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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 12, Pages 1879–1893 (Mi zvmmf10122)  

This article is cited in 8 scientific papers (total in 8 papers)

Investigation of the optimal control of metal solidification for a complex-geometry object in a new formulation

A. F. Albua, V. I. Zubovba

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Moscow Institute of Physics and Technology, Technical University, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

Abstract: New formulations of the optimal control problem for metal solidification in a furnace are proposed in the case of an object of complex geometry. The underlying mathematical model is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. The formulated problems are solved numerically with the help of gradient optimization methods. The gradient of the cost function is exactly computed by applying the fast automatic differentiation technique. The research results are described and analyzed. Some of the results are illustrated.

Key words: heat equation, metal solidification, Stefan problem, optimal control, fast automatic differentiation.

DOI: https://doi.org/10.7868/S0044466914120059

Full text: PDF file (643 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:12, 1804–1816

Bibliographic databases:

UDC: 519.626
Received: 26.06.2014

Citation: A. F. Albu, V. I. Zubov, “Investigation of the optimal control of metal solidification for a complex-geometry object in a new formulation”, Zh. Vychisl. Mat. Mat. Fiz., 54:12 (2014), 1879–1893; Comput. Math. Math. Phys., 54:12 (2014), 1804–1816

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Albu, V. Zubov, “An approach to solving control problems of heat processes with phase transitions”, 2017 International Conference on Control, Artificial Intelligence, Robotics & Optimization, ICCAIRO 2017, IEEE, 147–153  crossref  isi  scopus
    2. A. F. Albu, V. I. Zubov, “On the efficiency of solving optimal control problems by means of Fast Automatic Differentiation technique”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 1–10  mathnet  crossref  mathscinet  elib
    3. A. F. Albu, “Control of phase boundary evolution in metal solidification for new thermodynamic parameters of the metal”, Comput. Math. Math. Phys., 56:5 (2016), 756–763  mathnet  crossref  crossref  isi  elib
    4. V. I. Zubov, “Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation”, Comput. Math. Math. Phys., 56:10 (2016), 1743–1757  mathnet  crossref  crossref  isi  elib
    5. S. A. Nekrasov, V. S. Volkov, “Optimalnoe upravlenie v probleme Stefana i metody ego vychisleniya”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2016, no. 2, 87–100  mathnet  crossref  elib
    6. Yu. G. Evtushenko, V. I. Zubov, “Generalized fast automatic differentiation technique”, Comput. Math. Math. Phys., 56:11 (2016), 1819–1833  mathnet  crossref  crossref  isi  elib
    7. A. F. Albu, V. I. Zubov, “Identification of thermal conductivity coefficient using a given temperature field”, Comput. Math. Math. Phys., 58:10 (2018), 1585–1599  mathnet  crossref  crossref  isi  elib
    8. V. I. Zubov, A. F. Albu, “Identification of the thermal conductivity coefficient using a given surface heat flux”, Comput. Math. Math. Phys., 58:12 (2018), 2031–2042  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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