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

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    Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-Spline discretization of the Stokes system.pdf
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    Type
    Article
    Authors
    Cortes, Adriano Mauricio cc
    Coutinho, A.L.G.A.
    Dalcin, Lisandro
    Calo, Victor M. cc
    KAUST Department
    Earth Science and Engineering Program
    Numerical Porous Media SRI Center (NumPor)
    Physical Science and Engineering (PSE) Division
    Date
    2015-02-20
    Online Publication Date
    2015-02-20
    Print Publication Date
    2015-11
    Permanent link to this record
    http://hdl.handle.net/10754/558296
    
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    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.
    Citation
    Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system 2015 Journal of Computational Science
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Science
    DOI
    10.1016/j.jocs.2015.01.005
    Additional Links
    http://linkinghub.elsevier.com/retrieve/pii/S1877750315000095
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jocs.2015.01.005
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program

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