Trotter derivation of algorithms for Brownian and dissipative particle dynamics

This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to...

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Bibliographic Details
Published in:The Journal of chemical physics 2007-09, Vol.127 (12), p.124109-124109
Main Authors: Thalmann, Fabrice, Farago, Jean
Format: Article
Language:English
Subjects:
Condensed Matter
Physics
Statistical Mechanics
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Summary:This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same "weak order two" accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.2764481