Algorithms for Obtaining Cumulative Reaction Probabilities for Chemical Reactions
| Autor: | Xudong T. Wu, Edward F. Hayes |
|---|---|
| Rok vydání: | 1997 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Iterative method Applied Mathematics Computation Computer Science Applications Computational Mathematics Matrix (mathematics) Simple (abstract algebra) Modeling and Simulation Convergence (routing) Multiplication Boundary value problem Algorithm Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Journal of Computational Physics. 130:136-147 |
| ISSN: | 0021-9991 |
| DOI: | 10.1006/jcph.1996.5575 |
| Popis: | Miller and coworkers have proposed calculating the cumulative reaction probabilities of a chemical reaction through the computation of the few lowest eigenvalues of a matrixZ. In this study, the possibility of computing these eigenvalues using the iterative IRLM approach of Sorensen is investigated. The application to collinear H + H2? H + H2reactions shows that it is possible to compute the physical eigenvalues ofZiteratively using the IRLM formulation with a Chebychev preconditionedZmatrix as the primary matrix. Because the IRLM formulation only requires simple matrix?vector operations, one never needs to assemble and store the wholeZmatrix. Moreover, the multiplication ofZby a vector takes full advantage of the underlying sparseness of the matrix. This study presents several new and successful strategies to improve the convergence speed of IRLM, as well as strategies for obtaining the eigenvalues ofZwhen the eigenvalue span ofZis very large (1?1010). |
| Databáze: | OpenAIRE |
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