Equation-free multiscale computation: Algorithms and applications

Ioannis G. Kevrekidis, Giovanni Samaey

Research output: Contribution to journalReview article

151 Scopus citations

Abstract

In traditional physicochemical modeling, one derives evolution equations at the (macroscopic, coarse) scale of interest; these are used to perform a variety of tasks (simulation, bifurcation analysis, optimization) using an arsenal of analytical and numerical techniques. For many complex systems, however, although one observes evolution at a macroscopic scale of interest, accurate models are only given at a more detailed (fine-scale, microscopic) level of description (e.g., lattice Boltzmann, kinetic Monte Carlo, molecular dynamics). Here, we review a framework for computer-aided multiscale analysis, which enables macroscopic computational tasks (over extended spatiotemporal scales) using only appropriately initialized microscopic simulation on short time and length scales. The methodology bypasses the derivation of macroscopic evolution equations when these equations conceptually exist but are not available in closed form-hence the term equation-free. We selectively discuss basic algorithms and underlying principles and illustrate the approach through representative applications. We also discuss potential difficulties and outline areas for future research.

Original languageEnglish (US)
Pages (from-to)321-344
Number of pages24
JournalAnnual Review of Physical Chemistry
Volume60
DOIs
StatePublished - May 1 2009

All Science Journal Classification (ASJC) codes

  • Physical and Theoretical Chemistry

Keywords

  • Bifurcation analysis
  • Complex systems
  • Equation-free methods
  • Patch dynamics
  • Simulation

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