Assessing numerical methods for molecular and particle simulation

Abstract

We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more recently proposed "pairwise adaptive Langevin" (PAdL) method, which, like DPD but unlike Langevin dynamics, conserves momentum and better matches the relaxation rate of orientational degrees of freedom. PAdL is easy to code and suitable for a variety of problems in nonequilibrium soft matter modeling, our simulations of polymer melts indicate that this method can also provide dramatic improvements in computational efficiency. Moreover we show that PAdL gives excellent control of the relaxation rate to equilibrium. In the nonequilibrium setting, we further demonstrate that while PAdL allows the recovery of accurate shear viscosities at higher shear rates than are possible using the DPD method at identical timestep, it also outperforms Langevin dynamics in terms of stability and accuracy at higher shear rates.

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Cited by in corpus (11)

• On the effect of the thermostat in non-equilibrium molecular dynamics simulations
• Structure-preserving integrators for dissipative systems based on reversible-irreversible splitting
• Tuning the rheological behavior of colloidal gels through competing interactions
• Comparison of Modern Langevin Integrators for Simulations of Coarse-Grained Polymer Melts
• Rheological investigation of gels formed by competing interactions: A numerical study
• Accurate and robust splitting methods for the generalized Langevin equation with a positive Prony series memory kernel
• Time correlation functions of equilibrium and nonequilibrium Langevin dynamics: Derivations and numerics using random numbers
• Composition Methods for Dynamical Systems Separable into Three Parts
• Accurate and efficient splitting methods for dissipative particle dynamics
• Lees-Edwards boundary conditions for translation invariant shear flow: implementation and transport properties
• Stochastic Norton dynamics: An alternative approach for the computation of transport coefficients in dissipative particle dynamics