Skip to main content
SpringerLink
Log in

Derivation of formulas for the gradient of the error in the iterative solution of inverse problems of heat conduction

I. Determination of the gradient in terms of the Green's function

  • Published:
Journal of engineering physics Aims and scope

Abstract

We consider the construction of the gradient of the error functional for the iterative solution of inverse problems involving equations of the parabolic type. The linear formulation of the problem is analyzed.

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

Literature cited

  1. V. A. Morozov, Computational Methods and Programming [in Russian], Issue 8, Moscow (1967), pp. 63–93.

  2. O. M. Alifanov, Inzh.-Fiz. Zh.,26, No. 4, 682–689 (1974).

    Google Scholar 

  3. O. M. Alifanov, Identification of Heat-Exchange Processes in Aircraft (Introduction to the Theory of Inverse Problems of Heat Exchange) [in Russian], Moscow (1979).

  4. A. V. Kryanev, Zh. Vychisl. Mat. Mat. Fiz.,14, No. 1, 25–35 (1974).

    Google Scholar 

  5. O. M. Alifanov and S. V. Rumyantsev, Dokl. Akad. Nauk SSSR,248, No. 6, 1289–1291 (1979).

    Google Scholar 

  6. S. V. Rumyantsev, “Regularizing gradient algorithms and their application to the analysis and interpretation of the data of physical experiments,” Author's Abstract of Candidate's Dissertation, Physicomathematical Sciences, Moscow (1981).

    Google Scholar 

  7. V. M. Yudin, Tr. TsAGI, Issue 1267, Moscow (1970).

  8. O. M. Alifanov and S. V. Rumyantsev, Inzh.-Fiz. Zh.,39, No. 2, 253–258 (1980).

    Google Scholar 

  9. S. F. Gilyazov, Methods and Algorithms in Numerical Analysis [in Russian], Moscow (1981), pp. 50–65.

  10. O. M. Alifanov and V. V. Mikhailov, Inzh.-Fiz. Zh.,35, No. 6, 1124–1129 (1978).

    Google Scholar 

  11. E. A. Artyukhin, Inzh.-Fiz. Zh.,41, No. 4, 587–592 (1981).

    Google Scholar 

  12. O. M. Alifanov, Inzh.-Fiz. Zh.,45, No. 5, 742–752 (1983).

    Google Scholar 

  13. A. Fridman, Partial Differential Equations of the Parabolic Type [in Russian], Moscow (1968).

  14. R. Arima, J. Math. Kyoto Univ.,4, No. 1, 207–244 (1964).

    Google Scholar 

  15. A. G. Butkovskii, Characteristics of Systems with Distributed Parameters [in Russian], Moscow (1979).

  16. É. M. Kartashov, Analytical Methods in the Theory of Heat Conduction in Solids [in Russian], Moscow (1979).

Download references

Author information

Authors and Affiliations

  1. Sergo Ordzhonikidze Aviation Institute, Moscow

    O. M. Alifanov

Authors
  1. O. M. Alifanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 3, pp. 476–485, March, 1987.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alifanov, O.M. Derivation of formulas for the gradient of the error in the iterative solution of inverse problems of heat conduction. Journal of Engineering Physics 52, 352–359 (1987). https://doi.org/10.1007/BF00872522

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00872522

Keywords

Search

Navigation