Understand
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.
Built on
Higher order Hybrid Monte Carlo algorithms
Michael Creutz and Andreas Gocksch · 1989
Earlier work this paper cites.
A comparison of numerical algorithms for dynamical fermions
Massimo Campostrini and Paolo Rossi · 1990
Earlier work this paper cites.
Higher-order force gradient symplectic algorithms
Siu A. Chin and Donald W. Kidwell · 2000
Earlier work this paper cites.
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