Curvature-based r-adaptive isogeometric analysis with injectivity-preserving multi-sided domain parameterization
Date:日期：
Conference talk会议报告 at ，12th China Mathematical Society Conference on Computer Mathematics (第十二届中国数学会计算机数学大会, CM 2021), Guilin, China
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Inspired by the r-refinement method in isogeometric analysis, the authors propose a curvature-based r-adaptive isogeometric method for planar multi-sided computational domains parameterized by toric surface patches. The authors construct three absolute curvature metrics of the 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.
Keywords: Isogeometric Analysis, r-Adaptivity, Toric Surface Patches, Multi-Sided Domain Parameterization, Injectivity