Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes
Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes
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DOI：
10.1016/j.cma.2017.08.032
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发表时间：
2018
影响因子：
7.2
通讯作者：
C. Anitescu;Naim Hossain;T. Rabczuk
中科院分区：
文献类型：
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作者：
C. Anitescu;Naim Hossain;T. Rabczuk
介绍了一种基于多项式/有理样条在分层t网格上泛化的自适应高阶方法（PHT/ rht样条）。虽然等几何分析中考虑的大多数问题在解光滑时可以有效地解决，但许多非平凡模拟具有粗糙解。例如，这可能是由域中存在可重入角引起的。对于这样的问题，张量积基不太适合解决出现的奇点，因为细化在整个计算域传播。层次基础和自适应允许一种更有效的方法来处理奇点，只在必要的地方增加更多的自由度来改善近似。为了推动自适应改进，本文提出了一种有效的基于恢复的误差估计器。估计器产生一个“恢复解”，这是一个比计算数值解更精确的近似。一些具有更高阶和更大连续性的pht样条的二维和三维数值研究表明，与均匀细化相比，在自由度和计算成本方面表现出良好的性能。
An adaptive higher-order method based on a generalization of polynomial/rational splines over hierarchical T-meshes (PHT/RHT-splines) is introduced. While most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth, many non-trivial simulations have rough solutions. This can be caused, for example, by the presence of re-entrant corners in the domain. For such problems, a tensor-product basis is less suitable for resolving the singularities that appear, as refinement propagates throughout the computational domain. Hierarchical bases and adaptivity allow for a more efficient way of dealing with singularities, by adding more degrees of freedom only where they are necessary to improve the approximation. In order to drive the adaptive refinement, an efficient recovery-based error estimator is proposed in this work. The estimator produces a “recovered solution” which is a more accurate approximation than the computed numerical solution. Several 2D and 3D numerical investigations with PHT-splines of higher order and greater continuity show good performance compared to uniform refinement in terms of degrees of freedom and computational cost.