Editorial Type:
Article
Article Type:
Research Article

A Spectral Element Solution of the Shallow-Water Equations on Multiprocessor Computers

Enrique N. Curchitser Institute of Marine and Coastal Sciences, Rutgers University, New Brunswick, New Jersey

Search for other papers by Enrique N. Curchitser in
Current site
Google Scholar
PubMed Close
,
Mohamed Iskandarani Institute of Marine and Coastal Sciences, Rutgers University, New Brunswick, New Jersey

Search for other papers by Mohamed Iskandarani in
Current site
Google Scholar
PubMed Close
, and
Dale B. Haidvogel Institute of Marine and Coastal Sciences, Rutgers University, New Brunswick, New Jersey

Search for other papers by Dale B. Haidvogel in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Apr 1998
DOI:
https://doi.org/10.1175/1520-0426(1998)015<0510:ASESOT>2.0.CO;2
Page(s):
510–521
Restricted access

Abstract

A shallow-water spectral element ocean model is implemented on multiple instruction multiple data, distributed memory parallel computers. A communications-minimizing partitioning algorithm for unstructured meshes, based on graph theory, is presented and is shown to improve the efficiency in a limited range of granularities. A domain decomposition implementation with an architecture-independent communications scheme, using message passing, is devised and tested on an nCUBE/2, a Cray T3D, and an IBM SP2. The implementation exhibits high efficiencies over a wide range of granularities. An order of magnitude analysis shows that, to leading order, the efficiency stays constant when KN2 grows proportionally to P, where K is the total number of elements, N is the order of the spectral truncation within an element, and P is the number of processors.

Corresponding author address: Enrique N. Curchitser, Institute of Marine and Coastal Sciences, Rutgers University, P.O. Box 231-IMCS, New Brunswick, NJ 08903.

Abstract

A shallow-water spectral element ocean model is implemented on multiple instruction multiple data, distributed memory parallel computers. A communications-minimizing partitioning algorithm for unstructured meshes, based on graph theory, is presented and is shown to improve the efficiency in a limited range of granularities. A domain decomposition implementation with an architecture-independent communications scheme, using message passing, is devised and tested on an nCUBE/2, a Cray T3D, and an IBM SP2. The implementation exhibits high efficiencies over a wide range of granularities. An order of magnitude analysis shows that, to leading order, the efficiency stays constant when KN2 grows proportionally to P, where K is the total number of elements, N is the order of the spectral truncation within an element, and P is the number of processors.

Corresponding author address: Enrique N. Curchitser, Institute of Marine and Coastal Sciences, Rutgers University, P.O. Box 231-IMCS, New Brunswick, NJ 08903.

Save
Cover Journal of Atmospheric and Oceanic Technology
Journal of Atmospheric and Oceanic Technology

  • Abramowitz, M., and I. Stegun, 1964: Handbook of Mathematical Functions. Vol. 55, Applied Mathematics Series, 1st ed., National Bureau of Standards, 1046 pp.

  • Bernardi, C., and O. Pironneau, 1991: On the shallow water equations at low Reynolds number. Comm. Partial Differential Equations,16 (1), 59–104.

    • Crossref
    • Export Citation

  • Boyd, J., 1989: Chebyshev and Fourier Spectral Methods. Lecture Notes in Engineering. Springer-Verlag, 798 pp.

    • Crossref
    • Export Citation

  • Danabasoglu, G., J. McWilliams, and P. Gent, 1994: The role of mesoscale tracer transports in the global ocean circulation. Science,264, 1123–1126.

    • Crossref
    • Export Citation

  • Farhat, C., and M. Lesoinne, 1993: Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics Int. J. Numer. Meth. Eng.,36, 745–764.

    • Crossref
    • Export Citation

  • Fischer, P., 1989: Spectral element solution of the Navier–Stokes equations on high performance distributed-memory parallel processors, Ph.D. dissertation, Massachusetts Institute of Technology, 135 pp.

  • ——, and A. Patera, 1994: Parallel simulations of viscous incompressible flows. Annu. Rev. Fluid Mech.,26, 483–527.

    • Crossref
    • Export Citation

  • Gear, C., 1971: Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, 253 pp.

  • Gent, P., 1993: The energetically consistent shallow-water equations. J. Atmos. Sci.,50, 1323–1325.

    • Crossref
    • Export Citation

  • Haidvogel, D., E. Curchitser, M. Isksandarani, R. Hughes, and M. Taylor, 1997: Global modeling of the ocean and atmosphere using the spectral element method Numerical Methods in Atmospheric and Oceanic Modelling. The André J. Robert Memorial Volume, C. Lin, R. Laprise, and H. Ritchie, Eds., Canadian Meteorological Society, 505–531.

    • Crossref
    • Export Citation

  • Holland, W., 1978: The role of mesoscale eddies in the general circulation of the ocean—Numerical experiments using a wind-driven quasigeostrophic model. J. Phys. Oceanogr.,8, 363–392.

  • Iskandarani, M., D. Haidvogel, and J. Boyd, 1995: A staggered spectral finite element model for the shallow water equations. Int. J. Numer. Meth. Fluids,20, 393–414.

    • Crossref
    • Export Citation

  • Kruse, R., 1987: Data Structures and Program Design. 2d ed. Prentice Hall, 586 pp.

  • Ma, H., 1993: A spectral element basin model for the shallow water equations. J. Comput. Phys.,109, 133–149.

    • Crossref
    • Export Citation

  • Maday, Y., and A. Patera, 1988: Spectral element methods for the incompressible Navier-Stokes equations. State of the Arts Surveys in Computational Mechanics, A. K. Noor and J. T. Oden, Eds., ASME, 255–306.

  • Semtner, A., 1995: Modeling ocean circulation. Science,269, 1371–1379.

    • Crossref
    • Export Citation

  • Simon, H., 1991: Partitioning of unstructured problems for parallel processing. Comput. Syst. Eng.,2, 135–148.

    • Crossref
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 373 82 9
PDF Downloads 80 40 0