2024-03-29T08:21:17Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1237342022-10-27T14:39:24Zcom_10234_7037com_10234_9col_10234_8635
Repositori UJI
author
Blanes, Sergio
author
Casas, Fernando
author
Sanz-Serna, JM
2015-06-16T12:44:54Z
2015-06-16T12:44:54Z
2014-05
BLANES, Sergio; CASAS, Fernando; SANZ-SERNA, J. M. Numerical integrators for the Hybrid Monte Carlo method. SIAM Journal on Scientific Computing, 2014, 36.4: A1556-A1580.
http://hdl.handle.net/10234/123734
http://dx.doi.org/10.1137/130932740
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy of the integrator and/or reducing the size of its error constants; order and error constant are relevant concepts in the limit of vanishing step-length. We propose an alternative methodology based on the performance of the integrator when sampling from Gaussian distributions with not necessarily small step-lengths. We construct new splitting formulae that require two, three or four force evaluations per time-step. Limited, proof-of-concept numerical experiments suggest that the new integrators may provide an improvement on the efficiency of the standard Verlet method, especially in problems with high dimensionality.
eng
© 2014, Society for Industrial and Applied Mathematics
hybrid Monte Carlo method
Markov Chain Monte Carlo
acceptance probability
Hamiltonian dynamics
reversibility
volume preservation
symplectic integrators
Verlet method
split-step integrator
stability
error constant
molecular dynamics
Numerical Integrators for the Hybrid Monte Carlo Method
info:eu-repo/semantics/article
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