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Identification of Discontinuous Thermal Conductivity Coefficient Using Fast Automatic Differentiation

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Learning and Intelligent Optimization (LION 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10556))

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Abstract

The problem of determining the thermal conductivity coefficient that depends on the temperature is studied. The consideration is based on the Dirichlet boundary value problem for the one-dimensional unsteady-state heat equation. The mean-root-square deviation of the temperature distribution field and the heat flux from the empirical data on the left boundary of the domain is used as the objective functional. An algorithm for the numerical solution of the problem based on the modern approach of Fast Automatic Differentiation is proposed. The case of discontinuous thermal conductivity coefficient is considered. Examples of solving the problem are discussed.

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References

  1. Alifanov, O.M., Cherepanov, V.V.: Mathematical simulation of high-porosity fibrous materials and determination of their physical properties. High Temp. 47, 438–447 (2009)

    Article  Google Scholar 

  2. Kozdoba, L.A., Krukovskii, P.G.: Methods for Solving Inverse Thermal Transfer Problems. Naukova Dumka, Kiev (1982). [in Russian]

    Google Scholar 

  3. Alifanov, O.M.: Inverse Problems of Heat Transfer. Mashinostroenie, Moscow (1988). [in Russian]

    MATH  Google Scholar 

  4. Marchuk, G.I.: Adjoint Equation and the Analysis of Complex Systems. Nauka, Moscow (1992). [in Russian]

    MATH  Google Scholar 

  5. Samarskii, A.A., Vabishchevich, P.N.: Computational Heat Transfer. Editorial URSS, Moscow (2003). [in Russian]

    Google Scholar 

  6. Zubov, V.I.: Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation. Comput. Math. Math. Phys. 56(10), 1743–1757 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  7. Evtushenko, Y.G.: Computation of exact gradients in distributed dynamic systems. Optim. Methods Softw. 9, 45–75 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the Russian Foundation for Basic Research (project no. 17-07-00493a).

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, Federal Research Center “Computer Science, and Control” of Russian Academy of Sciences, Moscow, Russia

    Alla F. Albu, Yury G. Evtushenko & Vladimir I. Zubov

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia

    Alla F. Albu, Yury G. Evtushenko & Vladimir I. Zubov

Authors
  1. Alla F. Albu
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  2. Yury G. Evtushenko
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  3. Vladimir I. Zubov
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Corresponding author

Correspondence to Vladimir I. Zubov .

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Editors and Affiliations

  1. University of Trento, Trento, Italy

    Roberto Battiti

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

  3. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

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Albu, A.F., Evtushenko, Y.G., Zubov, V.I. (2017). Identification of Discontinuous Thermal Conductivity Coefficient Using Fast Automatic Differentiation. In: Battiti, R., Kvasov, D., Sergeyev, Y. (eds) Learning and Intelligent Optimization. LION 2017. Lecture Notes in Computer Science(), vol 10556. Springer, Cham. https://doi.org/10.1007/978-3-319-69404-7_21

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  • DOI: https://doi.org/10.1007/978-3-319-69404-7_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69403-0

  • Online ISBN: 978-3-319-69404-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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