Speaker: Hanno Rein Department for Physical and Environmental Sciences, UTSC
Title: (Non-)Symplectic Integrations of the Solar System
I'll discuss the differences between symplectic and non-symplecticintegrators in the context of long term orbit simulations of the SolarSystem. In particular, I'll present our recent implementation of anon-symplectic Gauss-Radau scheme, IAS15. This integrator achievessub-linear energy error growth (Brouwer's law) over a billion dynamicaltimes or more than 10^10 timesteps. I'll also present a newimplementation of a symplectic integrator. We were able to optimize thealgorithm to get a speed-up by about one order of magnitude compared toother implementations while at the same time push the energy errorgrowth to be sub-linear. I'll talk in detail about the tricks we usedto write code that is both fast but also ensures that all importantfloating-point operations are unbiased. Our integrators are freelyavailable and I plan to do a live demo on how to use them at the end ofmy talk.