Solving large-scale nonnormal eigenproblems in the aeronautical industry using parallel BLAS

  • M. Bennani
  • T. Braconnier
  • J. C. Dunyach
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 796)


We consider a large-scale nonnormal eigenvalue problem that occurs in flutter analysis. Matrices arising in such problems are usually sparse, of large order, and highly nonnormal. We use the incomplete Arnoldi method associated with the Tchebycheff acceleration in order to compute a subset of the eigenvalues and their associated eigenvectors. This method has been parallelized using BLAS kernels and has been tested on various vector and parallel machines.

This work has been conducted at CERFACS in cooperation with the Aerospatiale Avions (Structural research and development department).


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  1. 1.
    W.E. Arnoldi. The principle of minimized iterations in the solution of the matrix eigenvalue problem. Quart. Appl. Math., 9(1):17–29, 1951.Google Scholar
  2. 2.
    Z. Bai. A collection of test matrices for the large scale nonsymmetric eigenvalue problem. Technical report, University of Kentucky, 1993.Google Scholar
  3. 3.
    M. Bennani. A propos de la stabilité de la résolution d'équations sur ordinateurs. Ph. D. dissertation, Institut National Polytechnique de Toulouse, December 1991.Google Scholar
  4. 4.
    M. Bennani and T. Braconnier. Stopping criteria for eigensolvers, November 1993. Submitted to Jour. Num. Lin. Alg. Appl.Google Scholar
  5. 5.
    C. Bes and J. Locatelli. Structural optimisation at aerospatiale aircraft. In A.I.A.A. Structural Dynamics and Materials Conference, pages 2619–2624, April 1992.Google Scholar
  6. 6.
    T. Braconnier. The Arnoldi-Tchebycheff algorithm for solving large nonsymmetric eigenproblems. Tech. Rep. TR/PA/93/25, CERFACS, 1993.Google Scholar
  7. 7.
    T. Braconnier, F. Chatelin and J.C. Dunyach. Highly Nonnormal Eigenproblems in the Aeronautical Industry, January 1994. Submitted to Japan Jour. of Indus. Appl. Math.Google Scholar
  8. 8.
    F. Chatelin. Eigenvalues of matrices. Wiley, Chichester, 1993. Enlarged Translation.Google Scholar
  9. 9.
    M. J. Daydé and I. S. Duff. Use of level 3 BLAS in LU factorization in a multiprocessing environment on three vector multiprocessors, the ALLIANT FX/80, the CRAY-2, and the IBM 3090/VF. Int. J. of Supercomputer Applics., 5:92–110, 1991.Google Scholar
  10. 10.
    I.S. Duff, R.G. Grimes, and J.G. Lewis. User's Guide for the Harwell-Boeing Sparse Matrix Collection. Technical Report TR-PA-92-86, CERFACS, August 1992.Google Scholar
  11. 11.
    C.R. Freberg and E.N. Kemler. Aircraft Vibration and Flutter. Wiley, New-York, 1944.Google Scholar
  12. 12.
    W. W. Hager. Condition estimates. SIAM J. Sci. Stat. Comput., 5:311–316, 1984.Google Scholar
  13. 13.
    D. Ho, F. Chatelin, and M. Bennani. Arnoldi-Chebychev method for large scale nonsymmetric matrices. RAIRO Math. Modell. Num. Anal., 24:53–65, 1990.Google Scholar
  14. 14.
    Y. Saad. Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems. Math. Comp., 42(166):567–588, 1984.Google Scholar
  15. 15.
    Y. Saad. Numerical Methods for Large Eigenvalue Problems. Algorithms and Architectures for Advanced Scientific Computing. Manchester University Press, Manchester, U.K., 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • M. Bennani
    • 1
  • T. Braconnier
    • 2
  • J. C. Dunyach
    • 3
  1. 1.ENSIASAgdal RabatMaroc
  2. 2.CERFACS-ERINToulouse cedex
  3. 3.Aerospatiale Avions, A/DET/APToulouse Cedex

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