{
  "id": "math/0509228",
  "version": "v1",
  "published": "2005-09-09T22:30:55.000Z",
  "updated": "2005-09-09T22:30:55.000Z",
  "title": "Error analysis of coarse-grained kinetic Monte Carlo method",
  "authors": [
    "Markos A Katsoulakis",
    "Petr Plechac",
    "Alexandros Sopasakis"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NA",
    "math.PR"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-09T22:30:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C02",
      "65C20",
      "82C20",
      "82C26"
    ],
    "keywords": [
      "coarse-grained kinetic monte carlo method",
      "error analysis",
      "stochastic lattice spin flip dynamics",
      "cgmc algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9228K"
    }
  }
}