Isogeometric Analysis on Implicit Domains:Approximation,Stability and Error Estimates  

作　　者：Fang Deng Tianhui Yang Jingjing Liu Jiansong Deng 

机构地区：[1]School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450045,People’s Republic of China [2]Department of Mathematics,Harbin Institute of Technology Weihai,Weihai 264209,People’s Republic of China [3]School of Mathematics and Statistics,Hefei Normal University,Hefei 230061,People’s Republic of China [4]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2024年第4期633-658,共26页数学与统计通讯（英文）

摘　　要：The gap between finite element analysis and computer-aided design derives the development of isogeometric analysis(IGA),which uses the same representation in the geometry and the analysis.However,the parameterization in IGA is non-trivial.Weighted extended B-splines(WEB)method replaces grid generation and parameterization with weight function construction(R-function or distance function).By using implicit spline representation,isogeometric analysis on implicit domains(IGAID)adopts the merits of the“isoparametric”in IGA and“weight function generation”in WEB.But the theoretical properties have not been fully studied yet.In this paper,we study the theoretical aspects of IGAID using tensor-product B-splines.Both the approximation and stability properties of IGAID are considered.By setting appropriate constraints on the weight function,we can derive the optimal approximation order and stability.Numerical examples show the effectiveness of the approach and validate the theoretical results.

关 键 词：Isogeometric analysis WEB method Implicit domain Weight function Error estimates 

分 类 号：O17[理学—数学]