A New Variational Approach for Inverse Source Problems

doi:10.4208/nmtma.OA-2017-0124

	A New Variational Approach for Inverse Source Problems
	Hu, Qiya1,2 ; Shu, Shi 3; Zou, Jun 4
	2019-05-01
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
卷号	12 期号:2 页码:331-347
摘要	We propose a new variational approach for recovering a general source profile in an elliptic system, using measurement data from the interior of the physical domain. The solution of the ill-posed inverse source problem is achieved by solving only one well-posed direct elliptic problem, resulting in the same computational cost as the one for the direct problem, and hence making the whole solution process of the inverse problem much less expensive than most existing methods. The resulting approximate solution is shown to be stable with respect to the change of the noise in the observation data, and a desired error estimate is also established in terms of the mesh size and the noise level in observation data. Numerical experiments are presented to confirm the theoretical predictions.
关键词	Variational approach inverse source problem stability convergence
DOI	10.4208/nmtma.OA-2017-0124
语种	英语
资助项目	Natural Science Foundation of China[G11571352] ; NSFC[G11571293] ; Hunan Provincial Civil-Military Integration Industrial Development Project "Adaptive Multilevel Solver and Its Application in ICF Numerical Simulation" ; Hong Kong RGC General Research Fund[14322516] ; Hong Kong RGC General Research Fund[14306814]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000453759200001
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31888
专题	计算数学与科学工程计算研究所
通讯作者	Zou, Jun
作者单位	1.Chinese Acad Sci, SLSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Hunan 411105, Peoples R China 4.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Hu, Qiya,Shu, Shi,Zou, Jun. A New Variational Approach for Inverse Source Problems[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2019,12(2):331-347.
APA	Hu, Qiya,Shu, Shi,&Zou, Jun.(2019).A New Variational Approach for Inverse Source Problems.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,12(2),331-347.
MLA	Hu, Qiya,et al."A New Variational Approach for Inverse Source Problems".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 12.2(2019):331-347.