Equation-Free Multiscale Computation: Algorithms and Applications
Authored by Ioannis G Kevrekidis, Giovanni Samaey
Date Published: 2009
DOI: 10.1146/annurev.physchem.59.032607.093610
Sponsors:
United States Defense Advanced Research Planning Agency (DARPA)
United States Department of Energy (DOE)
United States National Science Foundation (NSF)
Platforms:
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Model Documentation:
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Mathematical description
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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 ire 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 conceptual), 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.
Tags
Differential-equations
Homogenization problems
Bifurcation-analysis
Molecular-dynamics
Brownian configuration fields
Monte-carlo simulations
Individual-based
models
Optimal prediction
Dimensionality reduction
Projective integration