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    Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem

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    Type
    Article
    Authors
    Chen, Meng-Huo cc
    Greenbaum, Anne
    KAUST Department
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2015-03-18
    Online Publication Date
    2015-03-18
    Print Publication Date
    2015-08
    Permanent link to this record
    http://hdl.handle.net/10754/594215
    
    Metadata
    Show full item record
    Abstract
    Summary: A two-grid convergence analysis based on the paper [Algebraic analysis of aggregation-based multigrid, by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), pp. 539-564] is derived for various aggregation schemes applied to a finite element discretization of a rotated anisotropic diffusion equation. As expected, it is shown that the best aggregation scheme is one in which aggregates are aligned with the anisotropy. In practice, however, this is not what automatic aggregation procedures do. We suggest approaches for determining appropriate aggregates based on eigenvectors associated with small eigenvalues of a block splitting matrix or based on minimizing a quantity related to the spectral radius of the iteration matrix. © 2015 John Wiley & Sons, Ltd.
    Citation
    Chen M-H, Greenbaum A (2015) Analysis of an aggregation-based algebraic two-grid method for a rotated anisotropic diffusion problem. Numerical Linear Algebra with Applications 22: 681–701. Available: http://dx.doi.org/10.1002/nla.1980.
    Sponsors
    National Science Foundation
    Publisher
    Wiley
    Journal
    Numerical Linear Algebra with Applications
    DOI
    10.1002/nla.1980
    ae974a485f413a2113503eed53cd6c53
    10.1002/nla.1980
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program

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