Subdivision based isogeometric analysis for geometric flows

doi:10.1002/nme.6870

CSpace

	Subdivision based isogeometric analysis for geometric flows
	Pan, Qing 1; Rabczuk, Timon 2; Chen, Chong 3
	2021-11-16
发表期刊	INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
ISSN	0029-5981
页码	24
摘要	We 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.
关键词	extended Loop subdivision geometric flows isogeometric analysis
DOI	10.1002/nme.6870
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[12171147] ; Natural Science Foundation of Beijing Municipality[Z180002]
WOS研究方向	Engineering ; Mathematics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000719127300001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59620
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Chong
作者单位	1.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
推荐引用方式 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.