Abstract
The inverse problem of determining the thermal conductivity coefficient depending on temperature is considered and investigated. The consideration is based on the initial boundary value problem for the non-stationary heat equation. The work is devoted to obtaining the necessary conditions for non-uniqueness of the considered inverse problem solution in the n-dimension case, and also to examine the possibility of applying the Fast Automatic Differentiation Technique to solve this problem by second-order methods. The examples of solving the inverse coefficient problem confirm the accuracy and efficiency of the proposed algorithm.
This work was partially supported by the Russian Foundation for Basic Research (project no. 19-01-00666 A).
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Albu, A., Zubov, V. (2021). Application of Second-Order Optimization Methods to Solving the Inverse Coefficient Problems. In: Olenev, N.N., Evtushenko, Y.G., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2021. Lecture Notes in Computer Science(), vol 13078. Springer, Cham. https://doi.org/10.1007/978-3-030-91059-4_25
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DOI: https://doi.org/10.1007/978-3-030-91059-4_25
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