| Issue |
ESAIM: Proc.
Volume 48, January 2015
CEMRACS 2013 - Modelling and simulation of complex systems: stochastic and deterministic approaches
|
|
|---|---|---|
| Page(s) | 341 - 363 | |
| DOI | https://doi.org/10.1051/proc/201448016 | |
| Published online | 09 March 2015 | |
Error analysis of the transport properties of Metropolized schemes*,**
1 LPMA, 4 place Jussieu, 75005
Paris,
France
2 CEA, DAM, DIF, F-91297
Arpajon,
France
3 Université Paris-Est,
CERMICS (ENPC), INRIA,
F-77455
Marne-la-Vallée,
France
We consider in this work the numerical computation of transport coefficients for Brownian dynamics. We investigate the discretization error arising when simulating the dynamics with the Smart MC algorithm (also known as Metropolis-adjusted Langevin algorithm). We prove that the error is of order one in the time step as Δt goes to zero, when using either the Green-Kubo or the Einstein formula to estimate the transport coefficients. We illustrate our results with numerical simulations.
Résumé
Nous nous intéressons dans cet article au calcul numérique des coefficients de transports pour des dynamiques browniennes. Nous étudions l’erreur de discrétisation qui apparait lorsqu’on simule la dynamique avec l’algorithme connu sous le nom de “Smart MC” dans la littérature. Nous prouvons que cette erreur est d’ordre un en le pas de temps lorsque Δt tend vers zéro, lorsqu’on utilise la formule de Green-Kubo ou la formule d’Einstein pour estimer les coefficients de transport. Nous illustrons ces résultats avec des simulations numériques.
We thank Marie Jardat and Vincent Dahirel for fruitful discussions on the practical aspects of the numerical methods we study here. We also benefited from the scientific environment of the Laboratoire International Associé between the Centre National de la Recherche Scientifique and the University of Illinois at Urbana-Champaign.
© EDP Sciences, SMAI 2015
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