KMS Of Academy of mathematics and systems sciences, CAS
| Subdivision based isogeometric analysis for geometric flows | |
| Pan, Qing1; Rabczuk, Timon2; Chen, Chong3 | |
| 2021-11-16 | |
| Source Publication | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
 |
| ISSN | 0029-5981 |
| Pages | 24 |
| Abstract | 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. |
| Keyword | extended Loop subdivision geometric flows isogeometric analysis |
| DOI | 10.1002/nme.6870 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[12171147] ; Natural Science Foundation of Beijing Municipality[Z180002] |
| WOS Research Area | Engineering ; Mathematics |
| WOS Subject | Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications |
| WOS ID | WOS:000719127300001 |
| Publisher | WILEY |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59620 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Chen, Chong |
| Affiliation | 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 |
| 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. |
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