Effortless quasi-interpolation in hierarchical spaces
Effortless quasi-interpolation in hierarchical spaces
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DOI：
10.1007/s00211-015-0711-z
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发表时间：
2015-03
影响因子：
2.1
通讯作者：
H. Speleers;C. Manni
中科院分区：
文献类型：
--
作者：
H. Speleers;C. Manni
给出了一个构造层次空间中拟插值的一般而简单的方法。这样的空间由嵌套空间的层次结构组成，并为局部细化提供了灵活的框架。所提出的分层拟插值描述在所谓的截断分层基础。假设一个准插值被选择为每个空间与一个特定的层次结构中的水平，层次的准插值得到没有任何额外的操作。在层次结构中，在每一层选择的拟插值的主要性质（如多项式再生）被局部地保持。给出了层次局部投影的构造方法，并研究了层次空间的局部逼近阶。详细介绍了截断层次B样条的基础上，我们讨论了其扩展到一个更一般的框架。
We present a general and simple procedure to construct quasi-interpolants in hierarchical spaces. Such spaces are composed of a hierarchy of nested spaces and provide a flexible framework for local refinement. The proposed hierarchical quasi-interpolants are described in terms of the so-called truncated hierarchical basis. Assuming a quasi-interpolant is selected for each space associated with a particular level in the hierarchy, the hierarchical quasi-interpolants are obtained without any additional manipulation. The main properties (like polynomial reproduction) of the quasi-interpolants selected at each level are locally preserved in the hierarchical construction. We show how to construct hierarchical local projectors, and the local approximation order of the underling hierarchical space is also investigated. The presentation is detailed for the truncated hierarchical B-spline basis, and we discuss its extension to a more general framework.