Comparative application of CGM and Wiener filtering techniques for the estimation of heat flux distribution. (English) Zbl 1220.65127
Summary: The conjugate gradient method (CGM), formulated with the adjoint problem, is adopted in this study as the functional minimization tool for the solution of the 2-D steady-state linear inverse heat conduction problem with the aim of estimating the heat flux density distribution on a given surface using the temperature distribution as input data. The robustness of the solution strategy, based on an iterative regularization scheme, is compared with another consolidated estimation methodology adopted in the literature to handle the same problem: the Wiener filtering technique. The comparison is performed by adopting a noisy test signal aimed at simulating infrared temperature maps. Using a comparative approach, the problem’s particular difficulties related to the high number of unknowns and to the deficiency of the estimation techniques at the domain’s geometrical boundaries are discussed.
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 35K05 | Heat equation |
| 35R30 | Inverse problems for PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
inverse heat conduction problem; conjugate gradient method; Wiener filter; numerical examples; iterative regularization schemeReferences:
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