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    RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

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    Type
    Article
    Authors
    Farrell, Patricio
    Wendland, Holger
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2013-01
    Permanent link to this record
    http://hdl.handle.net/10754/599450
    
    Metadata
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    Abstract
    In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.
    Citation
    Farrell P, Wendland H (2013) RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems. SIAM J Numer Anal 51: 2403–2425. Available: http://dx.doi.org/10.1137/120898383.
    Sponsors
    This work was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Numerical Analysis
    DOI
    10.1137/120898383
    ae974a485f413a2113503eed53cd6c53
    10.1137/120898383
    Scopus Count
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    Publications Acknowledging KAUST Support

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