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

Handle URI:
http://hdl.handle.net/10754/623547
Title:
Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors
Authors:
Bartoň, Michael ( 0000-0002-1843-251X ) ; Ait-Haddou, Rachid; Calo, Victor Manuel
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.
Publisher:
Elsevier BV
Journal:
Journal of Computational and Applied Mathematics
Issue Date:
21-Mar-2017
DOI:
10.1016/j.cam.2017.02.022
Type:
Article
ISSN:
0377-0427
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).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBartoň, Michaelen
dc.contributor.authorAit-Haddou, Rachiden
dc.contributor.authorCalo, Victor Manuelen
dc.date.accessioned2017-05-15T10:35:07Z-
dc.date.available2017-05-15T10:35:07Z-
dc.date.issued2017-03-21en
dc.identifier.citationBartoň 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.en
dc.identifier.issn0377-0427en
dc.identifier.doi10.1016/j.cam.2017.02.022en
dc.identifier.urihttp://hdl.handle.net/10754/623547-
dc.description.abstractWe 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.en
dc.description.sponsorshipThe 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).en
dc.publisherElsevier BVen
dc.subjectGaussian quadratureen
dc.subjectQuintic splinesen
dc.subjectPeano kernelen
dc.subjectB-splinesen
dc.subjectC1C1 continuityen
dc.subjectQuadrature for isogeometric analysisen
dc.titleGaussian quadrature rules for C 1 quintic splines with uniform knot vectorsen
dc.typeArticleen
dc.identifier.journalJournal of Computational and Applied Mathematicsen
dc.contributor.institutionBCAM–Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spainen
dc.contributor.institutionA-803 Mihogaoka 19, Ibaraki City 567-0047 Osaka, Japanen
dc.contributor.institutionCSIRO Professorial Chair in Computational Geoscience, Western Australian, School of Mines, Faculty of Science and Engineering, Curtin University, Kent Street, Bentley, Perth, Western Australia, 6102, Australiaen
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