Parallel implementation of an adaptive and parameter-free N-body integrator

Previously, Pruett et al. (2003) [3] described an N-body integrator of arbitrarily high order M with an asymptotic operation count of O(M²N²). The algorithm's structure lends itself readily to data parallelization, which we document and demonstrate here in the integration of point-mass systems subject to Newtonian gravitation. High order is shown to benefit parallel efficiency. The resulting N-body integrator is robust, parameter-free, highly accurate, and adaptive in both time-step and order. Moreover, it exhibits linear speedup on distributed parallel processors, provided that each processor is assigned at least a handful of bodies.

Program summary

Program title: PNB.f90Catalogue identifier: AEIK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 3052No. of bytes in distributed program, including test data, etc.: 68 600Distribution format: tar.gzProgramming language: Fortran 90 and OpenMPIComputer: All shared or distributed memory parallel processorsOperating system: Unix/LinuxHas the code been vectorized or parallelized?: The code has been parallelized but has not been explicitly vectorized.RAM: Dependent upon NClassification: 4.3, 4.12, 6.5Nature of problem: High accuracy numerical evaluation of trajectories of N point masses each subject to Newtonian gravitation.Solution method: Parallel and adaptive extrapolation in time via power series of arbitrary degree.Running time: 5.1 s for the demo program supplied with the package.