Gaussian quadrature rules for $C^1$ quintic splines with uniform knot vectors
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 g...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2017 |
| Country: | España |
| Institution: | Basque Center for Applied Mathematics (BCAM) |
| Repository: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/653 |
| Online Access: | http://hdl.handle.net/20.500.11824/653 |
| Access Level: | Open access |
| Keyword: | Gaussian quadrature quintic splines Peano kernel B-splines $C^1$ continuity quadrature for isogeometric analysis |
| Summary: | 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. [23] for infinite domains. |
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