Gaussian quadrature for \(C^1\) cubic Clough-Tocher macro-triangles

DOI10.1016/j.cam.2018.10.036zbMath1459.65031OpenAlexW2899774624MaRDI QIDQ1715788

Michael Bartoň, Jiří Kosinka

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

zbMATH Keywords

numerical integrationGaussian quadrature rulesClough-Tocher spline space

Mathematics Subject Classification ID

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

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• 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

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