Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 55, Issue 6, Pages 2745-2786Publisher
SIAM PUBLICATIONS
DOI: 10.1137/16M1066658
Keywords
accelerated Monte Carlo; entropy optimization; micro-macro simulations; multi-scale modeling; stochastic differential equations; finitely extensible nonlinear elastic dumbbells
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Funding
- Research Council of the University of Leuven [OT/13/66]
- Interuniversity Attraction Poles Programme of the Belgian Science Policy Office [IUAP/V/22]
- Research Foundation Flanders (FWO-Vlaanderen) [G.A003.13]
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We present and analyze a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time scale of individual trajectories and the (slow) time scale of the macroscopic function of interest. The algorithm combines short bursts of path simulations with extrapolation of a number of macroscopic state variables forward in time. The new microscopic state, consistent with the extrapolated variables, is obtained by a matching operator that minimizes the perturbation caused by the extrapolation. We provide a proof of the convergence of this method, in the absence of statistical error, and we analyze various strategies for matching, as an operator on probability measures. Numerical experiments we show illustrate the effects of the different approximations on the resulting error in macroscopic predictions.
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