Scalable Algorithms for Three-Dimensional Reactive Scattering: Evaluation of a New Algorithm for Obtaining Surface Functions
| Autor: | Danny C. Sorensen, Zareh Darakjian, Edward F. Hayes, Phil Pendergast |
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| Rok vydání: | 1994 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Scattering Applied Mathematics Numerical analysis Scalar (mathematics) Ranging Chebyshev filter Computer Science Applications Computational Mathematics Lanczos resampling symbols.namesake Modeling and Simulation symbols Hamiltonian (quantum mechanics) Algorithm Mathematics Principal axis theorem |
| Zdroj: | Journal of Computational Physics. 113:201-214 |
| ISSN: | 0021-9991 |
| DOI: | 10.1006/jcph.1994.1130 |
| Popis: | Implementation of the adiabatically adjusting, principal axis hyperspherical coordinate (APH) approach of Parker and Pack for three-dimensional reactive scattering requires solution of a series of two-dimensional (2D) surface eigenproblems. A new algorithm is presented that takes the discrete variable representation (DVR) of the surface Hamiltonian and transforms it implicitly to the sequential diagonalization truncation (SDT) representation of Light and coworkers. This implicit transformation step, when combined with the implicit restarted Lanczos method of Sorensen with Chebyshev preconditioning, can be used to obtain accurate solutions to the large-dimensionality surface eigenproblems encountered in three-dimensional reactive scattering. Timing results are presented and comparisons made with the previously employed SDT-DVR approach for these 2D eigenproblems. The new algorithm is faster than the SDT-DVR algorithm currently in use by about a factor ranging from 2.6 to 4.5 for both scalar and vector implementations. This algorithm also requires much less memory for the same order DVR Hamiltonian than previous approaches. This permits solution of larger eigenproblems without resorting to external storage. Strategies for implementing this algorithm on parallel architecture machines are presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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