Wu, Xudong T.; Korombath, Prakashan P.; Hayes, Edward F.; Sorensen, Danny C. Computation of rovibrational eigenvalues of van der Waals molecules on a CRAY T3D. (English) Zbl 0894.65053 J. Comput. Phys. 138, No. 2, 286-301 (1997). Two algorithms for computing rovibrational eigensolutions for van der Waals molecules are presented. The performance and scalability of these algorithms are evaluated on a CRAY T3D with 128 processors using Ar-HO as the test molecule. Both algorithms are based on a discrete variable representation (DVR) of the rovibrational Hamiltonian for van der Waals molecules. They make use of a Sylvester-type transformation to convert most DVR matrix-vector operations into a series of significantly lower-order matrix-matrix operations. The first algorithm has a significantly higher percentage of level-3 BLAS operations, which allows it to achieve higher Mflops. The implementation details are central to achieving maximum efficiency and nearly linear scalability of the algorithms. Reviewer: W.Heinrichs (Essen) MSC: 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65Y05 Parallel numerical computation 82D15 Statistical mechanics of liquids 81V55 Molecular physics 35P15 Estimates of eigenvalues in context of PDEs 35Q72 Other PDE from mechanics (MSC2000) 35Q40 PDEs in connection with quantum mechanics Keywords:rovibrational eigenvalues; van der Waals Molecules; CRAY T3D; parallel computation; performance; scalability; algorithms; discrete variable representation; Hamiltonian Software:eigs PDFBibTeX XMLCite \textit{X. T. Wu} et al., J. Comput. Phys. 138, No. 2, 286--301 (1997; Zbl 0894.65053) Full Text: DOI References: [1] Neuhauser, D., J. Chem. Phys., 93, 2611 (1990) [2] Wang, Y.; Carrington, T.; Corey, G. C., Chem. Phys. Lett., 228, 144 (1994) [3] Kouri, D. J.; Zhu, W.; Parker, G.; Hoffman, D. K., Chem. Phys. Lett., 238, 395 (1995) [4] Mandelshtam, V. A.; Grozdanov, T. P.; Taylor, H. S., J. Chem. Phys., 103, 10074 (1995) [5] Friesner, R. A.; Bentley, J. A.; Menou, M.; Leforestier, C., J. Chem. Phys., 99, 324 (1993) [6] Wyatt, R. E., Phys. Rev., 51, 3643 (1995) [7] Chang, B. C.; Yu, L.; Cullin, D.; Rehfuss, B.; Williamson, J.; Miller, T. A.; Fawzy, W. M.; Zheng, X.; Fei, S.; Heaven, M. C., J. Chem. Phys., 95, 7086 (1991) [8] Heaven, M. C., Ann. Rev. Phys. Chem., 43, 283 (1992) [9] Dubernet, M.-L.; Hutson, J. M., J. Chem. Phys., 99, 7477 (1993) [10] Yang, M.; Alexander, M. H., J. Chem. Phys., 103, 3400 (1995) [11] Ho, T. S.; Rabitz, H.; Choi, S. E.; Lester, M. I., J. Chem. Phys., 104, 1187 (1996) [12] Lester, M. I.; Loomis, R. A.; Giancarlo, L. C.; Berry, M. T.; Chakravarthy, C.; Clary, D. C., J. Chem. Phys., 98, 9320 (1993) [13] Korambath, P. P.; Wu, X. T.; Hayes, E. F.; Carter, C. C.; Miller, T. A., J. Chem. Phys., 107, 3460 (1997) [14] Korambath, P. P.; Wu, X. T.; Hayes, E. F., J. Phys. Chem., 100, 6116 (1996) [15] Lill, J. V.; Parker, G. A.; Light, J. C., Chem. Phys. Lett., 89, 483 (1982) [16] Sorensen, D. C., SIAM J. Matrix Anal. Appl., 13, 357 (1992) [17] Bačić, Z.; Whitnell, R. M.; Brown, D.; Light, J. C., Comput. Phys. Commun., 51, 35 (1988) [18] Golub, G. H.; Van Loan, C. F., Matrix Computations (1989), Johns Hopkins Univ. Press: Johns Hopkins Univ. Press Baltimore, p. 387- · Zbl 0733.65016 [19] Choi, S. E.; Light, J. C., J. Chem. Phys., 92, 2129 (1990) [20] D. Y. Hu, D. C. Sorensen, 1994, Dept. Computational and Applied Math Report, TR94-10, Rice University; D. Y. Hu, D. C. Sorensen, 1994, Dept. Computational and Applied Math Report, TR94-10, Rice University [21] Pendergast, P.; Darakjian, Z.; Hayes, E. F.; Sorensen, D. C., J. Comput. Phys., 113, 201 (1994) [22] Pack, R. T.; Parker, G. A., J. Chem. Phys., 87, 3888 (1987) [23] Wu, X. T.; Hayes, E. F., J. Chem. Phys., 107, 2705 (1997) [24] Saad, Y., Math. Comput., 42, 567 (1984) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.