Rational Construction of Stochastic Numerical Methods for Molecular Sampling
- 29 June 2012
- journal article
- Published by Oxford University Press (OUP) in Applied Mathematics Research eXpress
- Vol. 2013 (1), 34-56
- https://doi.org/10.1093/amrx/abs010
Abstract
In this article, we focus on the sampling of the configurational Gibbs–Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a molecular N-body system modeled at constant temperature. Using the Baker–Campbell–Hausdorff expansion, we compare Langevin dynamics integrators in terms of their invariant distributions and demonstrate a superconvergence property of a certain method in the high friction limit; this method, moreover, can be reduced to a simple modification of the Euler–Maruyama method for Brownian dynamics involving a non-Markovian (coloured noise) random process. In fully resolved (long run) molecular dynamics simulations, for our favored method, we observe up to two orders of magnitude improvement in the configurational sampling accuracy for given stepsize with no evident reduction in the size of the largest usable timestep compared with common alternatives.Keywords
Other Versions
This publication has 15 references indexed in Scilit:
- Nonequilibrium Shear Viscosity Computations with Langevin DynamicsMultiscale Modeling & Simulation, 2012
- Discretization errors in molecular dynamics simulations with deterministic and stochastic thermostatsJournal of Computational Physics, 2010
- Convergence of Numerical Time-Averaging and Stationary Measures via Poisson EquationsSIAM Journal on Numerical Analysis, 2010
- Long-Run Accuracy of Variational Integrators in the Stochastic ContextSIAM Journal on Numerical Analysis, 2010
- Accurate Stationary Densities with Partitioned Numerical Methods for Stochastic Differential EquationsSIAM Journal on Numerical Analysis, 2009
- Design of quasisymplectic propagators for Langevin dynamicsThe Journal of Chemical Physics, 2007
- Langevin stabilization of molecular-dynamics simulations of polymers by means of quasisymplectic algorithmsThe Journal of Chemical Physics, 2007
- Quasi-symplectic methods for Langevin-type equationsIMA Journal of Numerical Analysis, 2003
- Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noiseStochastic Processes and their Applications, 2002
- Hypoelliptic second order differential equationsActa Mathematica, 1967