Scalable Algorithms for Three-Dimensional Reactive Scattering: Evaluation of a New Algorithm for Obtaining Surface Functions

✍ Scribed by Phil Pendergast; Zareh Darakjian; Edward F. Hayes; Danny C. Sorensen

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 667 KB
• Volume: 113
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1994.1130

✦ Synopsis

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 twodimensional (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. c) 1994 Academic Press, Inc.