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    A FETI-DP TYPE DOMAIN DECOMPOSITION ALGORITHM FOR THREE-DIMENSIONAL INCOMPRESSIBLE STOKES EQUATIONS

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    Tu_2015_SIAM.pdf (279.9Kb)
    Issue Date
    2015-03-03
    Author
    Tu, Xuemin
    Li, Jing
    Publisher
    Society for Industrial and Applied Mathematics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Rights
    Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
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    Abstract
    The FETI-DP (dual-primal finite element tearing and interconnecting) algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp. 1235–1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp. 128–149] for solving incompressible Stokes equations, are extended to three-dimensional problems. A new analysis of the condition number bound for using the Dirichlet preconditioner is given. The algorithm and analysis are valid for mixed finite elements with both continuous and discontinuous pressures. An advantage of this new analysis is that the numerous coarse level velocity components, required in the previous analysis to enforce the divergence-free subdomain boundary velocity conditions, are no longer needed. This greatly reduces the size of the coarse level problem in the algorithm, especially for three-dimensional problems. The coarse level velocity space can be chosen as simple as those coarse spaces for solving scalar elliptic problems corresponding to each velocity component. Both the Dirichlet and lumped preconditioners are analyzed using the same framework in this new analysis. Their condition number bounds are proved to be independent of the number of subdomains for fixed subdomain problem size. Numerical experiments in both two and three dimensions, using mixed finite elements with both continuous and discontinuous pressures, demonstrate the convergence rate of the algorithms.
    URI
    http://hdl.handle.net/1808/22269
    DOI
    https://doi.org/10.1137/13094997X
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    • Mathematics Scholarly Works [253]
    Citation
    Tu, X., & Li, J. (2015). A FETI-DP Type Domain Decomposition Algorithm for Three-Dimensional Incompressible Stokes Equations. SIAM Journal on Numerical Analysis, 53(2), 720-742. doi:10.1137/13094997x

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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