Dimensions of biquadratic spline spaces over T-meshes
Dimensions of biquadratic spline spaces over T-meshes
复制标题
DOI：
10.1016/j.cam.2012.08.020
复制
发表时间：
2008-04
期刊：
影响因子：
--
通讯作者：
J. Deng;Falai Chen;Liangbing Jin
中科院分区：
文献类型：
--
作者：
J. Deng;Falai Chen;Liangbing Jin
本文讨论了低次T网格上的样条基空间的尺寸问题。提出了两个新的概念：具有齐次边界条件的T网格和样条空间的推广。在量纲分析中，关键策略是嵌入混合偏导数算子的线性空间。给出了一般T网格上双二次样条空间的一个下界。在此基础上，充分利用层次T-网格的层次结构，证明了层次T-网格上双二次样条空间的维度公式。此外，还给出了尺寸公式的拓扑解释。
This paper discusses the dimensions of spline spaces over T-meshes of low degree. Two new concepts are proposed: an extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimensional analysis, the key strategy is linear space embedding with the operator of the mixed partial derivative. A lower bound on the dimension of the biquadratic spline spaces over general T-meshes is provided. Furthermore, by making full use of the level structure of hierarchical T-meshes, a dimension formula of biquadratic spline space over hierarchical T-meshes is proved. Additionally, a topological explanation of the dimension formula is provided.