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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 5, Pages 734–745 (Mi zvmmf10028)  

This article is cited in 4 scientific papers (total in 4 papers)

Investigation of the optimal control problem for metal solidification in a new formulation

A. F. Albua, V. I. Zubovab

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 and studied. The underlying mathematical model of the process 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 computed by applying the fast automatic differentiation technique, which yields the exact value of the cost function gradient for a chosen discrete version of the optimal control problem. 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/S0044466914050056

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:5, 756–766

Bibliographic databases:

UDC: 519.626
Received: 21.11.2013

Citation: A. F. Albu, V. I. Zubov, “Investigation of the optimal control problem for metal solidification in a new formulation”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 734–745; Comput. Math. Math. Phys., 54:5 (2014), 756–766

Citation in format AMSBIB
\by A.~F.~Albu, V.~I.~Zubov
\paper Investigation of the optimal control problem for metal solidification in a new formulation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2014
\vol 54
\issue 5
\pages 734--745
\jour Comput. Math. Math. Phys.
\yr 2014
\vol 54
\issue 5
\pages 756--766

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    This publication is cited in the following articles:
    1. A. F. Albu, 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 (2014), 1804–1816  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    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  isi  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. 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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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