Subdivision based isogeometric analysis for geometric flows
Pan, Qing1; Rabczuk, Timon2; Chen, Chong3
AbstractWe present a new isogeometric analysis (IGA) approach based on extended Loop subdivision scheme for solving various geometric flows defined on subdivision surfaces. The studied flows include the second-order, fourth-order, and sixth-order geometric flows, such as averaged mean curvature flow, constant mean curvature flow, and minimal mean-curvature-variation flow, which are generally derived by minimizing the associate energy functionals with L2-gradient flow respectively. The geometric flows are discretized by means of subdivision based IGA, where the finite element space is formulated by the limit form of the extended Loop subdivision for different initial control meshes. The basis functions, consisting of quartic box-splines corresponding to each subdivided control mesh, are utilized to represent the geometry exactly. For the cases of the evolution of open surfaces with any shape boundary, high-order continuous boundary conditions derived from the mixed variational forms of the geometric flows should be implemented to be consistent with the isogeometric concept. For time discretization, we adopt an adaptive semi-implicit Euler scheme. By several numerical experiments, we study the convergence behaviors of the proposed approach for solving the geometric flows with high-order boundary conditions. Moreover, the numerical results also show the accuracy and efficiency of the proposed method.
Keywordextended Loop subdivision geometric flows isogeometric analysis
Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[12171147] ; Natural Science Foundation of Beijing Municipality[Z180002]
WOS Research AreaEngineering ; Mathematics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000719127300001
Citation statistics
Document Type期刊论文
Corresponding AuthorChen, Chong
Affiliation1.Hunan Normal Univ, Minist Educ China, Key Lab High Performance Comp & Stochast Informat, Changsha, Peoples R China
2.Bauhaus Univ Weimar, Dept Computat Mech, Weimar, Germany
3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Pan, Qing,Rabczuk, Timon,Chen, Chong. Subdivision based isogeometric analysis for geometric flows[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,2021:24.
APA Pan, Qing,Rabczuk, Timon,&Chen, Chong.(2021).Subdivision based isogeometric analysis for geometric flows.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING,24.
MLA Pan, Qing,et al."Subdivision based isogeometric analysis for geometric flows".INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2021):24.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Pan, Qing]'s Articles
[Rabczuk, Timon]'s Articles
[Chen, Chong]'s Articles
Baidu academic
Similar articles in Baidu academic
[Pan, Qing]'s Articles
[Rabczuk, Timon]'s Articles
[Chen, Chong]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Pan, Qing]'s Articles
[Rabczuk, Timon]'s Articles
[Chen, Chong]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.