| An issue on the surface integrals with face decomposition in the virtual element method and its improvement without the decomposition | |
Ru M(茹敏)1,2 ; Xu GT(许广涛)1,2; Liu CQ(刘传奇)1
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| Corresponding Author | Liu, Chuanqi([email protected]) |
| Source Publication | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
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| 2024-08-01 | |
| Volume | 428Pages:19 |
| ISSN | 0045-7825 |
| Abstract | The Virtual Element Method (VEM) is a promising approach developed in recent years. Within the energy-based framework of the VEM, we can directly compute the consistency and stabilization terms by automatically differentiating the separation of the energy functional. Surface integrals are involved in computing the consistency matrix, and we find that the results depend on the element-partitioning schemes for these integrals. Partitioning scheme that introduces facial centroids works well, but it can only be applied to star-convex polygons. Other partitioning schemes without introducing centroids cause significant errors since the integration weights are not computed from all nodes of the surface. In this paper, we provide a detailed derivation to illustrate these discrepancies. To overcome this challenge, we implement an integration scheme without element-partitioning, which converting the surface integrals into line integrals using a recursive procedure. We employ four examples to demonstrate the effectiveness of the proposed method for both convex and concave polyhedra. |
| Keyword | Virtual element method Surface integrals Element-partition Homogeneous integration scheme |
| DOI | 10.1016/j.cma.2024.117107 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:001263838500001 |
| WOS Research Area | Engineering ; Mathematics ; Mechanics |
| WOS Subject | Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics |
| Funding Project | Strategic Priority Research Program of Chinese Academy of Sciences (CAS)[XDB0620103] ; One Hundred Talents Program of CAS ; National Natural Science Foundation of China (NSFC)[12172368] |
| Funding Organization | Strategic Priority Research Program of Chinese Academy of Sciences (CAS) ; One Hundred Talents Program of CAS ; National Natural Science Foundation of China (NSFC) |
| Classification | 一类 |
| Ranking | 1 |
| Contributor | Liu, Chuanqi |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/95874 |
| Collection | 非线性力学国家重点实验室 |
| Affiliation | 1.Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China; 2.Univ Chinese Acad Sci, Sch Future Technol, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Ru M,Xu GT,Liu CQ. An issue on the surface integrals with face decomposition in the virtual element method and its improvement without the decomposition[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2024,428:19.Rp_Au:Liu, Chuanqi |
| APA | 茹敏,许广涛,&刘传奇.(2024).An issue on the surface integrals with face decomposition in the virtual element method and its improvement without the decomposition.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,428,19. |
| MLA | 茹敏,et al."An issue on the surface integrals with face decomposition in the virtual element method and its improvement without the decomposition".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 428(2024):19. |
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