An Adaptive Collocation Method with Weighted Extended PHT-Splines

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-spli...

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Published in:Journal of systems science and complexity 2021-02, Vol.34 (1), p.47-67
Main Authors: Ni, Qian, Deng, Jiansong, Wang, Xuhui
Format: Article
Language:English
Subjects:
Apexes
Basis functions
Collocation methods
Complex Systems
Control
Interpolation
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Relocation
Spline functions
Statistics
Systems Theory
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description 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 C 1 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.
doi_str_mv 10.1007/s11424-020-9390-7
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subjects Apexes
Basis functions
Collocation methods
Complex Systems
Control
Interpolation
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Relocation
Spline functions
Statistics
Systems Theory
title An Adaptive Collocation Method with Weighted Extended PHT-Splines
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