Strong convergence of integrators for nonequilibrium Langevin dynamics

ABSTRACT

Several numerical schemes are proposed for the solution of Nonequilibrium Langevin Dynamics (NELD), and the strong rate of convergence for each scheme is analyzed. The schemes considered here employ specialised periodic boundary conditions that deform with the flow, namely Lees-Edwards and Kraynik-Reinelt boundary conditions and their generalisations. We show that care must be taken when implementing standard stochastic integration schemes with these boundary conditions in order to avoid a breakdown in the strong order of convergence.

KEYWORDS:

• Nonequilibrium
• molecular dynamics
• strong convergence
• incompressible flow

Acknowledgments

We also wish to thank the valuable suggestions of the anonymous referees.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Matthew Dobson http://orcid.org/0000-0002-4245-7637

Additional information

Funding

MD was supported by the Defense Advanced Research Projects Agency (DARPA EQUiPS program) [W911NF1520122].