Splitting for Dissipative Particle Dynamics
SIAM Journal on Scientific Computing
A stochastic Trotter integration scheme for dissipative particle dynamics
Mathematics and Computers in Simulation - Special issue: Discrete simulation of fluid dynamics in complex systems
Numerical Methods for Second-Order Stochastic Differential Equations
SIAM Journal on Scientific Computing
Calculating effective diffusivities in the limit of vanishing molecular diffusion
Journal of Computational Physics
A comparison of generalized hybrid Monte Carlo methods with and without momentum flip
Journal of Computational Physics
Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability
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This paper presents a Lie-Trotter splitting for inertial Langevin equations (geometric Langevin algorithm) and analyzes its long-time statistical properties. The splitting is defined as a composition of a variational integrator with an Ornstein-Uhlenbeck flow. Assuming that the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the splitting approximates the invariant measure of inertial Langevin equations to within the accuracy of the variational integrator in representing the Hamiltonian. In particular, if the variational integrator admits no energy error, then the method samples the invariant measure of inertial Langevin equations without error. Numerical validation is provided using explicit variational integrators with first-, second-, and fourth-order accuracy.