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An Adaptive Collocation Method with Weighted Extended PHT-Splines

NI Qian · DENG Jiansong · WANG Xuhui   

  1. NI Qian · DENG Jiansong
    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China.
    WANG Xuhui (Corresponding author)
    School of Mathematics, Hefei University of Technology, Hefei 230009, China. Email: xhw@hfut.edu.cn.
  • Online:2021-02-25 Published:2021-02-02

NI Qian · DENG Jiansong · WANG Xuhui. An Adaptive Collocation Method with Weighted Extended PHT-Splines[J]. Journal of Systems Science and Complexity, 2021, 34(1): 47-67.

This paper presents an adaptive collocation method with weighted extended PHT-splines. The authors modify the classification rules for basis functions based on the relation between the basis vertices and the computational domain. The Gaussian points are chosen to be collocation points since PHT-splines are C1 continuous. The authors also provide relocation techniques to resolve the mismatch problem between the number of basis functions and the number of interpolation conditions. Compared to the traditional Greville collocation method, the new approach has improved accuracy with fewer oscillations. Several numerical examples are also provided to test our the proposed approach.

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