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Adaptive refinement of hierarchical T-splines

机译：分层T样条的自适应细化

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摘要

We present an adaptive local refinement technique for isogeometric analysis based on hierarchical T-splines. An element-wise point of view is adopted, which exploits Bezier extraction, and allows adaptive refinement of standard hierarchical T-splines and truncated hierarchical T-splines in a straightforward and unified manner. No explicit basis function operations are required to build the hierarchical basis function space, as only matrix manipulations are involved. This makes the efficiency superior to that of existing implementations. In particular, the implementation of truncated hierarchical T-splines requires no explicit truncation of the basis functions. In the analysis, a multi-level T-mesh is constructed by successive cell subdivisions of an initial, coarse T-mesh. An important feature is that Bezier extraction is employed to compute the refinement operator between two successive hierarchical levels, and that, at each level, Bezier extraction is applied to obtain the stiffness matrix without, initially, considering multi-level interaction. This interaction is recovered through a subdivision operator. Numerical examples are presented for validation purposes, and to assess the convergence properties. (C) 2018 Elsevier B.V. All rights reserved.
机译：我们提出了一种基于分层T样条曲线的自适应局部细化技术，用于等几何分析。采用基于元素的观点，该观点利用Bezier提取，并允许以直接和统一的方式对标准层次T样条和截断层次T样条进行自适应细化。由于只涉及矩阵操作，因此不需要显式的基函数操作即可构建层次基函数空间。这使得效率优于现有实施方式。特别是，截断的分层T样条的实现不需要基本函数的显式截断。在分析中，通过初始的粗略T网格的连续单元细分来构建多级T网格。一个重要的特征是，采用Bezier提取来计算两个连续层次级别之间的精化算子，并且在每个级别上，都将Bezier提取用于获得刚度矩阵，而最初无需考虑多级交互作用。此交互通过细分运算符恢复。给出了数值示例，以进行验证并评估收敛性。 （C）2018 Elsevier B.V.保留所有权利。

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