whfast: a fast and unbiased implementation of a symplectic Wisdom–Holman integrator for long-term gravitational simulations
Top Cited Papers
- 3 July 2015
- journal article
- research article
- Published by Oxford University Press (OUP) in Monthly Notices of the Royal Astronomical Society
- Vol. 452 (1), 376-388
- https://doi.org/10.1093/mnras/stv1257
Abstract
We present whfast, a fast and accurate implementation of a Wisdom–Holman symplectic integrator for long-term orbit integrations of planetary systems. whfast is significantly faster and conserves energy better than all other Wisdom–Holman integrators tested. We achieve this by significantly improving the Kepler solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error that is present in other implementations. For small enough timesteps, we achieve Brouwer's law, i.e. the energy error is dominated by an unbiased random walk due to floating-point round-off errors. We implement symplectic correctors up to order 11 that significantly reduce the energy error. We also implement a symplectic tangent map for the variational equations. This allows us to efficiently calculate two widely used chaos indicators the Lyapunov characteristic number and the Mean Exponential Growth factor of Nearby Orbits. whfast is freely available as a flexible C package, as a shared library, and as an easy-to-use python module.Keywords
This publication has 26 references indexed in Scilit:
- Application of the MEGNO technique to the dynamics of Jovian irregular satellitesMonthly Notices of the Royal Astronomical Society, 2010
- Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbitsPhysica D: Nonlinear Phenomena, 2003
- A Multiple Time Step Symplectic Algorithm for Integrating Close EncountersThe Astronomical Journal, 1998
- Practical Symplectic Methods with Time Transformation for the Few-Body ProblemCelestial Mechanics and Dynamical Astronomy, 1997
- Symplectic integrators and their application to dynamical astronomyCelestial Mechanics and Dynamical Astronomy, 1991
- Symplectic integrators for long-term integrations in celestial mechanicsCelestial Mechanics and Dynamical Astronomy, 1991
- The solution of Kepler's equation, IIICelestial Mechanics and Dynamical Astronomy, 1987
- An improved algorithm due to laguerre for the solution of Kepler's equationCelestial Mechanics and Dynamical Astronomy, 1986
- The solution of Kepler's equation, ICelestial Mechanics and Dynamical Astronomy, 1983
- On the accumulation of errors in numerical integrationThe Astronomical Journal, 1937