Cluster Design in the Earth Sciences Tethys

  • Jens Oeser
  • Hans-Peter Bunge
  • Marcus Mohr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4208)


Computational modeling is a powerful tool in the Earth Sciences. In the solid Earth important simulation areas include seismic wave propagation, rupture and fault dynamics in the lithosphere, creep in the mantle, and magneto-hydrodynamic flow linked to magnetic field generation in the core. These problems rank among the most demanding calculations computational physicists can perform today. They exceed the limitations of the largest high-performance computing systems by a factor of ten to one hundred measured both in terms of the demands on capacity and capability of systems. Off-the-shelf high-performance Linux clusters are useful to ease the limitations in capacity computing by exploiting price advantages in mass produced PC hardware. Here we review our experience of building a 128 processor AMD Opteron Gigabit Ethernet Linux cluster. The machine is operated at the scientific department level, targeted directly at large-scale geophysical and tectonic modeling and is funded by the German Ministry of Education and Science and the Free State of Bavaria. We observe an aggregate system performance of 140 GFLOPs out of a theoretical 624 GFLOPs peak.


Mantle Convection Message Size Spectral Element Method Seismic Wave Propagation Cluster Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bunge, H.-P., Richards, M.A., Lithgow-Bertelloni, C., Baumgardner, J.R., Grand, S., Romanowicz, B.: Time scales and heterogeneous structure in geodynamic earth models. Science 280, 91–95 (1998)CrossRefGoogle Scholar
  2. 2.
    Jarvis, G.T., McKenzie, D.P.: Convection in a compressible fluid with infinite prandtl number. Journal of Fluid Mechanics 96, 515–583 (1980)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Glatzmaier, G.A.: Numerical simulations of mantle convection: Time-dependent, three-dimensional, compressible, spherical shell. Geophysical and Astrophysical Fluid Dynamics 43, 223–264 (1988)MATHCrossRefGoogle Scholar
  4. 4.
    Tackley, P.J., Stevenson, D.J., Glatzmaier, G.A., Schubert, G.: Effects of an endothermic phase transition at 670 km depth on a spherical model of convection in Earth’s mantle. Nature 361, 699–704 (1993)CrossRefGoogle Scholar
  5. 5.
    Bunge, H.-P., Richards, M.A., Baumgardner, J.R.: Effect of depth dependent viscosity on the planform of mantle convection. Nature 379, 436–438 (1996)CrossRefGoogle Scholar
  6. 6.
    Zhong, S., Zuber, M.T., Moresi, L., Gurnis, M.: Role of temperature-dependent viscosity and surface plates in spherical shell models of mantle convection. Journal of Geophysical Research 105, 11063–11082 (2000)CrossRefGoogle Scholar
  7. 7.
    Glatzmaier, G.A., Roberts, P.H.: A three-dimensional, self-consistent computer simulation of a geomagnetic field reversal. Nature 377, 203–209 (1995)CrossRefGoogle Scholar
  8. 8.
    Kuang, W.L., Bloxham, J.: An earth-like numerical dynamo model. Nature 389, 371–374 (1997)CrossRefGoogle Scholar
  9. 9.
    Igel, H., Weber, M.: SH-wave propagation in the whole mantle using high-order finite differences. Geophysical Research Letters 22, 731–734 (1995)CrossRefGoogle Scholar
  10. 10.
    Komatitsch, D., Tromp, J.: Introduction to the spectral element method for three-dimensional seismic wave propagation. Geophysical Journal International 139, 806–822 (1999)CrossRefGoogle Scholar
  11. 11.
    Bunge, H.-P., Richards, M.A., Baumgardner, J.R.: Mantle circulation models with sequential data-assimilation: Inferring present-day mantle structure from plate motion histories. Philosophical Transactions of the Royal Society of London: Series A 360, 2545–2567 (2002)CrossRefGoogle Scholar
  12. 12.
    McNamara, A.K., Zhong, S.: Thermochemical structures beneath Africa and the Pacific Ocean. Nature 437, 1136 (2005)CrossRefGoogle Scholar
  13. 13.
    Courtier, P., Talagrand, O.: Variational assimilation of meterological observations with the adjoint vorticity equation I: Numerical results. Quarterly Journal of the Royal Meteorological Society 113, 1329–1347 (1987)CrossRefGoogle Scholar
  14. 14.
    Wunsch, C.: The Ocean Circulation Inverse Problem. Cambridge University Press, Cambridge (1996)CrossRefGoogle Scholar
  15. 15.
    Bunge, H.-P., Hagelberg, C.R., Travis, B.J.: Mantle circulation models with variational data-assimilation: Inferring past mantle flow and structure from plate motion histories and seismic tomography. Geophysical Journal International 152, 280–301 (2003)CrossRefGoogle Scholar
  16. 16.
    Landau, L., Lifschitz, E.: Fluid mechanics. Pergamon Press, Oxford (1987)MATHGoogle Scholar
  17. 17.
    Baumgardner, J.R.: Three-Dimensional Treatment of Convective Flow in the Earth’s Mantle. Journal of Statistical Physics 39, 501–511 (1985)CrossRefGoogle Scholar
  18. 18.
    Williamson, D.: Integration of the barotropic vorticity equations on a spherical geodesic grid. Tellus 20, 642–653 (1968)CrossRefGoogle Scholar
  19. 19.
    Baumgardner, J.R., Frederickson, P.O.: Icosahedral discretization of the two-sphere. SIAM Journal on Numerical Analysis 22, 1107–1115 (1985)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Benzi, M., Golub, G., Liesen, J.: Numerical solution of saddle point problems. Acta Numerica 14, 1–137 (2005)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Verfürth, R.: A Combined Conjugate Gradient-Multigrid Algorithm for the Numerical Solution of the Stokes Problem. IMA Journal of Numerical Analysis 4, 441–455 (1984)MATHMathSciNetGoogle Scholar
  22. 22.
    Yang, W.-S., Baumgardner, J.R.: A matrix-dependent transfer multigrid method for strongly variable viscosity infinite Prandtl number thermal convection. Geophysical and Astrophysical Fluid Dynamics 92, 151–195 (2000)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Trottenberg, U., Oosterlee, C., Schüller, A.: Multigrid. Academic Press, London (2001)MATHGoogle Scholar
  24. 24.
    Hülsemann, F., Kowarschik, M., Mohr, M., Rüde, U.: Parallel Geometric Multigrid. In: Bruaset, A.M., Tveito, A. (eds.) Numerical Solution of Partial Differential Equations on Parallel Computers. Lecture Notes in Computational Science and Engineering, vol. 51. Springer, Heidelberg (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jens Oeser
    • 1
  • Hans-Peter Bunge
    • 1
  • Marcus Mohr
    • 1
  1. 1.Department of Earth and Environmental Sciences, Geophysics SectionLudwigs-Maximilians-UniversityMunichGermany

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