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Error analysis of the transport properties of Metropolized schemes
Max Fathia b, Ahmed-Amine Hommanc d e, Gabriel Stoltzd f g
- aLPMA, 4 place Jussieu, 75005 Paris, France
- bLPMA - Laboratoire de Probabilités et Modèles Aléatoires (France)
- cCEA, DAM, DIF, F-91297 Arpajon, France
- dCERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2 - France)
- eDAM - Direction des Applications Militaires (France)
- fUniversité Paris-Est, CERMICS (ENPC), INRIA, F-77455 Marne-la-Vallée, France
- gMATHERIALS - MATHematics for MatERIALS (France)
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Abstract
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.