Skip to main content
SpringerLink
Log in

The optimization method in design problems of spherical layered thermal shells

  • Mechanics
  • Published:
Doklady Physics Aims and scope Submit manuscript

Abstract

The inverse problem of designing multilayered spherical shells, intended for thermal cloaking a spherical body or concentrating heat in it, has been analyzed. The stationary heat conduction equation for an anisotropic medium is applied as an original mathematical model. The optimization method is used to reduce this inverse problem to an extreme problem, where the role of controls is played by the thermal conductivities of shell layers. A numerical algorithm for solving the problem is proposed, and the results of computational experiments are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Guenneau, C. Amra, and D. Veynante, Opt. Express 20, 8207 (2012).

    Article  ADS  Google Scholar 

  2. T. Han and Z.-M. Wu, Prog. Electromagn. Res. 143, 131 (2013).

    Article  Google Scholar 

  3. T. Han and C.-W. Qiu, Optik 18, 044003 (2016).

    MathSciNet  Google Scholar 

  4. G. V. Alekseev, Problem of Invisibility in Acoustics, Optics, and Heat Transfer (Dal’nauka, Vladivostok, 2016) [in Russian].

    Google Scholar 

  5. A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving Ill-Posed Problems (Nauka, Moscow, 1986) [in Russian].

    MATH  Google Scholar 

  6. O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, Extreme Solutions of Ill-Posed Problem and Their Application to Inverse Heat Exchange Problems (Nauka, Moscow, 1988) [in Russian].

    MATH  Google Scholar 

  7. G. V. Alekseev, I. S. Vakhitov, and O. V. Soboleva, Comp. Math. Math. Phys. 52 (12), 1635 (2012).

    Article  Google Scholar 

  8. G. V. Alekseev and V. A. Levin, Dokl. Phys. 61 (11), 546 (2016).

    Article  ADS  Google Scholar 

  9. G. V. Alekseev, V. A. Levin, and D. A. Tereshko, Dokl. Phys. 62 (2), 71 (2017).

    Article  ADS  Google Scholar 

  10. J. Kennedy and R. Eberhart, Proc. IEEE Int. Conf. Neural Networks IV, 1942 (1995).

    Article  Google Scholar 

  11. R. Poli, J. Kennedy, and T. Blackwell, Swarm Intel. 1, 33 (2007).

    Article  Google Scholar 

  12. K. Chiba, Y. Makino, and T. Takatoya, J. Comp. Sci. Tech. 2 (1), 268 (2008).

    Article  Google Scholar 

  13. M. D. Ardakani and M. Khodadad, Inverse Probl. Sci. Eng. 17 (7), 855 (2009).

    Article  MathSciNet  Google Scholar 

  14. F.-B. Liu, Heat Mass Transfer 48, 99 (2012).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics, Far East Branch, Russian Academy of Sciences, Vladivostok, Russia

    G. V. Alekseev & D. A. Tereshko

  2. Far East State University, Vladivostok, Russia

    G. V. Alekseev, V. A. Levin & D. A. Tereshko

  3. Institute of Automation and Control Processes, Far East Branch, Russian Academy of Sciences, Vladivostok, Russia

    V. A. Levin

Authors
  1. G. V. Alekseev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Levin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. A. Tereshko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. V. Alekseev.

Additional information

Original Russian Text © G.V. Alekseev, V.A. Levin, D.A. Tereshko, 2017, published in Doklady Akademii Nauk, 2017, Vol. 476, No. 5, pp. 512–517.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alekseev, G.V., Levin, V.A. & Tereshko, D.A. The optimization method in design problems of spherical layered thermal shells. Dokl. Phys. 62, 465–469 (2017). https://doi.org/10.1134/S1028335817100044

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1028335817100044

Search

Navigation