Gaussian quadrature rules for C1 quintic splines with uniform knot vectors
We provide explicit quadrature rules for spaces of C1 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 give...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Elsevier
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/53784 |
| _version_ | 1848759227349204992 |
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| author | Barton, M. Ait-Haddou, R. Calo, Victor |
| author_facet | Barton, M. Ait-Haddou, R. Calo, Victor |
| author_sort | Barton, M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We provide explicit quadrature rules for spaces of C1 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. |
| first_indexed | 2025-11-14T09:56:32Z |
| format | Journal Article |
| id | curtin-20.500.11937-53784 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:56:32Z |
| publishDate | 2017 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-537842019-03-29T07:56:21Z Gaussian quadrature rules for C1 quintic splines with uniform knot vectors Barton, M. Ait-Haddou, R. Calo, Victor We provide explicit quadrature rules for spaces of C1 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. 2017 Journal Article http://hdl.handle.net/20.500.11937/53784 10.1016/j.cam.2017.02.022 Elsevier fulltext |
| spellingShingle | Barton, M. Ait-Haddou, R. Calo, Victor Gaussian quadrature rules for C1 quintic splines with uniform knot vectors |
| title | Gaussian quadrature rules for C1 quintic splines with
uniform knot vectors |
| title_full | Gaussian quadrature rules for C1 quintic splines with
uniform knot vectors |
| title_fullStr | Gaussian quadrature rules for C1 quintic splines with
uniform knot vectors |
| title_full_unstemmed | Gaussian quadrature rules for C1 quintic splines with
uniform knot vectors |
| title_short | Gaussian quadrature rules for C1 quintic splines with
uniform knot vectors |
| title_sort | gaussian quadrature rules for c1 quintic splines with
uniform knot vectors |
| url | http://hdl.handle.net/20.500.11937/53784 |