Parallel implementation of an adaptive and parameter-free \(N\)-body integrator
type: Item
instance of: scholarly article
title: Parallel implementation of an adaptive and parameter-free \(N\)-body integrator
zbMATH Open document ID: 1252.70001
author: C. David Pruett
author: William H. Ingham
author: Ralph D. Herman
published in: Computer Physics Communications
publication date: 2011-05-25T00:00:00Z
review text: This paper is concerned with numerical integration of \(N\)-body problems in a parallel implementation, where \(N\) is assumed to be large. The authors consider only \(N\)-body systems under gravitational interactions, and the original \(6N\)-dimensional system in positions \({\mathbf{x}}_i\), \(i=1, \dots ,N\), and velocities \({\mathbf{v}}_i\), \(i=1, \dots ,N\), is extended to an autonomous polynomial system of dimension \( 6N +N(N-1)/2 \) that includes the inverse distances \( S_{ij}= | {\mathbf{x}}_i -{\mathbf{x}}_j |^{-1}\), \( 1 \leq i < j \leq N\). The time evolution of such a system is carried out by a Taylor series expansion of all variables up to order \(m \leq 28\), and variable step sizes are selected dynamically according to a local error estimate algorithm. Parallelization is achieved by a suitable distribution of the bodies in the processors. In particular, a detailed study of the parallelization with 4 processors is given estimating the operation count per processor. In the second part, some numerical experiments are presented to show the advantages and shortcomings of the proposed method. After some introductory numerical experiments with a two-body problem, the authors examine as a test problem long time evolution of the solar system under gravitational forces and some ``swarms'' of particles with \(N\) between 18 and 480. The results are compared with other standard Runge-Kutta methods.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 70-08
Mathematics Subject Classification ID: 70F10
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 5899705
zbMATH Keywords: long time evolution
zbMATH Keywords: Taylor series method
zbMATH Keywords: solar system
MaRDI profile type: Publication
full work available at URL: j.cpc.2011.01.014
OpenAlex ID: W2045091026
cites work: Q4677313
cites work: An adaptive \(N\)-body algorithm of optimal order.
cites work: Solution of theN-body problem with recurrent power series
cites work: Q4531870
cites work: FOURTH ORDER SYMPLECTIC INTEGRATION WITH REDUCED PHASE ERROR
DOI: 10.1016/J.CPC.2011.01.014
description: scientific article; zbMATH DE number 5899705