Error analysis of coarse-grained kinetic Monte Carlo method
摘要
In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice stochastic dynamics. We 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 accuracy of the CGMC algorithm as an approximation of stochastic lattice spin flip 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 particle/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.
引用
@article{arxiv.math/0509228,
title = {Error analysis of coarse-grained kinetic Monte Carlo method},
author = {Markos A Katsoulakis and Petr Plechac and Alexandros Sopasakis},
journal= {arXiv preprint arXiv:math/0509228},
year = {2007}
}
备注
30 pages