Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization

Inspired by the r -refinement method in isogeometric analysis, in this paper, 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 isogeomet...

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Bibliographic Details
Published inJournal of systems science and complexity Vol. 36; no. 1; pp. 53 - 76
Main Authors Ji, Ye, Wang, Mengyun, Yu, Yingying, Zhu, Chungang
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2023
Springer Nature B.V
Subjects
Complex Systems
Control
Curvature
Domains
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Parameterization
Statistics
Systems Theory
Isogeometric analysis
parameterization
adaptive
toric surface patches
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Summary:Inspired by the r -refinement method in isogeometric analysis, in this paper, 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 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.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-022-1293-3