IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION

doi:10.1137/21M1457400

CSpace

	IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION
	Gong, Wei 1,2; Li, Jiajie 3; Zhu, Shengfeng 4,5
	2022
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	44 期号:4 页码:A2464-A2505
摘要	We propose in this paper two kinds of continuity preserving discrete shape gradients of boundary type for PDE-constrained shape optimizations. First, a modified boundary shape gradient formula for shape optimization problems governed by elliptic Dirichlet problems was proposed recently based on the discrete variational outward normal derivatives. The advantages of this new formula over the previous one lie in the improved numerical accuracy and the continuity along the boundary. In the current paper we generalize this new formula to other shape optimization problems including the Laplace and Stokes eigenvalue optimization problems, the shape optimization of Stokes or Navier-Stokes flows, and the interface identification problems. We verify this new formula's numerical accuracy in different shape optimization problems and investigate its performance in several popular shape optimization algorithms. The second contribution of this paper is to propose a continuous discrete shape gradients of boundary type for Neumann problems, by using the ideas of gradient recovery techniques. The continuity property of the discrete boundary shape gradient is helpful in certain shape optimization algorithms and provides certain flexibility compared to the previous discontinuous ones, which are extensively discussed in the current paper.
关键词	shape optimization shape gradient boundary formulation boundary correction gradient recovery finite element method
DOI	10.1137/21M1457400
收录类别	SCI
语种	英语
资助项目	Strategic Priority Research Program of the Chinese Academy of Sciences[XDB 41000000] ; National Key Basic Research Program[2018YFB0704304] ; NSFC[12071149] ; Science and Technology Commission of Shanghai Municipality[18dz2271000] ; Science and Technology Commission of Shanghai Municipality[21JC1402500] ; Science and Technology Commission of Shanghai Municipality[19ZR1414100]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000881310800018
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60432
专题	中国科学院数学与系统科学研究院
通讯作者	Gong, Wei
作者单位	1.Chinese Acad Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, NCMIS, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China 4.East China Normal Univ, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China 5.East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
推荐引用方式 GB/T 7714	Gong, Wei,Li, Jiajie,Zhu, Shengfeng. IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2022,44(4):A2464-A2505.
APA	Gong, Wei,Li, Jiajie,&Zhu, Shengfeng.(2022).IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION.SIAM JOURNAL ON SCIENTIFIC COMPUTING,44(4),A2464-A2505.
MLA	Gong, Wei,et al."IMPROVED DISCRETE BOUNDARY TYPE SHAPE GRADIENTS FOR PDE-CONSTRAINED SHAPE OPTIMIZATION".SIAM JOURNAL ON SCIENTIFIC COMPUTING 44.4(2022):A2464-A2505.