On the Stability of the Algorithm of Identification of the Thermal Conductivity Coefficient
The paper is devoted to the inverse problem of determining the thermal conductivity coefficient of substance depending on the temperature. The consideration is based on the first boundary value problem for the non-stationary heat equation. The mean-root-square deviation of the temperature distribution field and the heat flux on the boundary of the domain from the experimental data is used as the cost functional. The algorithm for the numerical solution of the problem based on the modern approach of Fast Automatic Differentiation was proposed by the authors in previous works. In the present paper, a numerical stability analysis of the obtained solutions is carried out. It is shown that the perturbation of the restored thermal conductivity coefficient is of the same order as the perturbation of the experimental data that caused it. Many illustrative examples are presented.
KeywordsInverse coefficient problems Heat equation Numerical algorithm
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