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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Ye Ji, Mengyun Wang & Chungang Zhu

  2. Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province, Dalian, 116024, China

    Ye Ji, Mengyun Wang & Chungang Zhu

  3. School of Mathematics, Liaoning Normal University, Dalian, 116029, China

    Yingying Yu

Authors
  1. Ye Ji
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  2. Mengyun Wang
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  3. Yingying Yu
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  4. Chungang Zhu
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Corresponding author

Correspondence to Chungang Zhu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 12071057, 11671068, and 12001327.

This paper was recommended for publication by Editor CHEN Shaoshi.

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Ji, Y., Wang, M., Yu, Y. et al. Curvature-Based r-Adaptive Isogeometric Analysis with Injectivity-Preserving Multi-Sided Domain Parameterization. J Syst Sci Complex 36, 53–76 (2023). https://doi.org/10.1007/s11424-022-1293-3

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  • DOI: https://doi.org/10.1007/s11424-022-1293-3

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