Optimal Control in a Bounded Domain for Wave Propagating in the Whole Space: Coupling Through Boundary Integral Equations

doi:10.1007/s10915-022-01953-1

CSpace

	Optimal Control in a Bounded Domain for Wave Propagating in the Whole Space: Coupling Through Boundary Integral Equations
	Gong, Wei 1,2; Li, Buyang 3; Yang, Huanhuan 4
	2022-09-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	92 期号:3 页码:52
摘要	This paper is concerned with an optimal control problem in a bounded-domain Omega(0) under the constraint of a wave equation in the whole space. The problem is regularized and then reformulated as an initial-boundary value problem of the wave equation in a bounded domain Omega( )superset of (Omega) over bar (0 )coupled with a set of boundary integral equations on partial derivative Omega taking account of wave propagation through the boundary. The well-posedness and stability of the reformulated problem are proved. A fully discrete finite element method is proposed for solving the reformulated problem. In particular, the wave equation in the bounded domain is discretized by an averaged central difference method in time, and the boundary integral equations are discretized in time by using the convolution quadrature generated by the second-order backward difference formula. The finite and boundary element methods are used for spatial discretization of the wave equation and the boundary integral equations, respectively. The stability and convergence of the numerical method are also proved. Finally, the spatial and temporal convergence rates are validated numerically in 2D.
关键词	Wave equation Unbounded domain Boundary integral equation Well-posedness Convolution quadrature Stability Convergence Error estimate
DOI	10.1007/s10915-022-01953-1
收录类别	SCI
语种	英语
资助项目	Key Research Program of the Chinese Academy of Sciences[XDPB11] ; National Key Basic Research Program[2018YFB0704304] ; National Natural Science Foundation of China[11671391] ; Research Grants Council of the Hong Kong Special Administrative Region, China (GRF Project)[PolyU15300817] ; Hong Kong Polytechnic University (PolyU)[P0031035] ; key research projects of general universities in Guangdong Province[2019KZDXM034] ; basic research and applied basic research projects in Guangdong Province (Projects of Guangdong, Hong Kong and Macao Center for Applied Mathematics)[2020B1515310018]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000831254300001
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61152
专题	中国科学院数学与系统科学研究院
通讯作者	Yang, Huanhuan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing 100190, Peoples R China 3.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China 4.Shantou Univ, Dept Math, Shantou 515063, Peoples R China
推荐引用方式 GB/T 7714	Gong, Wei,Li, Buyang,Yang, Huanhuan. Optimal Control in a Bounded Domain for Wave Propagating in the Whole Space: Coupling Through Boundary Integral Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2022,92(3):52.
APA	Gong, Wei,Li, Buyang,&Yang, Huanhuan.(2022).Optimal Control in a Bounded Domain for Wave Propagating in the Whole Space: Coupling Through Boundary Integral Equations.JOURNAL OF SCIENTIFIC COMPUTING,92(3),52.
MLA	Gong, Wei,et al."Optimal Control in a Bounded Domain for Wave Propagating in the Whole Space: Coupling Through Boundary Integral Equations".JOURNAL OF SCIENTIFIC COMPUTING 92.3(2022):52.