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Isogeometric analysis of minimal surfaces on the basis of extended Catmull-Clark subdivision
Pan, Qing1; Rabczuk, Timon2; Chen, Chong3; Xu, Guoliang3; Pan, Kejia4
2018-08-01
Source PublicationCOMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN0045-7825
Volume337Pages:128-149
AbstractWe study the application of Isogeometric Analysis based on extended Catmull-Clark subdivision approach for the minimal surface models on planar domains. Subdivision approaches are compatible with NURBS as the standard of CAD systems which are capable of the refinability of B-spline techniques. The exactness of the physical domain of interest is fixed patchwise by the coarsest quadrilateral mesh and maintained through refinement. By performing extended Catmull-Clark subdivision, the control mesh can be repeatedly refined, and the geometry is described as an infinite set of bicubic splines while maintaining its original exactness. The finite element space is spanned by the limit form of extended Catmull-Clark subdivision, which possesses C-1 smoothness and the flexibility of mesh topology. In this work we establish the approximation properties and inverse inequalities for this space which are similar to the ones of classical finite elements. The approximation estimates for the minimal surface models are developed with the aid of the H-1-norm convergence property of its linearization model. The performance of numerical tests is consistent with the theoretical results. We also compare these numerical calculations with classical linear finite element methods. (C) 2018 Elsevier B.V. All rights reserved.
KeywordIsogeometric analysis Extended Catmull-Clark subdivision Error estimation Minimal surfaces
DOI10.1016/j.cma.2018.03.040
Language英语
Funding ProjectNational Natural Science Foundation of China (NSFC)[11671130] ; National Natural Science Foundation of China (NSFC)[11301520] ; National Natural Science Foundation of China (NSFC)[41474103] ; Scientific Research Fund of Hunan Provincial Education Department[15A110] ; Hunan Provincial Natural Science Foundation of China[2018JJ2248] ; Excellent Youth Foundation of Hunan Province of China[2018JJ1042] ; Innovation-Driven Project of Central South Univeristy[2018CX042]
WOS Research AreaEngineering ; Mathematics ; Mechanics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS IDWOS:000433143200006
PublisherELSEVIER SCIENCE SA
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30469
Collection计算数学与科学工程计算研究所
Affiliation1.Hunan Normal Univ, Minist Educ China, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China
2.Bauhaus Univ Weimar, Inst Struct Mech, D-99423 Weimar, Germany
3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
4.Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
Recommended Citation
GB/T 7714
Pan, Qing,Rabczuk, Timon,Chen, Chong,et al. Isogeometric analysis of minimal surfaces on the basis of extended Catmull-Clark subdivision[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2018,337:128-149.
APA Pan, Qing,Rabczuk, Timon,Chen, Chong,Xu, Guoliang,&Pan, Kejia.(2018).Isogeometric analysis of minimal surfaces on the basis of extended Catmull-Clark subdivision.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,337,128-149.
MLA Pan, Qing,et al."Isogeometric analysis of minimal surfaces on the basis of extended Catmull-Clark subdivision".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 337(2018):128-149.
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