Advanced

Error analysis of coarse-graining for stochastic lattice dynamics

Katsoulakis, Markos; Plechac, Petr and Sopasakis, Alexandros LU (2006) In SIAM Journal on Numerical Analysis 44(6). p.2270-2296
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
coarse‐grained stochastic processes, Monte Carlo simulations, birth‐death process, detailed balance, Arrhenius dynamics, Gibbs measures, weak error estimates, microscopic reconstruction
in
SIAM Journal on Numerical Analysis
volume
44
issue
6
pages
2270 - 2296
publisher
SIAM Publications
external identifiers
  • scopus:34547927269
ISSN
0036-1429
DOI
10.1137/050637339
language
English
LU publication?
no
id
d0cf474e-b789-4f51-ae9b-851cd5789f28 (old id 2201713)
date added to LUP
2011-12-30 18:57:43
date last changed
2019-04-10 01:48:01
@article{d0cf474e-b789-4f51-ae9b-851cd5789f28,
  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.},
  author       = {Katsoulakis, Markos and Plechac, Petr and Sopasakis, Alexandros},
  issn         = {0036-1429},
  keyword      = {coarse‐grained stochastic processes,Monte Carlo simulations,birth‐death process,detailed balance,Arrhenius dynamics,Gibbs measures,weak error estimates,microscopic reconstruction},
  language     = {eng},
  number       = {6},
  pages        = {2270--2296},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Numerical Analysis},
  title        = {Error analysis of coarse-graining for stochastic lattice dynamics},
  url          = {http://dx.doi.org/10.1137/050637339},
  volume       = {44},
  year         = {2006},
}