Numerical Integrators for the Hybrid Monte Carlo Method
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Title
Numerical Integrators for the Hybrid Monte Carlo MethodDate
2014-05Publisher
Society for Industrial and Applied MathematicsBibliographic citation
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.Type
info:eu-repo/semantics/articlePublisher version
http://epubs.siam.org/doi/abs/10.1137/130932740Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
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 ... [+]
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. [-]
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SIAM J. Sci. Comput., 36(4)Rights
© 2014, Society for Industrial and Applied Mathematics
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