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A model for parallel one dimensional eigenvalues and eigenfunctions calculations

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Recent Advances in Parallel Virtual Machine and Message Passing Interface (EuroPVM/MPI 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1497))

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Abstract

The calculation of eigenvalues and eigenfunctions of one-dimensional cuts of reactive potentials is often a key step of scattering calculations of higher dimensions. Parallelized versions of related computer codes do not consider a parallelization at the level of individual eigenvalue calculations. In this paper we present an attempt to push the parallelism to this level and compare the sequential and parallel performances of the restructured code.

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References

  1. J.C. Light, In The Theory of Chemical Reaction Dynamics ed. by D.C. Clary, Reidel, Dordrecht (1986) p. 215.

    Google Scholar 

  2. Y.M. Wu, S.A. Cuccaro, P.G. Hipes, and A. Kuppermann, Theor. Chim. Acta 79, 225 (1991).

    Article  Google Scholar 

  3. J. Manz, Mol. Phys. 28, 399 (1974).

    Article  Google Scholar 

  4. J. Manz, Mol. Phys. 30, 899 (1975).

    Article  Google Scholar 

  5. J.N.L. Connor, W. Jakubetz, and J. Manz, Mol. Phys. 29, 347 (1975).

    Article  Google Scholar 

  6. R.B. Walker, and E. Hayes, In The Theory of Chemical Reaction Dynamics ed. by D.C. Clary, Reidel, Dordrecht (1986) p. 105.

    Google Scholar 

  7. E.F. Hayes, Z. Darakjian, and R.B. Walker, Theor. Chim. Acta 79, 199 (1991).

    Article  Google Scholar 

  8. D.C. Clary, and J.P. Henshaw, In The Theory of Chemical Reaction Dynamics ed. by D.C. Clary, Reidel, Dordrecht (1986) p. 331.

    Google Scholar 

  9. L. Fox, Numerical Solutions of two-points Boundary problems in Ordinary Differential Equations, Oxford, London (1957).

    Google Scholar 

  10. D.F. Mayers, Numerical Solutions of Ordinary and Partial Differential Equations, Pergamon, New York (1962), Chap. 7.

    Google Scholar 

  11. H. Heller, Numerical Methods for two-points Boundary value problems: Shooting Methods, Oxford, London (1957).

    Google Scholar 

  12. J. Choi, J. Dongarra, S. Ostrouchov, A. Petitet, D. Walker and R.C. Whaley, Lecture Notes in Comp. Science 1041, 107 (1996).

    Google Scholar 

  13. J.C. Light, I.P. Hamilton, and J.V. Lill, J. Chem. Phys. 82, 1400 (1985).

    Article  Google Scholar 

  14. J.M. Cooley, Math. Comp. 15, 363 (1961).

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Laganà, E. Garcia, and O. Gervasi, J. Chem. Phys. 89, 7238 (1988).

    Article  Google Scholar 

  16. A. Laganà, E. Garcia, O. Gervasi, R. Baraglia, D. Laforenza, and R. Perego, Theor. Chim. Acta 79, 323 (1991).

    Article  Google Scholar 

  17. R. Baraglia, D. Laforenza, and A. Laganà, Lecture Notes in Comp. Science 919, 554 (1995).

    Article  Google Scholar 

  18. R. Baraglia, R. Ferrini, D. Laforenza, A. Laganà, MPCS96, 200 (1996); A. Bolloni, A. Riganelli, S. Crocchianti, and A. Laganà, Parallel quantum scattering calculations applied to Dynamics of elementary Reactions, Lecture notes in Computer Science (present issue).

    Google Scholar 

  19. L.D. Landau and E.M. Lifshitz, Quantum Mechanics, Pergamon, New York (1977), Chap. 3.

    Google Scholar 

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Vassil Alexandrov Jack Dongarra

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© 1998 Springer-Verlag Berlin Heidelberg

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Laganà, A., Grossi, G., Riganelli, A., Ferraro, G. (1998). A model for parallel one dimensional eigenvalues and eigenfunctions calculations. In: Alexandrov, V., Dongarra, J. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 1998. Lecture Notes in Computer Science, vol 1497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0056596

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  • DOI: https://doi.org/10.1007/BFb0056596

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65041-6

  • Online ISBN: 978-3-540-49705-9

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