Isogeometric Least-Squares Collocation Method with Consistency and Convergence Analysis

• 作者: HU Qianqian LIN Hongwei REN Jingwen WANG Xiao XIONG Yunyang
• 来源期刊: 系统科学与复杂性学报（英文版）
• 年，卷（期）: 2020,（5）
• 页码范围: 1656-1693
• 页数: 38页
• 语种: 英文
• DOI: 10.1007/s11424-020-9052-9

摘要

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.