The PDE-constrained optimization method based on MFS for solving inverse heat conduction problems
Received:July 06, 2017  Revised:July 06, 2017
Key Word: Inverse heat conduction problem   PDE-constrained optimization   Method of fundamental solutions   Time-dependent heat source   Tikhonov regularization method  
Fund ProjectL:the National Natural Science Foundation of China(Nos. 11290143, 11471066, 11572081), the Fundamental Research of Civil Aircraft (No.MJ-F-2012-04), the Fundamental Research Funds for the Central Universities (DUT15LK44), and the Scientific Research Funds of Inner Mongolia University for the Nationalities(NMD1304)
Author NameAffiliationE-mail
Yong-Fu Zhang Dalian University of Technology 
Chong-Jun Li Dalian University of Technology  
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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. The 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. Due to the initial measured data containing the noisy error, and the resultant systems of equations are usually extremely sensitive and 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 accurate, effective and robust by some numerical tests
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