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AMLI Preconditioning of Pure Displacement Non-conforming Elasticity FEM Systems

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Numerical Analysis and Its Applications (NAA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1988))

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Abstract

This paper is concerned with the pure displacement problem of planar linear elasticity. Our interest is focussed to a locking-free FEM approximation of the problem in the case when the material is almost incompressible. The approximation space is constructed using the Crouzeix-Raviart linear finite elements. Choosing a proper hierarchical basis of this space we define an optimal order algebraic multilevel (AMLI) preconditioner for the related stiffness matrix. Local spectral analysis is applied to find the scaling parameter of the preconditioner as well as to estimate the related constants in the strengthened C.B.S. inequality. A set of numerical tests which illustrate the accuracy of the FEM solution, and the convergence rate of the AMLI PCG method is presented.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

    Tzanio Kolev

  2. Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bontchev Str., Bl. 25A, 1113, Sofia, Bulgaria

    Svetozar Margenov

Authors
  1. Tzanio Kolev
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  2. Svetozar Margenov
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rousse, 7000, Rousse, Bulgaria

    Lubin Vulkov  & Plamen Yalamov  & 

  2. UNI-C,Danish Computing Center for Research and Education, DTU,Building 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2001 Springer-Verlag Berlin Heidelberg

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Kolev, T., Margenov, S. (2001). AMLI Preconditioning of Pure Displacement Non-conforming Elasticity FEM Systems. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_56

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  • DOI: https://doi.org/10.1007/3-540-45262-1_56

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41814-6

  • Online ISBN: 978-3-540-45262-1

  • eBook Packages: Springer Book Archive

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