Speeding up HMC with better integrators

Details Speeding up HMC with better integrators Speeding up HMC with better integrators

2007-10-18

arxiv.org/abs/0710.3611v2

PoSLAT2007:038,2007

Physics

High Energy Physics

High Energy Physics - Lattice

6 pages, talk presented by ADK at Lattice 2007 (Algorithms and Machines), Regensburg, 30th July-4th August, 2007

Scientific paper

We discuss how dynamical fermion computations may be made yet cheaper by using symplectic integrators that conserve energy much more accurately without decreasing the integration step size. We first explain why symplectic integrators exactly conserve a ``shadow'' Hamiltonian close to the desired one, and how this Hamiltonian may be computed in terms of Poisson brackets. We then discuss how classical mechanics may be implemented on Lie groups and derive the form of the Poisson brackets and force terms for some interesting integrators such as those making use of second derivatives of the action (Hessian or force gradient integrators). We hope that these will be seen to greatly improve energy conservation for only a small additional cost and that their use will significantly reduce the cost of dynamical fermion computations.

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