Gaussian quadrature rules for C1 quintic splines with uniform knot vectors

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:322

Article

Barton, Michael¹  Ait-Haddou, Rachid²  Calo, Victor Manuel³ 

[1] BCAM, Alameda Mazarredo 14, Bilbao 48009, Basque Country, Spain

[2] A-803 Mihogaoka 19, Ibaraki, Osaka 5670047, Japan

[3] Curtin Univ, Fac Sci & Engn, Sch Mines, CSIRO Professorial Chair Computat Geosci, Kent St, Perth, WA 6102, Australia

关键词: Gaussian quadrature;    Quintic splines;    Peano kernel;    B-splines;    C-1 continuity;    Quadrature for isogeometric analysis;   

DOI  :  10.1016/j.cam.2017.02.022

来源: Elsevier

【 摘 要 】

We provide explicit quadrature rules for spaces of C-1 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 n subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as n grows, to the two-third quadrature rule of Hughes et al. (2010) for infinite domains. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free