| The PDE-Constrained Optimization Method Based on MFS for Solving Inverse Heat Conduction Problems |
| Received:July 06, 2017 Revised:August 04, 2017 |
| Key Words:
inverse heat conduction problem PDE-constrained optimization method of fundamental solutions time-dependent heat source term Tikhonov regularization method
|
| Fund Project: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). |
|
| Hits: 1860 |
| Download times: 1620 |
| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.03.009 |
| View Full Text View/Add Comment |
