Geodesic
Error analysis of the transport properties of Metropolized schemes
Max Fathi1 ; Ahmed-Amine Homman2 ; Gabriel Stoltz3
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
ESAIM. Proceedings, Tome 48 (2015), pp. 341-363.

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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.
DOI : 10.1051/proc/201448016

Max Fathi 1 ; Ahmed-Amine Homman 2 ; Gabriel Stoltz 3

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 
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     author = {Max Fathi and Ahmed-Amine Homman and Gabriel Stoltz},
     title = {Error analysis of the transport properties of {Metropolized} schemes},
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     doi = {10.1051/proc/201448016},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201448016/}
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Max Fathi; Ahmed-Amine Homman; Gabriel Stoltz. Error analysis of the transport properties of Metropolized schemes. ESAIM. Proceedings, Tome 48 (2015), pp. 341-363. doi : 10.1051/proc/201448016. http://geodesic.mathdoc.fr/articles/10.1051/proc/201448016/

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