Multilevel coarse graining and nano-pattern discovery in many particle stochastic systems

  • Authors:

  • Evangelia Kalligiannaki;Markos A. Katsoulakis;Petr Plecháč;Dionisios G. Vlachos

  • Affiliations:

  • Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA;Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA and Department of Applied Mathematics, University of Crete and Foundation of Research and Technology-H ...;Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA;Department of Chemical Engineering, University of Delaware, Newark, DE 19716, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

In this work we propose a hierarchy of Markov chain Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub-steps efficiently coupling coarse and finer state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.