SECOND-ORDER DYNAMIC METHOD FOR OBTAINING APPROXIMATE SOLUTIONS TO MULTIDIMENSIONAL INVERSE HEAT CONDUCTION PROBLEMS

Authors

  • Yu.M. Matsevity A. Pidgorny Institute of Mechanical Engineering Problems of the NAS of Ukraine, Kharkiv
  • Yu.O. Tymoshenko Institute for Applied System Analysis National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv https://orcid.org/0000-0001-7812-6437

DOI:

https://doi.org/10.15407/dopovidi2023.04.020

Keywords:

inverse heat conduction problems, ill-posted problems, dynamic regularization method

Abstract

The formulation of the non-stationary thermal conductivity inverse problem is discussed in its general form. It is demonstrated that such formulations belong to the class of ill-posed problems. A dynamic method employing first- and second-order regularization is proposed to address these ill-posed problems. It is proven that the second-order dynamic regularization method enables the derivation of approximate solutions even in the presence of disturbances in the input data

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References

Tikhonov, A. N. & Arsenin, V. Ya. (1979). Methods for solving ill-posed problems. Moscow: Nauka (in Russian).

Matsevity, Yu. M. (1986). On regularization by coarsening and increasing its accuracy in solving inverse problems of heat conduction. Dopov. Acad. nauk USSR, No. 5, pp. 486-488 (in Russian).

Matsevity, Yu. M. (2002). Inverse problems of heat conduction. Vol. 1. Methodology. Kyiv: Naukova Dumka (in Russian).

Alifanov, O. M., Artyukhin, E. A., & Rumyantsev, S. V. (1988). Extremal methods for solving non-correct problems. Moscow: Nauka (in Russian).

Alifanov, O. M. (1988). Inverse problems of heat transfer. Moscow: Mashinostroenie (in Russian).

Gutenmakher, L. I., Timoshenko, Yu. A. & Tikhonchuk, S. T. (1977). On a dynamic method for solving ill-posed problems. Dokl. AN SSSR. 237, No. 4, pp. 776-778 (in Russian).

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Published

08.09.2023

How to Cite

Matsevity, Y., & Tymoshenko, Y. (2023). SECOND-ORDER DYNAMIC METHOD FOR OBTAINING APPROXIMATE SOLUTIONS TO MULTIDIMENSIONAL INVERSE HEAT CONDUCTION PROBLEMS. Reports of the National Academy of Sciences of Ukraine, (4), 20–25. https://doi.org/10.15407/dopovidi2023.04.020

Section

Mechanics

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