The PDE-Constrained Optimization Method Based on MFS for Solving Inverse Heat Conduction Problems
Received:July 06, 2017  Revised:August 04, 2017
Key Word: inverse heat conduction problem   PDE-constrained optimization   method of fundamental solutions   time-dependent heat source term   Tikhonov regularization method  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11290143; 11471066; 11572081), the Fundamental Research of Civil Aircraft (Grant No.MJ-F-2012-04), the Fundamental Research Funds for the Central Universities (Grant No.DUT15LK44) and the Scientific Research Funds of Inner Mongolia University for the Nationalities (Grant No.NMD1304).
Author NameAffiliation
Yongfu ZHANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
College of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia 028043, P. R. China 
Chongjun LI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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      In this paper, we present an effective meshless method for solving the inverse heat conduction problems, with the Neumann boundary condition. A PDE-constrained optimization method is developed to get a global approximation scheme in both spatial and temporal domains, by using the fundamental solution of the governing equation as the basis function. Since the initial measured data contain some noises, and the resulting systems of equations are usually ill-conditioned, the Tikhonov regularization technique with the generalized cross-validation criterion is applied to obtain more stable numerical solutions. It is shown that the proposed schemes are effective by some numerical tests.
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