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Published in:
2012 | OriginalPaper | Chapter
Coupled Coarse Graining and Markov Chain Monte Carlo for Lattice Systems
Authors : Evangelia Kalligiannaki, Markos A. Katsoulakis, Petr Plecháč
Published in: Numerical Analysis of Multiscale Computations
Publisher: Springer Berlin Heidelberg
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We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models. The method is capable of handling correctly and efficiently long and short-range particle interactions. The proposed method is a Metropolis-type algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in (Katsoulakis et al. Proc. Natl. Acad. Sci. 100(3):782–787, 2003; Katsoulakis et al. ESAIM-Math. Model. Numer. Anal. 41(3):627–660, 2007). The proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.