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    Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors

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    Type
    Article
    Authors
    Barton, Michael cc
    Ait-Haddou, Rachid
    Calo, Victor Manuel
    Date
    2017-03-21
    Online Publication Date
    2017-03-21
    Print Publication Date
    2017-10
    Permanent link to this record
    http://hdl.handle.net/10754/623547
    
    Metadata
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    Abstract
    We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.
    Citation
    Bartoň M, Ait-Haddou R, Calo VM (2017) Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors. Journal of Computational and Applied Mathematics 322: 57–70. Available: http://dx.doi.org/10.1016/j.cam.2017.02.022.
    Sponsors
    The first and the third author have been supported by the Center for Numerical Porous Media at King Abdullah University of Science and Technology (KAUST) and the European Union’s Horizon 2020 Research and Innovation Program of the Marie Skodowska-Curie grant agreement No. 644202. The first author has been partially supported by the Basque Government through the BERC 2014-2017 program, by Spanish Ministry of Economy and Competitiveness under Grant MTM2016-76329-R. The third author as been partially supported by National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation).
    Publisher
    Elsevier BV
    Journal
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2017.02.022
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cam.2017.02.022
    Scopus Count
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