N-body integrators with individual time steps from Hierarchical splitting

Pelupessy, F. I.; Jänes, Jürgen; Zwart, Simon Portegies

doi:10.1016/j.newast.2012.05.009

Cited by 79 publications

(113 citation statements)

References 31 publications

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“…Time-symmetric integrators are popular in astrophysics due to their ability to accommodate adaptive stepping. An exactly time-symmetric integrator was proposed by Hut et al (1995), and approximately time-symmetric integrators have been developed by Pelupessy et al (2012) and Kokubo et al (1998). We focus on the proposal by Hut et al (1995), because it is exactly time-symmetric, under certain conditions we describe.…”

Section: Modified Differential Equation With Adaptive Time Stepsmentioning

confidence: 99%

Time-symmetric integration in astrophysics

Hernández

Bertschinger

2018

Monthly Notices of the Royal Astronomical Society

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Calculating the long term solution of ordinary differential equations, such as those of the Nbody problem, is central to understanding a wide range of dynamics in astrophysics, from galaxy formation to planetary chaos. Because generally no analytic solution exists to these equations, researchers rely on numerical methods which are prone to various errors. In an effort to mitigate these errors, powerful symplectic integrators have been employed. But symplectic integrators can be severely limited because they are not compatible with adaptive stepping and thus they have difficulty accommodating changing time and length scales. A promising alternative is time-reversible integration, which can handle adaptive time stepping, but the errors due to time-reversible integration in astrophysics are less understood. The goal of this work is to study analytically and numerically the errors caused by time-reversible integration, with and without adaptive stepping. We derive the modified differential equations of these integrators to perform the error analysis. As an example, we consider the trapezoidal rule, a reversible non-symplectic integrator, and show it gives secular energy error increase for a pendulum problem and for a Hénon-Heiles orbit. We conclude that using reversible integration does not guarantee good energy conservation and that, when possible, use of symplectic integrators is favored. We also show that time-symmetry and time-reversibility are properties that are distinct for an integrator.

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Section: Modified Differential Equation With Adaptive Time Stepsmentioning

confidence: 99%

Time-symmetric integration in astrophysics

Hernández

Bertschinger

2018

Monthly Notices of the Royal Astronomical Society

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“…We also consider stellar evolution effects. We used the huayno code (Pelupessy et al 2012) to compute the internal gravitational force in the Sun's birth cluster. To compute the force due to the external Galactic potential, we use a high-order Rotating bridge (Martínez-Barbosa et al 2015).…”

Section: Simulations Set Upmentioning

confidence: 99%

The solar siblings in the Gaia era

Martínez-Barbosa

Zwart

2014

EAS Publications Series

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Abstract. We perform realistic simulations of the Sun's birth cluster in order to predict the current distribution of solar siblings in the Galaxy. We study the possibility of finding the solar siblings in the Gaia catalogue by using only positional and kinematic information. We find that the number of solar siblings predicted to be observed by Gaia will be around 100 in the most optimistic case, and that a phase space only search in the Gaia catalogue will be extremely difficult. It is therefore mandatory to combine the chemical tagging technique with phase space selection criteria in order to have any hope of finding the solar siblings.

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“…We combine BRIDGE with the ideas introduced in Ref. 4 and construct a family of 48 quasi-symplectic maps with different orders of convergence (2nd-, 4th-& 6th-order) and three time-stepping schemes: i) 16 using constant time-steps, ii) 16 using shared adaptive time-steps, and iii) 16 using hierarchical (individual) time-steps. In all cases we took special care to respect the time-symmetry of the maps which also includes post-Newtonian corrections up to order 3.5PN.…”

Section: Fpgas Nowadays Moderate Sized (N ∼ 10mentioning

confidence: 99%

A Family of Hierarchical Symplectic Maps for N-body Simulations with Post-Newtonian Corrections

Ferrari

2017

Int. J. Mod. Phys. Conf. Ser.

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Symplectic maps are well known for preserving the phase-space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times, such as the N -body problem. However, when combined with a varying time-step scheme, they end up losing its symplecticity and become numerically inefficient. We address this problem by using a recursive Hamiltonian splitting based on the time-symmetric value of the individual time-steps required by the particles in the system. We present a family of 48 quasi-symplectic maps with different orders of convergence (2nd-, 4th-& 6th-order) and three time-stepping schemes: i) 16 using constant time-steps, ii) 16 using shared adaptive time-steps, and iii) 16 using hierarchical (individual) time-steps. All maps include post-Newtonian corrections up to order 3.5PN. We describe the method and present some details of the implementation.

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N-body integrators with individual time steps from Hierarchical splitting

Cited by 79 publications

References 31 publications

Time-symmetric integration in astrophysics

Time-symmetric integration in astrophysics

The solar siblings in the Gaia era

A Family of Hierarchical Symplectic Maps for N-body Simulations with Post-Newtonian Corrections

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