GSHMC: an efficient method for molecular simulation

Akhmatskaya, E. and Reich, S. (2008) GSHMC: an efficient method for molecular simulation. Journal of Computational Physics, 227 (10). pp. 4934-4954. ISSN 0021-9991 doi: 10.1016/j.jcp.2008.01.023

Abstract/Summary

The hybrid Monte Carlo (HMC) method is a popular and rigorous method for sampling from a canonical ensemble. The HMC method is based on classical molecular dynamics simulations combined with a Metropolis acceptance criterion and a momentum resampling step. While the HMC method completely resamples the momentum after each Monte Carlo step, the generalized hybrid Monte Carlo (GHMC) method can be implemented with a partial momentum refreshment step. This property seems desirable for keeping some of the dynamic information throughout the sampling process similar to stochastic Langevin and Brownian dynamics simulations. It is, however, ultimate to the success of the GHMC method that the rejection rate in the molecular dynamics part is kept at a minimum. Otherwise an undesirable Zitterbewegung in the Monte Carlo samples is observed. In this paper, we describe a method to achieve very low rejection rates by using a modified energy, which is preserved to high-order along molecular dynamics trajectories. The modified energy is based on backward error results for symplectic time-stepping methods. The proposed generalized shadow hybrid Monte Carlo (GSHMC) method is applicable to NVT as well as NPT ensemble simulations.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/33544
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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