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Displacement decomposition circulant preconditioners for almost incompressible 2D elasticity systems

  • Ivan Lirkov
  • Svetozar Margenov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1196)

Abstract

The robustness of the recently introduced circulant blockfactorization (CBF) preconditioners is studied in the case of finite element matrices arising from the discretization of the 2D Navier equations of elasticity. Conforming triangle finite elements are used for the numerical solution of the differential problem. The proposed preconditioner M C is constructed by CBF approximation of the block-diagonal part of the stiffness matrix. In other words, we implement in our algorithm the circulant block-factorization into the framework of the displacement decomposition technique. The estimate κ(M C −1 K)=O(√N/1−v) is proved asymptotically on N, where N is the size of the discrete problem. Note, that the corresponding known estimate for the widely used incomplete factorization displacement decomposition preconditioner M ILU is κ(M ILU −1 K)=O(√N/1−v)

The theoretical estimate as well as the presented numerical tests show some significant advantages of this new approach for a PCG iterative solution of almost incompressible elastic problems, that is when the modified Poisson ratio v tends to the incompressible limit case v=1.

Key words

almost incompressible elasticity finite elements circulant preconditioning displacement decomposition 

AMS subject classifications

65F10 65F20 65N30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ivan Lirkov
    • 1
  • Svetozar Margenov
    • 1
  1. 1.Central Laboratory of Parallel ProcessingBulgarian Academy of SciencesSofiaBulgaria

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