A subdivision-based implementation of the hierarchical b-spline finite element method
A subdivision-based implementation of the hierarchical b-spline finite element method
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DOI：
10.1016/j.cma.2012.06.023
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发表时间：
2013-01-01
影响因子：
7.2
通讯作者：
Cirak, F.
中科院分区：
文献类型：
--
作者：
Bornemann, P. B.;Cirak, F.
提出了一种新的方法，以方便实现分层b样条及其与传统有限元实现的接口。双尺度关系的离散解释，作为常见的细分方案，用于建立基函数及其系数在不同层次的b样条基之间的代数关系。引入的细分投影技术允许我们首先使用固定数量的同层基函数来计算所有元素矩阵和向量。在组装阶段，它们随后与细分矩阵的乘法将它们投影到分层b样条基的正确级别。该方法适用于一维、二维和三维空间线性和几何非线性问题的收敛性研究。(C) 2012 Elsevier B.V.版权所有
A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. (C) 2012 Elsevier B.V. All rights reserved.