Towards time symmetric N-body integration

Abstract

Computational efficiency demands discretised, hierarchically organised, and individually adaptive time-step sizes (known as the block-step scheme) for the time integration of N-body models. However, most existing N-body codes adapt individual step sizes in a way that violates time symmetry (and symplecticity), resulting in artificial secular dissipation (and often secular growth of energy errors). Using single-orbit integrations, I investigate various possibilities to reduce or eliminate irreversibility from the time stepping scheme. Significant improvements over the standard approach are possible at little extra effort. However, in order to reduce irreversible step-size changes to negligible amounts, such as suitable for long-term integrations of planetary systems, more computational effort is needed, while exact time reversibility appears elusive for discretised individual step sizes.

arXiv comment13 pages, 16 figures, accepted for publication in MNRAS

References in corpus (10)

• The cosmological simulation code GADGET-2
• A Hierarchical O(N) Force Calculation Algorithm
• A Very Fast and Momentum-Conserving Tree Code
• N-body simulations of gravitational dynamics
• Long-term planetary integration with individual time steps
• N-body Integrators with Individual Time Steps from Hierarchical Splitting
• A Time-Symmetric Block Time-Step Algorithm for N-Body Simulations
• An optimum time-stepping scheme for N-body simulations
• Variational Integrators for the Gravitational N-Body Problem
• GALAXY package for N-body simulation

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• Switching integrators reversibly in the astrophysical $N$-body problem
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