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ABSTRACT
In this paper, we shall derive and propose an efficient algorithm for simultaneously reconstructing the Robin coefficient and heat flux in an elliptic system from part of the boundary measurements. The uniqueness of the simultaneous identification is demonstrated. The ill-posed inverse problem is formulated into an output least-squares nonlinear and non-convex minimization with Tikhonov regularization, while the regularizing effects of the regularized system are justified. The Levenberg–Marquardt method is applied to change the non-convex minimization into convex minimization, which will be solved by surrogate functional method so as to get the explicit expression of the minimizer. Numerical experiments are provided to show the accuracy and efficiency of the algorithm.
Acknowledgements
The author would like to thank Professor Masahiro Yamamoto (University of Tokyo) and Professor Jun Zou (Chinese University of Hong Kong) for their valuable discussions and comments, two anonymous referees for their many constructive comments and suggestions, which have helped us improve the organization and the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
The work of Daijun Jiang has been financially supported by self-determined research funds of CCNU from the colleges' basic research and operation of MOE [No. CCNU14A05039], National Natural Science Foundation of China [Nos. 11326233, 11401241 and 11571265] and China Postdoctoral Science Foundation [Grant no. 2012M521444].