A patch that imparts unconditional stability to explicit integrators for Langevin-like equations

Nawaf Bou-Rabee, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review

Abstract

This paper extends the results in [8] to stochastic differential equations (SDEs) arising in molecular dynamics. It implements a patch to explicit integrators that consists of a Metropolis-Hastings step. The 'patched integrator' preserves the SDE's equilibrium distribution and is accurate on finite time intervals. As a corollary this paper proves the integrator's accuracy in estimating finite-time dynamics along an infinitely long solution - a first in molecular dynamics. The paper also covers multiple time-steps, holonomic constraints and scalability. Finally, the paper provides numerical tests supporting the theory.

Original languageEnglish (US)
Pages (from-to)2565-2580
Number of pages16
JournalJournal of Computational Physics
Volume231
Issue number6
DOIs
StatePublished - Mar 20 2012

Keywords

  • Metropolis-Hastings
  • Molecular dynamics
  • RATTLE
  • RESPA
  • Verlet

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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