Gaussian quadrature for \(C^1\) cubic Clough-Tocher macro-triangles
From MaRDI portal
Publication:1715788
DOI10.1016/j.cam.2018.10.036zbMath1459.65031OpenAlexW2899774624MaRDI QIDQ1715788
Publication date: 29 January 2019
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2018.10.036
Numerical computation using splines (65D07) Spline approximation (41A15) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)
Related Items (7)
Generalized \(C^1\) Clough-Tocher splines for CAGD and FEM ⋮ An adaptive element subdivision method based on the affine transformations and partitioning techniques for evaluating the weakly singular integrals ⋮ Numerical quadrature for Gregory quads ⋮ On numerical quadrature for \(C^1\) quadratic Powell-Sabin 6-split macro-triangles ⋮ A geometric characterization of Powell-Sabin triangulations allowing the construction of \(C^2\) quartic splines ⋮ A new multivariate quadrature rule for calculating statistical moments of stochastic response ⋮ A binary-tree element subdivision method for evaluation of nearly singular domain integrals with continuous or discontinuous kernel
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis
- Generalized Gaussian quadrature rules over two-dimensional regions with linear sides
- Nonnegativity preserving macro-element interpolation of scattered data
- A normalized basis for reduced Clough-Tocher splines
- Efficient quadrature for NURBS-based isogeometric analysis
- Gaussian quadrature for splines via homotopy continuation: rules for \(C^2\) cubic splines
- A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions
- A trivariate Clough-Tocher scheme for tetrahedral data
- An \(n\)-dimensional Clough-Tocher interpolant
- Box splines
- Smooth macro-elements based on Clough-Tocher triangle splits
- An encyclopaedia of cubature formulas.
- Watertight conversion of trimmed CAD surfaces to Clough-Tocher splines
- On numerical quadrature for \(C^1\) quadratic Powell-Sabin 6-split macro-triangles
- Optimal quadrature for univariate and tensor product splines
- Fast formation of isogeometric Galerkin matrices by weighted quadrature
- Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis
- Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis
- Gaussian quadrature rules for \(C^1\) quintic splines with uniform knot vectors
- Numerical Integration Over Simplexes
- Spline Functions on Triangulations
- Extended numerical integration method for triangular surfaces
- Moment Theory for Weak Chebyshev Systems with Applications to Monosplines, Quadrature Formulae and Best One-Sided $L^1 $-Approximation by Spline Functions with Fixed Knots
- Isogeometric Analysis
- Generalized Gaussian Quadrature Rules for Systems of Arbitrary Functions
- Generalized Gaussian quadrature rules on arbitrary polygons
- Macro-elements and stable local bases for splines on Clough-Tocher triangulations
This page was built for publication: Gaussian quadrature for \(C^1\) cubic Clough-Tocher macro-triangles
