ias15: a fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits

By H. Rein, D. Spiegel. 2014

523 citations recorded by the source corpus.

We present IAS15, a 15th-order integrator to simulate gravitational dynamics. The integrator is based on a Gaus-Radau quadrature and can handle conservative as well as non-conservative forces. We develop a step-size control that can automatically choose an optimal timestep. The algorithm can handle close encounters and high-eccentricity orbits. The systematic errors are kept well below machine precision and long-term orbit integrations over 10 9 orbits show that IAS15 is optimal in the sense that it follows Brouwer’s law, i.e. the energy error behaves like a random walk. Our tests show that IAS15 is superior to a mixed-variable symplectic integrator (MVS) and other high-order integrators in both speed and accuracy. In fact, IAS15 preserves the symplecticity of Hamiltonian systems better than the commonly-used nominally symplectic integrators to which we compared it. We provide an open-source implementation of IAS15. The package comes with several easy-to-extend examples involving resonant planetary systems, Kozai-Lidov cycles, close encounters, radiation pressure, quadrupole moment, and generic damping functions that can, among other things, be used to simulate planet-disc interactions. Other non-conservative forces can be added easily.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/54f31d2ceaf80e88707fa26c39f81e04a51ddad4

How researchers see this paper

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In Astronomy and Astrophysics

1. S. Tremaine
2. K. Silsbee
3. D. Tamayo
4. Pengshuai Shi
5. David M. Hernandez
6. H. Rein
7. Jo Bovy
8. M. Volonteri

Citations in the corpus

• WHFAST: a fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long-term gravitational simulations (2015, background): “See also Rein & Spiegel (2015) for a similar discussion for non-symplectic integrators.”
• REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations (2019, methodology): “Instead, as a proxy for the exact propagator P, we also integrate the system with IAS15 (Rein & Spiegel 2015), a high-order adaptive-timestep method whose accuracy reaches machine precision.”
• Lidov–Kozai Cycles with Gravitational Radiation: Merging Black Holes in Isolated Triple Systems (2016, methodology): “In order to get a more accurate estimate of the fraction of triple systems that lead to merger, we ran three-body simulations using the Rebound package (Rein & Liu 2012) with the IAS15 integrator (Rein & Spiegel 2015).”