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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 10, Pages 1760–1774
DOI: https://doi.org/10.7868/S0044466916100148 (Mi zvmmf10466) 		 
This article is cited in 15 scientific papers (total in 15 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
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DOI: https://doi.org/10.7868/S0044466916100148
Abstract: 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.
Key words: heat conduction, inverse coefficient problems, gradient, heat equation, adjoint equations, numerical algorithm.
Funding agency Grant number
Russian Science Foundation 14-11-00782
Received: 18.05.2016
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 10, Pages 1743–1757
DOI: https://doi.org/10.1134/S0965542516100146
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: 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
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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