Isogeometric analysis based on extended Catmull-Clark subdivision
Pan, Qing1; Xu, Guoliang2; Xu, Gang3; Zhang, Yongjie4
AbstractIn this paper, we propose a subdivision-based finite element method as an integration of the isogeometric analysis (IGA) framework which adopts the uniform representation for geometric modeling and finite element simulation. The finite element function space is induced from the limit form of Catmull-Clark surface subdivision containing boundary subdivision schemes which has Cl continuity everywhere. It is capable of exactly representing complex geometries with any shaped boundaries which are represented as piecewise cubic B-spline curves. It is compatible with modern Computer Aided Design (CAD) software systems. The advantage of this strategy admits quadrilateral meshes of arbitrary topology. In this work, the computational domains with planar geometries are considered. We establish the approximation properties of Catmull-Clark surface subdivision function based on the Bramble-Hilbert lemma. Numerical tests are performed through three Poisson's equations with the Dirichlet boundary condition to corroborate the theoretical proof. (C) 2015 Elsevier Ltd. All rights reserved.
KeywordCatmull-Clark subdivision Isogeometric analysis Computer Aided Design Finite element analysis
Funding ProjectNational Natural Science Foundation of China[11171103] ; Scientific Research Fund of Hunan Provincial Education Department[15A110] ; NSFC Funds for Creative Research Groups of China[11321061] ; National Nature Science Foundation of China[61472111] ; Zhejiang Provincial Natural Science Foundation of China[LR16F020003] ; NSF CAREER Award[OCI-1149591] ; ONR-YIP award[N00014-10-1-0698] ; AFOSR grant[FA9550-11-1-0346]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000369455000007
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Document Type期刊论文
Corresponding AuthorPan, Qing
Affiliation1.Hunan Normal Univ, Minist Educ China, Key Lab High Performance Comp & Stochast Informat, Changsha, Hunan, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing, Peoples R China
3.Hangzhou Dianzi Univ, Dept Comp Sci, Hangzhou 310018, Zhejiang, Peoples R China
4.Carnegie Mellon Univ, Dept Mech Engn, Pittsburgh, PA 15213 USA
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GB/T 7714
Pan, Qing,Xu, Guoliang,Xu, Gang,et al. Isogeometric analysis based on extended Catmull-Clark subdivision[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2016,71(1):105-119.
APA Pan, Qing,Xu, Guoliang,Xu, Gang,&Zhang, Yongjie.(2016).Isogeometric analysis based on extended Catmull-Clark subdivision.COMPUTERS & MATHEMATICS WITH APPLICATIONS,71(1),105-119.
MLA Pan, Qing,et al."Isogeometric analysis based on extended Catmull-Clark subdivision".COMPUTERS & MATHEMATICS WITH APPLICATIONS 71.1(2016):105-119.
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