High-performance Computing in Molecular Sciences

  • Wojciech Cencek
  • Jacek Komasa
  • Jacek Rychlewski
Chapter
Part of the International Handbooks on Information Systems book series (INFOSYS)

Summary

A task which is very common in theoretical chemistry, physics, and engineering — solving the generalized symmetric eigenvalue problem — is discussed. In the considered examples modern quantum chemical methods are applied to solve the Schrödinger equation with a molecular Hamiltonian operator. The solution of the Schrödinger equation is of fundamental importance in quantum chemistry and molecular physics since it gives knowledge of the microscopic world. Two subproblems of completely different character — evaluating matrix elements (a scalar task) and solving the eigenequations (a vector task) are analyzed in terms of the overall computational cost, its scaling with the dimension of the algebraic space and with the size of the molecular system, and of the appropriateness of different computer architectures. The most logical way to achieve a good performance is to use distributed processing on heterogeneous (scalar-vector) systems employing message passing. Experiences in testing one of such systems are discussed and compared with speedups obtained on shared-and distributed-memory homogeneous machines.

Keywords

Lithium Helium Hydride Lution Paral 

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References

  1. [ABB+90]
    Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., DuCroz, J., Greenbaum, S., Hammarling, A., McKenney, S., Sorensen, D., LA-PACK: A Portable Linear Algebra Library for High-Performance Computers, University of Tennessee, Technical Report CS-90–105, 1990.Google Scholar
  2. [ABD+92]
    Anderson, E., Bai, Z., Demmel, J., Dongarra, J., DuCroz, J., Greenbaum, S., Hammarling, A., McKenney, S., Ostrouchov, S., Sorensen, D., LAPACK Users’ Guide, SIAM Press, Philadelphia, 1992.Google Scholar
  3. [ABB+95]
    ABB+95] Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., DuCroz, J., Greenbaum, S., Hammarling, A., McKenney, S., Ostrouchov, S.Google Scholar
  4. Sorensen, D., LAPACK User’s Guide, Second Edition, SIAM Press, Philadelphia, 1995.Google Scholar
  5. [ABD+91]
    Anderson, E., Benzoni, A., Dongarra, J., Moulton, S., Ostrouchov, S., Tourancheau, B., van de Geijn, R., Basic Linear Algebra Communication Subprograms, Proc. of Sixth Distributed Memory Computing Conference, IEEE Computer Society Press, 1991, 287–290.Google Scholar
  6. [BCC+97a]
    Blackford, L. S., Cleary, A., Choi, J., Dongarra, J. J., Petitet, A., Whaley, R. C., Demmel, J., Dhillon, I., Stanley, K., Walker, D., Installation Guide for ScaLAPACK, LAPACK Working Note #93, University of Tennessee, Technical Report CS-95–280, 1997.Google Scholar
  7. [BCC+97b]
    Blackford, L. S., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R. C., ScaLAPACK Users’ Guide, Society for Industrial and Applied Mathematics, Philadelphia, 1997, ( See http://www.netlib.org/scalapack/slug).CrossRefGoogle Scholar
  8. [Boy60]
    Boys, S. F., The integral formulae for the variational solution of the molecular many-electron wave equation in terms of Gaussian functions with direct electronic correlation, Proc. of the Royal Society A258, 1960, 402–411.CrossRefGoogle Scholar
  9. CA95] Computer Architecture, A chapter in Computational Science Education Project,1995, (See ).http://csepl.phy.ornl.gov/-csep.htmlhonavar/gi/gi.html Google Scholar
  10. [CKR95]
    Cencek, W., Komasa, J., Rychlewski, J., Benchmark calculations for two-electron systems using explicitly correlated Gaussian functions, Chemical Physics Letters 246, 1995, 417–420.CrossRefGoogle Scholar
  11. [CK96]
    Cencek, W., Kutzelnigg, W., Accurate relativistic corrections of one-and two-electron systems using Gaussian wave functions, Journal of Chemical Physics 105, 1996, 5878–5885.CrossRefGoogle Scholar
  12. [CR95]
    Cencek, W., Rychlewski, J., Many-electron explicitly correlated Gaus-sian functions. II. Ground state of the helium molecular ion He, Journal of Chemical Physics 102, 1995, 2533–2538.CrossRefGoogle Scholar
  13. [CRJ+98]
    Cencek, W., Rychlewski, J., Jaquet, R., Kutzelnigg, W., Submicrohartree accuracy potential energy surface for H3 including adiabatic and relativistic effects. I. Calculation of the potential points, Journal of Chemical Physics 108, 1998, 2831–2836.CrossRefGoogle Scholar
  14. [CDO+94]
    Choi, J., Dongarra, J., Ostrouchov, S., Petitet, A. P., Walker, D. W., Whaley, R. C., The Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines, LAPACK Working Note #80, University of Tennessee, Technical Report CS-94–246, 1994.Google Scholar
  15. [CDO+95]
    Choi, J., Dongarra, J., Ostrouchov, S., Petitet, A., Walker, D., Whaley, R. C., A Proposal for a Set of Parallel Basic Linear Algebra Subprograms, LAPACK Working Note #100, University of Tennessee, Technical Report CS-95–292, 1995.Google Scholar
  16. [CDP+92a]
    Choi, J., Dongarra, J., Pozo, R., Walker, D., ScaLAPACK: A Scalable Linear Algebra for Distributed Memory Concurrent Computers, LA-PACK Working Note #55, University of Tennessee, Technical Report CS-92–181, 1992.Google Scholar
  17. [CDP+92b]
    Choi, J., Dongarra, J. J., Pozo, R., Walker, D., ScaLAPACK: a scalable linear algebra library for distributed memory concurrent computers, Proc. of the Fourth Symposium on the Frontiers of Massively Parallel Computation (FRONTIERS ‘82), IEEE Computer Society Press, 1992.Google Scholar
  18. [CDW94a]
    Choi, J., Dongarra, J. J., Walker, D. W., PB-BLAS: A set of parallel block basic linear algebra subprograms, Technical Report ORNL/TM-12468, Oak Ridge National Laboratory, Mathematical Sciences Section, Oak Ridge, Tennessee, 1994.Google Scholar
  19. [CDW94b]
    Choi, J., Dongarra, J. J., Walker, D. W., PB-BLAS: Reference manual, Technical Report ORNL/TM-12469, Oak Ridge National Laboratory, Mathematical Sciences Section, Oak Ridge, Tennessee, 1994.Google Scholar
  20. [DDH+88a]
    Dongarra, J. J., DuCroz, J., Hammarling, S., Hanson, R. J., An extended set of FORTRAN basic linear algebra subprograms, ACM Transactions on Mathematical Software 14, 1988, 1–17.CrossRefGoogle Scholar
  21. [DDH+88b]
    Dongarra, J. J., DuCroz, J., Hammarling, S., Hanson, R. J., Algorithm 656. An extended set of basic linear algebra subprograms: model implementation and test programs, ACM Transaction on Mathematical Software 14, 1988, 18–32.CrossRefGoogle Scholar
  22. [DDH+90]
    Dongarra, J. J., DuCroz, J., Hammarling, S., Duff, I., A set of level 3 basic linear algebra subprograms, ACM Transactions on Mathematical Software 16, 1990, 1–17.CrossRefGoogle Scholar
  23. [DG91]
    Dongarra, J. J., van de Geijn, R. A., Two Dimensional Basic Linear Algebra Communication Subprogram, LAPACK Working Note #37, University of Tennessee, Technical Report CS-91–138, 1991.Google Scholar
  24. [DGW92]
    Dongarra, J., van de Geijn, R., Walker, D., A Look at Scalable Dense Linear Algebra Libraries, LAPACK Working Note #43, University of Tennessee, Technical Report CS-92–155, 1992.Google Scholar
  25. [DW95]
    Dongarra, J. J., Whaley, R. C., A User’s Guide to the BLACS v1.0,LAPACK Working Note #94, University of Tennessee, Technical Report CS-95–281, 1995.Google Scholar
  26. FOS95] Foster, Designing and Building Parallel Programs,1995, http://www.mcs.anl.gov/dbpp/
  27. HPFF97] The High Performance Fortran Forum (HPFF), 1997, http://www.crpc.rice.edu/HPFF
  28. [KLS+94]
    Koelbel, C., Loveman, D., Schreiber, R., Steele Jr., G., Zosel, M., The High Performance Fortran Handbook, The MIT Press, Cambridge, MA, London, England, 1994.Google Scholar
  29. [KW65]
    Kolos, W., Wolniewicz, L., Potential-energy curves for the X 1 Eÿ,b 3Eú, and C’H u states of the hydrogen molecule, Journal of Chemical Physics 43, 1965, 2429–2441.CrossRefGoogle Scholar
  30. [KCR95]
    Komasa, J., Cencek, W., Rychlewski, J., Explicitly correlated Gaussian functions in variational calculations: The ground state of the beryllium atom, Physical Review A 52, 1995, 4500–4507.CrossRefGoogle Scholar
  31. [KCR96]
    Komasa, J., Cencek, W., Rychlewski, J., Application of explicitly correlated Gaussian functions to large scale calculations on small atoms and molecules, Computational Methods in Science and Technology 2, Scientific Publishers OWN, Poznan, 1996, 87–100.Google Scholar
  32. [KR97]
    Komasa, J., Rychlewski, J., Explicitly correlated Gaussian functions in variational calculations: the ground state of helium dimer, Molecular Physics 91, 1997, 909–915.Google Scholar
  33. [LHK-1-79]
    Lawson, C. L., Hanson, R. J., Kincaid, D., Krogh, F. T., Basic linear algebra subprograms for fortran usage, ACM Transaction on Mathematical Software 5, 1979, 308–323.CrossRefGoogle Scholar
  34. [MFS94]
    Mechoso, C. R., Farrara, J. D., Spahr, J. A., Achieving superlinear speedup on a heterogeneous, distributed system, IEEE Parallel ê? Distributed Technology 2, 1994, 57–61.CrossRefGoogle Scholar
  35. PBLAS] An electronic PBLAS manual, 1999,http://www.netlib.org/scalapack/html/pblas_gref.html
  36. [Pow64]
    Powell, M. J. D., An efficient method for finding the minimum of a function of several variables without calculating derivatives, Computer Journal 7, 1964–1965, 155–162.Google Scholar
  37. [RCK94]
    Rychlewski, J., Cencek, W., Komasa, J., The equivalence of explicitly correlated Slater and Gaussian functions in variational quantum chemistry computations. The ground state of H2, Chemical Physics Letters 229, 1994, 657–660.CrossRefGoogle Scholar
  38. [Sin60]
    Singer, K., The use of Gaussian (exponential quadratic) wave functions in molecular problems. I. General formulae for the evaluation of integrals, Proc. of the Royal Society A258, 1960, 412–420.CrossRefGoogle Scholar
  39. [ZY95]
    Zhang, X., Yan, Y., Modelling and characterizing parallel computing performance on heterogeneous networks of workstations, Proc. of the Seventh IEEE Symposium on Parallel and Distributed Processing, 1995, 25–34.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Wojciech Cencek
    • 1
  • Jacek Komasa
    • 1
  • Jacek Rychlewski
    • 1
    • 2
  1. 1.Quantum Chemistry Group, Department of ChemistryAdam Mickiewicz UniversityPoznańPoland
  2. 2.Poznań Supercomputing and Networking CenterPoznańPoland

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