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Title:
A Keplerian-based Hamiltonian splitting for gravitational N-body simulations
Authors:
Gonçalves Ferrari, G.; Boekholt, T.; Portegies Zwart, S. F.
Affiliation:
AA(Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands; Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil ), AB(Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands), AC(Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands)
Publication:
Monthly Notices of the Royal Astronomical Society, Volume 440, Issue 1, p.719-730 (MNRAS Homepage)
Publication Date:
05/2014
Origin:
OUP
Astronomy Keywords:
Methods: numerical
Abstract Copyright:
2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society
DOI:
10.1093/mnras/stu282
Bibliographic Code:
2014MNRAS.440..719G

Abstract

We developed a Keplerian-based Hamiltonian splitting for solving the gravitational N-body problem. This splitting allows us to approximate the solution of a general N-body problem by a composition of multiple, independently evolved two-body problems. While the Hamiltonian splitting is exact, we show that the composition of independent two-body problems results in a non-symplectic non-time-symmetric first-order map. A time-symmetric second-order map is then constructed by composing this basic first-order map with its self-adjoint. The resulting method is precise for each individual two-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with primordial binaries. The superposition of Kepler solutions for each pair of particles makes the method excellently suited for parallel computing; we achieve ≳64 per cent efficiency for only eight particles per core, but close to perfect scaling for 16 384 particles on a 128 core distributed-memory computer. We present several implementations in SAKURA, one of which is publicly available via the AMUSE framework.
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