Advertisement

A Parallel Implementation of FEM for a Boundary Value Problem for the Shallow Water Equations

  • Evgeniya D. Karepova
  • Vladimir V. Shaidurov
Conference paper
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 115)

Abstract

In the present paper efficiency of several parallel implementations of an algorithm for the numerical solution of a boundary value problem for the shallow water equations with the use of the MPI library for the C language is studied. Theoretical estimates of acceleration for parallel algorithms are given. Numerical results on a special model grid and on a non-structured grid for the Sea of Okhotsk are presented. The calculations ware performed with the MVS1000 cluster of ICM SB RAS and the SKIF Cyberia cluster of the Tomsk state university.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agoshkov, V.I.: Inverse problems of the mathematical theory of tides: boundary-function problem. Russ. J. Numer. Anal. Math. Modelling 20(1), 1–18 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Balay, S.: Efficient management of parallelism in object-oriented numerical software libraries. In: Balay, S., Gropp, W.D., McInnes, L.C., et al. (eds.) Modern Software Tools in Scientific Computing, pp. 163–202. Birkhauser Press (1997)Google Scholar
  3. 3.
    Isaev, S.V., Malyshev, A.V., Shaidurov, V.V.: Development of the Krasnoyarsk center of parallel computations. Computat. Technologies, Special Issue 11, 28–33 (2006) (in Russian)Google Scholar
  4. 4.
    Kamenshchikov, L.P., Karepova, E.D., Shaidurov, V.V.: Simulation of surface waves in basins by the finite element method. Russian J. Numer. Anal. Math. Modelling 21(4), 305–320 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kamenshchikov, L.P., Karepova, E.D., Shaidurov, V.V.: Numerical solution of the boundary value problem for shallow water equations for modelling surface waves in world ocean by finite elements methods. In: Proceedings of Fourth International Conference FDM:T&A 2006, Finite Difference Methods: Theory and Applications, Rousse, Bulgaria, pp. 227–233 (2007)Google Scholar
  6. 6.
    Kamenshchikov, L.P., Karepova, E.D., Pyataev, S.F., Shaidurov, V.V.: The modeling of gravitation vawes in the World Ocean with the finite element method with parallelizing. In: Proceeding of the Sixth school ’Distributed and cluster calculations’, pp. 52–64. ICM SB RAS, Krasnoyarsk (2006) (in Russian)Google Scholar
  7. 7.
    Marchuk, G.I.: Dynamics of Ocean Tides. Gidrometizdat, Leningrad (1983) (in Russian)Google Scholar
  8. 8.
    McBryan, O.A.: An overwiev of message passing environments. Parallel Computing 20, 417–441 (1994)zbMATHCrossRefGoogle Scholar
  9. 9.
    National Geophysical Data Center, http://www.ngdc.noaa.gov/ngdc.html
  10. 10.
    Ortega, J.M.: Introduction to parallel and vector solution of linear systems. Springer, New York (1988)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Evgeniya D. Karepova
    • 1
  • Vladimir V. Shaidurov
    • 1
  1. 1.Institute of Computational Modeling SB RASAkademgorodokRussia

Personalised recommendations