Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization

doi:10.1007/s10543-019-00782-3

	Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization
	Zhu, Shengfeng 1,2; Hu, Xianliang 3; Liao, Qifeng4
	2019-11-16
发表期刊	BIT NUMERICAL MATHEMATICS
ISSN	0006-3835
EISSN	1572-9125
发表状态	已发表
DOI	10.1007/s10543-019-00782-3
摘要	This paper concerns the accuracy of Galerkin finite element approximations to two types of shape gradients for eigenvalue optimization. Under certain regularity assumptions on domains, a priori error estimates are obtained for the two approximate shape gradients. Our convergence analysis shows that the volume integral formula converges faster and offers higher accuracy than the boundary integral formula. Numerical experiments validate the theoretical results for the problem with a pure Dirichlet boundary condition. For the problem with a pure Neumann boundary condition, the boundary formulation numerically converges as fast as the distributed type.
关键词	Shape optimization Shape gradient Eigenvalue problem Finite element Error estimate Multiple eigenvalue
收录类别	SCI ; SCIE
语种	英语
资助项目	Natural Science Foundation of Shanghai[19ZR1414100] ; Science and Technology Commission of Shanghai Municipality[18dz2271000] ; National Natural Science Foundation of China[11201153][11571115][11601329]
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000541900300001
出版者	SPRINGER
WOS关键词	LEVEL SET METHODS ; DESIGN SENSITIVITY
原始文献类型	Article
引用统计
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/102143
专题	信息科学与技术学院信息科学与技术学院_PI研究组_廖奇峰组
通讯作者	Zhu, Shengfeng
作者单位	1.East China Normal Univ, Sch Math Sci, Dept Data Math, Shanghai 200241, Peoples R China 2.East China Normal Univ, Sch Math Sci, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China 3.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China 4.ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai 201210, Peoples R China
推荐引用方式 GB/T 7714	Zhu, Shengfeng,Hu, Xianliang,Liao, Qifeng. Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization[J]. BIT NUMERICAL MATHEMATICS,2019.
APA	Zhu, Shengfeng,Hu, Xianliang,&Liao, Qifeng.(2019).Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization.BIT NUMERICAL MATHEMATICS.
MLA	Zhu, Shengfeng,et al."Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization".BIT NUMERICAL MATHEMATICS (2019).