Quasi Equilibrium Grid Algorithm: geometric construction for model reduction

The Method of Invariant Grid (MIG) is an iterative procedure for model reduction in chemical kinetics which is based on the notion of Slow Invariant Manifold (SIM) [1-4]. Important role, in that method, is played by the initial grid which, once refined, gives a description of the invariant manifold:...

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Bibliographic Details
Published inarXiv.org
Main Authors Chiavazzo, E, Karlin, I V
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.04.2007
Subjects
Algorithms
Approximation
Equilibrium
Invariants
Iterative methods
Manifolds (mathematics)
Mathematical analysis
Mathematical models
Model reduction
Numerical methods
Organic chemistry
Oxidation
Physics - Statistical Mechanics
Reaction kinetics
Two dimensional models
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Summary:The Method of Invariant Grid (MIG) is an iterative procedure for model reduction in chemical kinetics which is based on the notion of Slow Invariant Manifold (SIM) [1-4]. Important role, in that method, is played by the initial grid which, once refined, gives a description of the invariant manifold: the invariant grid. A convenient way to get a first approximation of the SIM is given by the Spectral Quasi Equilibrium Manifold (SQEM) [1-2]. In the present paper, a flexible numerical method to construct the discrete analog of a Quasi Equilibrium Manifold, in any dimension, is presented. That object is named Quasi Equilibrium Grid (QEG), while the procedure Quasi Equilibrium Grid Algorithm. Extensions of the QEM notion are also suggested. The QEG is a numerical tool which can be used to find a grid-based approximation for the locus of minima of a convex function under some linear constraints. The method is validated by construction of one and two-dimensional grids for model hydrogen oxidation reaction.
ISSN:2331-8422
DOI:10.48550/arxiv.0704.2317