Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 440, Issue 1, Pages 719-730Publisher
OXFORD UNIV PRESS
DOI: 10.1093/mnras/stu282
Keywords
Methods: numerical
Categories
Funding
- CAPES Foundation (Brazil) [5772-11-7]
- Netherlands Research Council NWO [643.200.503, 639.073.803, 614.061.608]
- Netherlands Research School for Astronomy (NOVA)
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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 greater than or similar to 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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