This article is cited in 3 scientific papers (total in 3 papers)
Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation
V. I. Zubovab
a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia
The problem of determining the thermal conductivity coefficient that depends on temperature is studied. The consideration is based on the initial-boundary value problem for the one-dimensional unsteady heat equation. The mean-root-square deviation of the temperature distribution field and the heat flux from the experimental data on the left boundary of the domain is used as the objective functional. An analytical expression for the gradient of the objective functional is obtained. An algorithm for the numerical solution of the problem based on the modern fast automatic differentiation technique is proposed. Examples of solving the problem are discussed.
heat conduction, inverse coefficient problems, gradient, heat equation, adjoint equations, numerical algorithm.
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Computational Mathematics and Mathematical Physics, 2016, 56:10, 1743–1757
V. I. Zubov, “Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation”, Zh. Vychisl. Mat. Mat. Fiz., 56:10 (2016), 1760–1774; Comput. Math. Math. Phys., 56:10 (2016), 1743–1757
Citation in format AMSBIB
\paper Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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This publication is cited in the following articles:
A. F. Albu, Yu. G. Evtushenko, V. I. Zubov, “Identification of discontinuous thermal conductivity coefficient using fast automatic differentiation”, 11th International Conference on Learning and Intelligent Optimization (LION 2017), Lecture Notes in Computer Science, 10556, eds. R. Battiti, D. Kvasov, Y. Sergeyev, Springer, 2017, 295–300
A. F. Albu, V. I. Zubov, “Identification of thermal conductivity coefficient using a given temperature field”, Comput. Math. Math. Phys., 58:10 (2018), 1585–1599
V. I. Zubov, A. F. Albu, “Identification of the thermal conductivity coefficient using a given surface heat flux”, Comput. Math. Math. Phys., 58:12 (2018), 2031–2042
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