Trotter Derivation of Algorithms for Brownian and Dissipative Particle Dynamics

TL;DR

This paper derives and compares numerical algorithms for Langevin and dissipative particle dynamics using operator exponentiation, showing their accuracy and efficiency through simulations.

Contribution

It introduces a new derivation method for Langevin and DPD algorithms, demonstrating their equivalence and improved performance.

Findings

Derived a Langevin integrator equivalent to Ermak's scheme

Developed two DPD algorithms with competitive accuracy and speed

Confirmed similar weak order two accuracy for Langevin schemes

Abstract

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, that we found equivalent to the proposal of Ermak, 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 (DPD). The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.