Constructing fully symmetric cubature formulae for the sphere

DOI10.1090/S0025-5718-00-01198-4zbMath0982.65027OpenAlexW2086585111MaRDI QIDQ4517521

Yuan Xu, Sangwoo Heo

Publication date: 22 November 2000

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-00-01198-4

zbMATH Keywords

cubature formulaesimplexoctahedral symmetryon the triangleon the unit spheresymmetric formula on a triangle

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (13)

Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling ⋮ On the accuracy of numerical integration over the unit sphere applied to full network models ⋮ On the use of the Bingham statistical distribution in microsphere-based constitutive models for arterial tissue ⋮ A computational model of the biochemomechanics of an evolving occlusive thrombus ⋮ A thermo-mechanical material model for rubber curing and tire manufacturing simulation ⋮ Framework for deformation induced anisotropy in glassy polymers ⋮ Constructing cubature formulae for spheres and balls ⋮ Numerical integration on the sphere and its effect on the material symmetry of constitutive equations-A comparative study ⋮ Electroelasticity of dielectric elastomers based on molecular chain statistics ⋮ Efficient evaluation of the material response of tissues reinforced by statistically oriented fibres ⋮ Orthogonal polynomials and cubature formulae on balls, simplices, and spheres ⋮ An exponential constitutive model excluding fibres under compression: Application to extension–inflation of a residually stressed carotid artery ⋮ On the use of non-linear transformations for the evaluation of anisotropic rotationally symmetric directional integrals. Application to the stress analysis in fibred soft tissues

Cites Work

• Moderate-degree tetrahedral quadrature formulas
• A note on Presburger arithmetic with array segments, permutation and equality
• An upper bound for the Laguerre polynomials
• Monomial cubature rules since ``Stroud: A compilation
• Cubature formulas for the surface of the sphere
• Constructing cubature formulae for spheres and balls
• Fully Symmetric Integration Formulas for the Surface of the Sere in S Dimensions
• High degree efficient symmetrical Gaussian quadrature rules for the triangle
• Moderate Degree Symmetric Quadrature Rules for the Triangle
• Consistent Structures of Invariant Quadrature Rules for the n-Simplex
• Optimal Numerical Integration on a Sphere
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Constructing fully symmetric cubature formulae for the sphere