Numerical methods for the solution of large kinetic systems
type: Item
instance of: scholarly article
title: Numerical methods for the solution of large kinetic systems
zbMATH Open document ID: 0839.65077
DOI: 10.1016/0168-9274(95)00054-X
author: Oswald Knoth
author: Ralf Wolke
published in: Applied Numerical Mathematics
publication date: 1996-06-16T00:00:00Z
review text: The paper is concerned with a numerical modeling of atmospheric chemistry in air pollution models. The photochemical reaction mechanism contain 40 to 100 polluant species and more than 150 reactions. The chemical reactions are described by stiff systems of nonlinear ordinary differential equations. The authors investigate a new approach of solving the sparse linear equations during the Newton iteration by linear Gauss-Seidel iterations. The Jacobian of the method has many elements equal to zero, and the positions of the nonzero elements are fixed and can be determined in advance. Also, the diagonal elements of the Jacobian are nonpositive. In atmospheric chemistry models the number of nonzero elements in the Jacobian is approximately ten times the number of chemical species involved. With only one iteration the results obtained by the authors are very encouraging in comparison to the quasi-steady state approximation (QSSA) with respect to accuracy and speed. [See \textit{J. G. Verwer} and \textit{M. van Loan}, An evaluation of explicit spendo-steady state approximation schemes for stiff ODE's from chemical kinetics, CWI Report NM-R 9312, Centre for Mathematics and Computer Science, Amsterdam (1993), or J. Comput. Phys. 113, No. 2, 347-352 (1994; Zbl 0810.65068).] Unfortunately, there is no explanation why this approach works well for this class of problems from chemical kinetics.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 92E20
Mathematics Subject Classification ID: 34E13
zbMATH DE Number: 815823
zbMATH Keywords: atmospheric chemistry
zbMATH Keywords: air pollution models
zbMATH Keywords: photochemical reaction
zbMATH Keywords: stiff systems
zbMATH Keywords: sparse linear equations
zbMATH Keywords: Newton iteration
zbMATH Keywords: linear Gauss-Seidel iterations
reviewed by: Iulian Coroian
describes a project that uses: ODEPACK
MaRDI profile type: Publication
cites work: ICIAM/GAMM 95 Applied sciences, especially Mechanics Contributed Lecture and Poster Presentations
cites work: Dynamic Sparsing in Stiff Extrapolation Methods
cites work: Gauss–Seidel Iteration for Stiff ODES from Chemical Kinetics
cites work: An evaluation of explicit pseudo-steady-state approximation schemes for stiff ODE systems from chemical kinetics
cites work: Explicit methods for stiff ODEs from atmospheric chemistry
cites work: Q4001836
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description: scientific article; zbMATH DE number 815823