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

Michael Barton; Rachid Ait-Haddou; Victor Manuel Calo

doi:10.1016/j.cam.2017.02.022

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

Michael Barton, Rachid Ait-Haddou, Victor Manuel Calo

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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.

Original language	English (US)
Pages (from-to)	57-70
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	322
DOIs	https://doi.org/10.1016/j.cam.2017.02.022
State	Published - Mar 21 2017
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.cam.2017.02.022

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@article{fde5e51748224cdfaf6d81316a632f5f,

title = "Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors",

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.",

author = "Michael Barton and Rachid Ait-Haddou and Calo, {Victor Manuel}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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{\textquoteright}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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2017",

month = mar,

day = "21",

doi = "10.1016/j.cam.2017.02.022",

language = "English (US)",

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journal = "Journal of Computational and Applied Mathematics",

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AU - Barton, Michael

AU - Ait-Haddou, Rachid

AU - Calo, Victor Manuel

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2017/3/21

Y1 - 2017/3/21

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/623547

UR - https://linkinghub.elsevier.com/retrieve/pii/S0377042717300870

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DO - 10.1016/j.cam.2017.02.022

M3 - Article

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SP - 57

EP - 70

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

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

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