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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 10, Pages 1760–1774 (Mi zvmmf10466)  

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

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


DOI: https://doi.org/10.7868/S0044466916100148

Full text: PDF file (593 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:10, 1743–1757

Bibliographic databases:

UDC: 519.633
Received: 18.05.2016

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  isi  scopus
    2. 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  mathnet  crossref  crossref  isi  elib
    3. 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  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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