Isogeometric Least-Squares Collocation Method with Consistency and Convergence Analysis  

作　　者：LIN Hongwei XIONG Yunyang WANG Xiao HU Qianqian REN Jingwen 

机构地区：[1]School of Mathematical Science,State Key Lab.of CAD&CG,Zhejiang University,Hangzhou 310027,China [2]Department of Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China

出　　处：《Journal of Systems Science & Complexity》2020年第5期1656-1693,共38页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.61872316;the Natural Science Foundation of Zhejiang Province under Grant No.LY19F020004。

摘　　要：This paper presents the isogeometric least-squares collocatio 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.

关 键 词：Collocation method consistency and convergence least-squares fitting isogeometric analysis NURBS 

分 类 号：O241.5[理学—计算数学]