On numerical quadrature for C1 quadratic Powell-Sabin 6-split macro-triangles.
Journal of Computational and Applied Mathematics(2019)
摘要
The quadrature rule of Hammer and Stroud (1956) for cubic polynomials has been shown to be exact for a larger space of functions, namely the C1 cubic Clough–Tocher spline space over a macro-triangle if and only if the split-point is the barycentre of the macro-triangle Kosinka and Bartoň (2018). We continue the study of quadrature rules for spline spaces over macro-triangles, now focusing on the case of C1 quadratic Powell–Sabin 6-split macro-triangles. We show that the 3-node Gaussian quadrature(s) for quadratics can be generalised to the C1 quadratic Powell–Sabin 6-split spline space over a macro-triangle for a two-parameter family of inner split-points, not just the barycentre as in Kosinka and Bartoň (2018). The choice of the inner split-point uniquely determines the positions of the edge split-points such that the whole spline space is integrated exactly by a corresponding polynomial quadrature. Consequently, the number of quadrature points needed to exactly integrate this special spline space reduces from twelve to three.
更多查看译文
关键词
Numerical integration,Powell–Sabin spline space,Gaussian quadrature rules
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络