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A New Variational Approach for Inverse Source Problems
Hu, Qiya1,2; Shu, Shi3; Zou, Jun4
AbstractWe 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.
KeywordVariational approach inverse source problem stability convergence
Funding ProjectNatural 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 Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000453759200001
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Document Type期刊论文
Corresponding AuthorZou, Jun
Affiliation1.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
Recommended Citation
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.
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