Abstract
The problem of determining the temperature-dependent thermal conductivity coefficient of a substance in a parallelepiped is considered and investigated. The consideration is carried out on the basis of the first boundary value problem for a three-dimensional non-stationary heat conduction equation. The inverse coefficient problem is reduced to a variational problem and is solved numerically using gradient methods for minimizing the cost functional. The mean-root-square deviations of the temperature field from the experimental data is used as the cost functional. It is well known that it is very important for the gradient methods to determine accurate values of the gradients. For this reason, in this paper we used the efficient Fast Automatic Differentiation technique, which gives the exact functional gradient for the discrete optimal control problem. In this work special attention is paid to the practically important cases when the experimental field is specified only in the subdomain of the object under consideration. The working capacity and effectiveness of the proposed approach are demonstrated by solving a number of nonlinear inverse problems.
This work was supported by the Russian Foundation for Basic Research (project no. 19-01-00666 A).
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Zubov, V., Albu, A. (2021). Identification of the Thermal Conductivity Coefficient of a Substance from a Temperature Field in a Three-Dimensional Domain. In: Pardalos, P., Khachay, M., Kazakov, A. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2021. Lecture Notes in Computer Science(), vol 12755. Springer, Cham. https://doi.org/10.1007/978-3-030-77876-7_26
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