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Error analysis of coarse-graining for stochastic lattice dynamics
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Katsoulakis, Markos A., Plechac, Petr and Sopasakis, Alexandros (2006) Error analysis of coarse-graining for stochastic lattice dynamics. SIAM Journal on Numerical Analysis, 44 (6). pp. 2270-2296. doi:10.1137/050637339 ISSN 0036-1429.
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Official URL: http://dx.doi.org/10.1137/050637339
Abstract
The coarse-grained Monte Carlo (CGMC) algorithm was originally proposed in the series of works [M. A. Katsoulakis, A. J. Majda, and D. G. Vlachos, J. Comput. Phys., 186 ( 2003), pp. 250 - 278; M. A. Katsoulakis, A. J. Majda, and D. G. Vlachos, Proc. Natl. Acad. Sci. USA, 100 ( 2003), pp. 782 - 787; M. A. Katsoulakis and D. G. Vlachos, J. Chem. Phys., 119 ( 2003), pp. 9412 - 9427]. 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 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 demonstrate a CPU speed-up in demanding computational regimes that involve nucleation, phase transitions, and metastability.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | SIAM Journal on Numerical Analysis | ||||
Publisher: | SIAM PUBLICATIONS | ||||
ISSN: | 0036-1429 | ||||
Official Date: | 2006 | ||||
Dates: |
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Volume: | 44 | ||||
Number: | 6 | ||||
Number of Pages: | 27 | ||||
Page Range: | pp. 2270-2296 | ||||
DOI: | 10.1137/050637339 | ||||
Publication Status: | Published |
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