Numerical methods for the solution of large kinetic systems
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.
scientific article; zbMATH DE number 815823