SCS Colloquium : Novel Hamiltonian splitting methods for direct N-body integration.

 Speaker: Jürgen Jänes (SCS, UvA)

Abstract:
We present two new methods for direct N-body integration by recursively splitting the time evolution operator of the Hamiltonian. The integrators are approximately time-reversible and symplectic.
The Connected Components Hamiltonian split uses a connected component search on the time step graph of the system and evolves the detected components with higher accuracy than the rest system. The Optimal Kick Hamiltonian split evaluates every interaction in the system at the closest block time step, thereby using the optimal amount of block time steps to evolve the system. We present second and fourth order versions of both splitting methods, higher order splits are also possible.
Numerical experiments show that (1) both methods reduce the number of force evaluations and (2) the Connected Components Hamiltonian split reduces considerably the number of time step evaluations compared to previously known splitting methods. Implementations of the splitting methods are incorporated in the Huayno integrator, which is available as a part of the AMUSE framework.