Advertisement

Computational Mathematics and Mathematical Physics

, Volume 58, Issue 12, pp 2031–2042 | Cite as

Identification of the Thermal Conductivity Coefficient Using a Given Surface Heat Flux

  • A. F. Albu
  • V. I. ZubovEmail author
Article
  • 2 Downloads

Abstract

The inverse problem of determining a temperature-dependent thermal conductivity coefficient is studied. The study is based on the Dirichlet boundary value problem for the two-dimensional nonstationary heat equation. The cost functional is defined as the rms deviation of the surface heat flux from experimental data. For the numerical solution of the problem, an algorithm based on the modern fast automatic differentiation technique is proposed. Examples of solving the posed problem are given.

Keywords:

heat conduction inverse coefficient problems gradient heat equation adjoint equations numerical algorithm 

Notes

ACKNOWLEDGMENTS

This work was supported in part by the Russian Foundation for Basic Research, no. 17-07-00493a.

REFERENCES

  1. 1.
    O. M. Alifanov and V. V. Cherepanov, “Mathematical simulation of high-porosity fibrous materials and determination of their physical properties,” High Temp. 47 (3), 438–447 (2009).CrossRefGoogle Scholar
  2. 2.
    O. M. Alifanov, Inverse Heat Transfer Problems (Mashinostroenie, Moscow, 1988; Springer, Berlin, 2011).Google Scholar
  3. 3.
    V. I. Zubov, “Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation,” Comput. Math. Math. Phys. 56 (10), 1743–1757 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Yu. G. Evtushenko, Optimization and Fast Automatic Differentiation (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2013) [in Russian].Google Scholar
  5. 5.
    Yu. G. Evtushenko and V. I. Zubov, “Generalized fast automatic differentiation technique,” Comput. Math. Math. Phys. 56 (11), 1819–1833 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Yu. G. Evtushenko, E. S. Zasukhina, and V. I. Zubov, “Numerical optimization of solutions to Burgers’ problems by means of boundary conditions,” Comput. Math. Math. Phys. 37 (12), 1406–1414 (1997).MathSciNetzbMATHGoogle Scholar
  7. 7.
    A. F. Albu and V. I. Zubov, “Investigation of the optimal control of metal solidification for a complex-geometry object in a new formulation,” Comput. Math. Math. Phys. 54 (12), 1804–1816 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    A. F. Albu and V. I. Zubov, “On the efficient solution of optimal control problems using the fast automatic differentiation approach,” Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk 21 (4), 20–29 (2015).Google Scholar
  9. 9.
    A. F. Albu, Y. G. Evtushenko, and V. I. Zubov, “Identification of discontinuous thermal conductivity coefficient using fast automatic differentiation,” Lect. Notes Comput. Sci. 10556, 295–300 (2017).CrossRefGoogle Scholar
  10. 10.
    A. F. Albu and V. I. Zubov, “Identification of thermal conductivity coefficient using a given temperature field,” Comput. Math. Math. Phys. 58 (10), 1585–1599 (2018).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    F. P. Vasil’ev, Optimization Methods (Faktorial, Moscow, 2002) [in Russian].Google Scholar
  12. 12.
    A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, 2001).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of SciencesMoscowRussia
  2. 2.Moscow Institute of Physics and Technology (State University)DolgoprudnyiRussia

Personalised recommendations