A novel hybrid IGA-EIEQ numerical method for the Allen-Cahn/Cahn-Hilliard equations on complex curved surfaces

doi:10.1016/j.cma.2022.115767

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	A novel hybrid IGA-EIEQ numerical method for the Allen-Cahn/Cahn-Hilliard equations on complex curved surfaces
	Pan, Qing 1; Chen, Chong 2; Zhang, Yongjie Jessica 3; Yang, Xiaofeng 4
	2023-02-01
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN	0045-7825
卷号	404 页码:21
摘要	We present an efficient fully discrete algorithm for solving the Allen-Cahn and Cahn-Hilliard equations on complex curved surfaces. The spatial discretization employs the recently developed IGA (isogeometric analysis) framework, where we adopt the strategy of Loop subdivision with the superior adaptability of any topological structure, and the basis functions are quartic box-splines used to define the subdivided surface. The time discretization is based on the so-called EIEQ (explicit-Invariant Energy Quadratization) approach, which applies multiple newly defined variables to linearize the nonlinear potential and realize the efficient decoupled type computation. The combination of these two methods can help us to gain a linear, second-order time accurate scheme with the property of unconditional energy stability, whose rigorous proof is given. We also develop a nonlocal splitting technique such that we only need to solve decoupled, constant-coefficient elliptic equations at each time step. Finally, the effectiveness of the developed numerical algorithm is verified by various numerical experiments on the complex benchmark curved surfaces such as bunny, splayed, and head surfaces.(c) 2022 Elsevier B.V. All rights reserved.
关键词	Loop subdivision IGA-EIEQ Decoupled Unconditional energy stability Allen-Cahn Cahn-Hilliard
DOI	10.1016/j.cma.2022.115767
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[12171147] ; National Natural Science Foundation of China[11971076] ; key research project of Beijing Natural Science Foundation, China[Z180002] ; National Science Foundation of USA[DMS-2012490]
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000896882700003
出版者	ELSEVIER SCIENCE SA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60486
专题	中国科学院数学与系统科学研究院
通讯作者	Yang, Xiaofeng
作者单位	1.Changsha Univ Sci & Technol, Sch Comp & Commun Engn, Changsha 410114, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 3.Carnegie Mellon Univ, Dept Mech Engn, Pittsburgh, PA 15213 USA 4.Univ South Carolina, Dept Math, Columbia, SC 29208 USA
推荐引用方式 GB/T 7714	Pan, Qing,Chen, Chong,Zhang, Yongjie Jessica,et al. A novel hybrid IGA-EIEQ numerical method for the Allen-Cahn/Cahn-Hilliard equations on complex curved surfaces[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2023,404:21.
APA	Pan, Qing,Chen, Chong,Zhang, Yongjie Jessica,&Yang, Xiaofeng.(2023).A novel hybrid IGA-EIEQ numerical method for the Allen-Cahn/Cahn-Hilliard equations on complex curved surfaces.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,404,21.
MLA	Pan, Qing,et al."A novel hybrid IGA-EIEQ numerical method for the Allen-Cahn/Cahn-Hilliard equations on complex curved surfaces".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 404(2023):21.