Gaussian quadrature for C1 cubic Clough–Tocher macro-trianglesKosinka, J. & Bartoň, M., 1-May-2019, In : Journal of Computational and Applied Mathematics. 351, p. 6-13 8 p.
Research output: Contribution to journal › Article › Academic › peer-review
A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed by Hammer and Stroud (1956). The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and n + 1 points that lie on the connecting lines between the barycentre and the vertices of the simplex. In the planar case, this particular rule belongs to a two-parameter family of quadrature rules that admit exact integration of bivariate polynomials of total degree three over triangles. We prove that this rule is exact for a larger space, namely the C1 cubic Clough–Tocher spline space over macro-triangles if and only if the split-point is the barycentre. This results in a factor of three reduction in the number of quadrature points needed to integrate the Clough–Tocher spline space exactly.
|Number of pages||8|
|Journal||Journal of Computational and Applied Mathematics|
|Publication status||Published - 1-May-2019|
- Clough–Tocher spline space, Gaussian quadrature rules, Numerical integration, RULES, SPLINES, ELEMENTS, SYSTEMS