High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations.

Eric Cancès (1, 2) , François Castella (3, 4) , Philippe Chartier (4) , Erwan Faou (3, 4) , Claude Le Bris (1, 2) , Frédéric Legoll (1, 5) , Gabriel Turinici (1, 6)

1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 IPSO - Invariant Preserving SOlvers
5 navier umr 8205 - Laboratoire Navier
6 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We introduce high-order formulas for the computation of statistical averages based on the long-time simulation of molecular dynamics trajectories. In some cases, this allows us to significantly improve the convergence rate of time averages toward ensemble averages. We provide some numerical examples that show the efficiency of our scheme. When trajectories are approximated using symplectic integration schemes (such as velocity Verlet), we give some error bounds that allow one to fix the parameters of the computation in order to reach a given desired accuracy in the most efficient manner.

Domaines: Analyse numérique [math.NA]

Eric Cancès, François Castella, Philippe Chartier, Erwan Faou, Claude Le Bris, et al.. High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations.. Journal of Chemical Physics, 2004, 121 (21), pp.10346-55. ⟨10.1063/1.1794611⟩. ⟨hal-00536562⟩