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    Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs

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    Type
    Article
    Authors
    Farrell, Patricio
    Pestana, Jennifer
    KAUST Grant Number
    KUK- C1-013-04
    Date
    2015-04-30
    Online Publication Date
    2015-04-30
    Print Publication Date
    2015-08
    Permanent link to this record
    http://hdl.handle.net/10754/597686
    
    Metadata
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    Abstract
    © 2015John Wiley & Sons, Ltd. Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right-hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners.
    Citation
    Farrell P, Pestana J (2015) Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs. Numerical Linear Algebra with Applications 22: 731–747. Available: http://dx.doi.org/10.1002/nla.1984.
    Sponsors
    We thank the referees for their helpful comments that improved the paper. This work was supported in part by award KUK- C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Wiley
    Journal
    Numerical Linear Algebra with Applications
    DOI
    10.1002/nla.1984
    ae974a485f413a2113503eed53cd6c53
    10.1002/nla.1984
    Scopus Count
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