Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization
Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization
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DOI：
10.1007/s11424-022-1293-3
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发表时间：
2022-10
影响因子：
2.1
通讯作者：
Ye Ji;Meng Wang;Yingying Yu;Chungang Zhu
中科院分区：
文献类型：
--
作者：
Ye Ji;Meng Wang;Yingying Yu;Chungang Zhu
受等几何分析中的其他精化方法的启发，本文提出了一种基于曲率的自适应等几何方法，用于用环面斑块参数化的平面多面计算域。构造了三个等几何解曲面的绝对曲率度量来表征其梯度信息，更为直观有效。该方法以内部权值作为优化变量，得到的参数化具有分析适宜性和保注入性，并有理论保证。在以环面补丁参数化的多个计算域上求解了多个偏微分方程，验证了该方法的有效性和效率。
Inspired by ther-refinement method in isogeometric analysis, in this paper, the authors propose a curvature-basedr-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches. The authors construct three absolute curvature metrics of isogeometric solution surface to characterize its gradient information, which is more straightforward and effective. The proposed method takes the internal weights as optimization variables and the resulting parameterization is analysis-suitable and injectivity-preserving with a theoretical guarantee. Several PDEs are solved over multi-sided computational domains parameterized by toric surface patches to demonstrate the effectiveness and efficiency of the proposed method.