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Markos A. Katsoulakis, Petr Plechac, Alexandros Sopasakis:Error Analysis Of Coarse-Grained Kinetic Monte Carlo MethodThe coarse-grained Monte Carlo (CGMC) algorithm was originally proposed in the series of works [20, 21, 24]. In this paper we further investigate the approximation properties of the coarse-graining procedure and provide both analytical and numerical evidence that the hierarchy of the coarse models is built in a systematic way that allows for error control in both transient and long-time simulations. We demonstrate that the numerical accu- racy of the CGMC algorithm as an approximation of stochastic lattice spin ?ip dynamics is of order two in terms of the coarse-graining ratio and that the natural small parameter is the coarse-graining ratio over the range of parti- cle/particle interactions. The error estimate is shown to hold in the weak convergence sense. We employ the derived analytical results to guide CGMC algorithms and we demonstrate a CPU speed-up in demanding computational regimes that involve nucleation, phase transitions and metastability.Bibliographical note: |