The PDE-Constrained Optimization Method Based on MFS for Solving Inverse Heat Conduction Problems  

作　　者：Yongfu ZHANG Chongjun LI 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology [2]College of Mathematics, Inner Mongolia University for Nationalities

出　　处：《Journal of Mathematical Research with Applications》2018年第3期303-330,共28页数学研究及应用（英文版）

基　　金：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);the Scientific Research Funds of Inner Mongolia University for the Nationalities(Grant No.NMD1304)

摘　　要：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 crossvalidation criterion is applied to obtain more stable numerical solutions. It is shown that the proposed schemes are effective by some numerical tests.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 crossvalidation criterion is applied to obtain more stable numerical solutions. It is shown that the proposed schemes are effective by some numerical tests.

关 键 词：inverse heat conduction problem PDE-constrained optimization method offundamental solutions time-dependent heat source term Tikhonov regularization method 

分 类 号：O551.3[理学—热学与物质分子运动论]