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Isogeometric Least-Squares Collocation Method with Consistency and Convergence Analysis

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Abstract

This paper presents the isogeometric least-squares collocation (IGA-L) method, which determines the numerical solution by making the approximate differential operator fit the real differential operator in a least-squares sense. The number of collocation points employed in IGA-L can be larger than that of the unknowns. Theoretical analysis and numerical examples presented in this paper show the superiority of IGA-L over state-of-the-art collocation methods. First, a small increase in the number of collocation points in IGA-L leads to a large improvement in the accuracy of its numerical solution. Second, IGA-L method is more flexible and more stable, because the number of collocation points in IGA-L is variable. Third, IGA-L is convergent in some cases of singular parameterization. Moreover, the consistency and convergence analysis are also developed in this paper.

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Author information

Authors and Affiliations

  1. School of Mathematical Science, State Key Lab. of CAD & CG, Zhejiang University, Hangzhou, 310027, China

    Hongwei Lin, Yunyang Xiong, Xiao Wang & Jingwen Ren

  2. Department of Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China

    Qianqian Hu

Authors
  1. Hongwei Lin
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  2. Yunyang Xiong
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  3. Xiao Wang
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  4. Qianqian Hu
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  5. Jingwen Ren
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Corresponding author

Correspondence to Hongwei Lin.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant No. 61872316, and the Natural Science Foundation of Zhejiang Province under Grant No. LY19F020004.

This paper was recommended for publication by Editor-in-Chief GAO Xiao-Shan.

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Lin, H., Xiong, Y., Wang, X. et al. Isogeometric Least-Squares Collocation Method with Consistency and Convergence Analysis. J Syst Sci Complex 33, 1656–1693 (2020). https://doi.org/10.1007/s11424-020-9052-9

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  • DOI: https://doi.org/10.1007/s11424-020-9052-9

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