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    Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system

    Access Status
    Fulltext not available
    Authors
    Côrtes, A.
    Coutinho, A.
    Dalcin, L.
    Calo, Victor
    Date
    2014
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Côrtes, A. and Coutinho, A. and Dalcin, L. and Calo, V. 2014. Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system. Journal of Computational Science. 11: pp. 123-136.
    Source Title
    Journal of Computational Science
    DOI
    10.1016/j.jocs.2015.01.005
    ISSN
    1877-7503
    School
    Department of Applied Geology
    URI
    http://hdl.handle.net/20.500.11937/51453
    Collection
    • Curtin Research Publications
    Abstract

    The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.

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