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