there are n(n - 1)/2 pairs, direct method requires Θ(n2) time. In this paper, we report our computational experiences with a new O(n log n) time algorithm for fast evaluation of potential and force field in large Lennard-Jones clusters. This algorithm is based on a fair-split tree which guarantees O(n log n) worst-case time complexity without any restriction on particle distributions. For randomly generated particle systems, our implementation outperforms the direct method when the number of particles is 500 or larger. This is the lowest cross over point ever reported in the literature.

KW - Fair-split tree

KW - Force field evaluation

KW - Particle systems

UR - http://www.scopus.com/inward/record.url?scp=0034994748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034994748&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034994748

VL - 14

SP - 245

EP - 265

JO - Optimization Methods and Software

JF - Optimization Methods and Software

SN - 1055-6788

IS - 4

ER -