“Brute-Force” Solution of Large-Scale Systems of Equations in a MPI-PBLAS-ScaLAPACK Environment

  • M. Roth
  • O. Baur
  • W. Keller
Conference paper


Space-borne gravity field recovery requires the solution of large-scale linear systems of equations to estimate tens of thousands of unknown gravity field parameters from tens of millions of observations. Satellite gravity data can only be exploited efficiently by the adaption of HPC technologies. The extension of the GOCE (Gravity field and steady-state Ocean Circulation Explorer) mission, in particular, poses unprecedented computational challenges in geodesy. In continuation of our work presented in the annual report in 2010, we succeeded in the preparation of a distributed memory version of our program using the MPI, PBLAS and ScaLAPACK programming standards. The tailored implementation enhances the range of usable computer architectures to computers with less memory per node than the NEC SX-8 and SX-9 systems we used. We present implementation details and runtime results using the NEC SX systems as distributed memory systems. A comparison with our OpenMP version shows that the MPI implementation of our program brings forth a speedup of around 12% for large-scale problems.


High Performance Computing Computing Node Memory Version Normal Equation System Distribute Memory System 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baur O. (2009) Tailored least-squares solvers implementation for high-performance gravity field research, Computers and Geosciences 35: 548–556, DOI  10.1016/j.cageo.2008.09.004 CrossRefGoogle Scholar
  2. 2.
    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. (1997) ScaLAPACK Users’ Guide, (retrieval on 7th April 2011)
  3. 3.
    ESA (2011) GOCE website: (retrieval on 7th April 2011)
  4. 4.
    Heiskanen W. A., Moritz H. (1967) Physical Geodesy, W.H. Freeman and Company San Francisco Google Scholar
  5. 5.
    Hobson E. W. (1931) The Theory of Spherical and Ellipsoidal Harmonics, University Press, Cambridge Google Scholar
  6. 6.
    Koch K.-R. (1999) Parameter Estimation and Hypothesis Testing in Linear Models, Springer Berlin Heidelberg New York zbMATHGoogle Scholar
  7. 7.
    Roth M. (2010a) GOCE Data analysis: Optimized brute force solutions of large-scale linear equation systems on parallel computers, Diploma Thesis, University of Stuttgart, URN urn:nbn:de:bsz:93-opus-58910 Google Scholar
  8. 8.
    Roth M., Baur O., Keller W. (2010) Tailored Usage of the NEC SX-8 and SX-9 Systems in Satellite Geodesy, in: Nagel W. E. et al. (eds.) High Performance Computing in Science and Engineering ’10: 561–572, Springer Verlag Berlin Heidelberg 2011, DOI  10.1007/978-3-642-15748-6_41 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of GeodesyUniversity of StuttgartStuttgartGermany

Personalised recommendations