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

doi:10.1007/s11424-022-1293-3

Journal of Systems Science and Complexity ›› 2023, Vol. 36 ›› Issue (1): 53-76.DOI: 10.1007/s11424-022-1293-3

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

JI Ye^1,2, WANG Mengyun^1,2, YU Yingying³, ZHU Chungang^1,2

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2. Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province, Dalian 116024, China;
3. School of Mathematics, Liaoning Normal University, Dalian 116029, China

Received:2021-08-12 Revised:2021-11-10 Online:2023-01-25 Published:2023-02-09
Supported by:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 12071057, 11671068, and 12001327.

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JI Ye, WANG Mengyun, YU Yingying, ZHU Chungang. Curvature-Based $r$-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization[J]. Journal of Systems Science and Complexity, 2023, 36(1): 53-76.

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

Key words: Isogeometric analysis, parameterization, $r$-adaptive, toric surface patches

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