2016/01/27 by Hongwei Lin, Lin, Hongwei, Yunyang Xiong +5 · 2 citations
Engineering · Mathematics · #65N12 #65N30 #Advanced Measurement and Metrology Techniques #Advanced Numerical Analysis Techniques #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1601.07244
openalex publication_date 2016/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we present 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.