Highly Accurate Computation of Spatial-Dependent Heat Conductivity and Heat Capacity in Inverse Thermal Problem
Chein-Shan Liu, Li-Wei Liu and Hong-Ki Hong

doi:10.3970/cmes.2007.017.001
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 17, No. 1, pp. 1-18, 2007
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Keywords Inverse problem, One-step group preserving scheme, Inverse thermal problem, Estimation of thermophysical parameters, Lie-group estimation method, Closed-form estimation.
Abstract In this paper we are concerned with the parameters identification of the inverse heat conduction problems governed by linear parabolic partial differential equations (PDEs). It is the first time that one can construct a closed-form estimation method for the inverse thermal problems of estimating the spatial-dependent thermophysical parameters. The key points hinge on an establishment of a one-step group preserving scheme (GPS) for the semi-discretization of PDEs, as well as a closed-form solution of the resulting algebraic equations. The new method, namely the Lie-group estimation method, has four advantages: it does not require any prior information on the functional forms of thermal conductivity and heat capacity; no initial guesses are required; no iterations are required; and the inverse problem can be solved in closed-form. Numerical examples were examined to convince that the new approach is highly accurate and efficient with the maximum estimation error very small even for identifying the highly discontinuous and oscillatory parameters. Although the estimation is carried out under a large measurement noise, our method is also stable.
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