Adaptive isogeometric analysis by local h-refinement with T-splines
Adaptive isogeometric analysis by local h-refinement with T-splines
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DOI：
10.1016/j.cma.2008.07.012
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发表时间：
2010-01-01
影响因子：
7.2
通讯作者：
Simeon, Bernd
中科院分区：
文献类型：
--
作者：
Doerfel, Michael R.;Juettler, Bert;Simeon, Bernd
基于非均匀有理B样条（NURBS）作为基函数的等几何分析保留了精确的几何形状，但存在参数空间中控制点的矩形网格的缺点，这使得纯粹的局部细化是不可能的。本文演示了如何通过使用T样条来克服这一困难。T样条允许引入所谓的T形连接，这与标准FEM中的悬挂节点有关。服从一些简单的规则，矩形补丁的参数空间的T样条可以细分，从而局部细化成为可行的，同时仍然保持准确的几何形状。此外，它示出了如何国家的最先进的后验误差估计技术可以与细化T样条相结合。数值算例强调了T样条等几何分析的潜力，并为进一步的发展提供了提示。(C)2008 Elsevier B.V.保留所有权利。
Isogeometric analysis based on non-uniform rational B-splines (NURBS) as basis functions preserves the exact geometry but suffers from the drawback of a rectangular grid of control points in the parameter space, which renders a purely local refinement impossible. This paper demonstrates how this difficulty can be overcome by using T-splines instead. T-splines allow the introduction of so-called T-junctions, which are related to hanging nodes in the standard FEM. Obeying a few straightforward rules, rectangular patches in the parameter space of the T-splines can be subdivided and thus a local refinement becomes feasible while still preserving the exact geometry. Furthermore, it is shown how state-of-the-art a posteriori error estimation techniques can be combined with refinement by T-splines. Numerical examples underline the potential of isogeometric analysis with T-splines and give hints for further developments. (C) 2008 Elsevier B.V. All rights reserved.