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On a Multigrid Eigensolver for Linear Elasticity Problems

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Numerical Methods and Applications (NMA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2542))

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Abstract

In the early eighties the direct application of a multigrid technique for solving the partial eigenvalue problem of computing few of the smallest eigenvalues and their corresponding eigenvectors of a differential operator was proposed by Brandt, McCormick and Ruge [1]. In the present paper an experimental study of the method for model linear elasticity problems is carried out. Based on these results we give some practical advices for a good choice of multigrid-related parameters.

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References

  1. Brandt, A., McCormick, S. and Ruge, J.: Multigrid Methods for Differential Eigenproblems. SIAM J. Sci. Stat. Comput., 4(2) (1983) 244–260.

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  2. Hackbusch, W.: Multigrid Methods and Applications. Springer-Verlag, Berlin-Heidelberg-New York (1985)

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  3. Knyazev, A. V.: Preconditioned Eigensolvers-an Oxymoron? Electronic Transaction on Numerical Analysis, Vol. 7 (1998) 104–123.

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  4. Lur'e, A. I.: Theory of Elasticity. Moscow, Nauka (1970)

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  5. Parlett, B.: The Symmetric Eigenvalue Problem. Prentice-Hall, Inc. (1980)

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  6. Trottenberg, U., Oosterlee, C. and Schüller, A.: Multigrid. Academic Press (2001)

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Authors and Affiliations

  1. Rheinisch-Wesfälische Technische Hochschule Aachen, Institut für Geometrie und Praktische Mathematik, Templergraben 55, D-52056, Aachen, Germany

    Maxim Larin

Authors
  1. Maxim Larin
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Editor information

Editors and Affiliations

  1. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, bl. 25A, 1113, Sofia, Bulgaria

    Ivan Dimov , Ivan Lirkov  & Svetozar Margenov ,  & 

  2. National Environmental Research Institute, Frederiksborgvej 399, P.O. Box 358, 4000, Roskilde, Denmark

    Zahari Zlatev

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© 2003 Springer-Verlag Berlin Heidelberg

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Larin, M. (2003). On a Multigrid Eigensolver for Linear Elasticity Problems. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_20

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  • DOI: https://doi.org/10.1007/3-540-36487-0_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00608-4

  • Online ISBN: 978-3-540-36487-0

  • eBook Packages: Springer Book Archive

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