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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 1, Pages 51–75 (Mi zvmmf52)  

This article is cited in 11 scientific papers (total in 11 papers)

Determination of functional gradient in an optimal control problem related to metal solidification

A. F. Albu, V. I. Zubov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: The gradient of the cost functional in the discrete optimal control problem of metal solidification in casting is exactly evaluated. The mathematical model describing the solidification process is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. Formulas determining exact gradient determination are derived using the fast automatic differentiation technique.

Key words: heat conduction, solidification, Stefan problem, optimal control, fast automatic differentiation, adjoint problem.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:1, 47–70

Bibliographic databases:

UDC: 519.626
Received: 21.03.2008

Citation: A. F. Albu, V. I. Zubov, “Determination of functional gradient in an optimal control problem related to metal solidification”, Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 51–75; Comput. Math. Math. Phys., 49:1 (2009), 47–70

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. Alla Albu, Vladimir Zubov, “Optimal control for one complex dynamic system, II”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, no. 2, 3–18  mathnet  mathscinet  zmath
    2. A. V. Albu, V. I. Zubov, “Choosing a cost functional and a difference scheme in the optimal control of metal solidification”, Comput. Math. Math. Phys., 51:1 (2011), 21–34  mathnet  crossref  mathscinet  isi
    3. A. V. Albu, A. F. Albu, V. I. Zubov, “Functional gradient evaluation in the optimal control of a complex dynamical system”, Comput. Math. Math. Phys., 51:5 (2011), 762–780  mathnet  crossref  mathscinet  isi
    4. Albu A., Zubov V., “On the controlling of liquid metal solidification in foundry practice”, Operations Research Proceedings 2011, Operations Research Proceedings, eds. Klatte D., Luthi H., Schmedders K., Springer-Verlag, Berlin, 2012, 3–8  crossref  mathscinet  isi
    5. A. V. Albu, A. F. Albu, V. I. Zubov, “Control of substance solidification in a complex-geometry mold”, Comput. Math. Math. Phys., 52:12 (2012), 1612–1623  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. A. F. Albu, V. I. Zubov, “On the influence of setup parameters on the control of solidification in metal casting”, Comput. Math. Math. Phys., 53:2 (2013), 170–179  mathnet  crossref  crossref  zmath  adsnasa  isi  elib  elib
    7. A. F. Albu, V. I. Zubov, “Investigation of the optimal control problem for metal solidification in a new formulation”, Comput. Math. Math. Phys., 54:5 (2014), 756–766  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. 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
    9. 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
    10. 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
    11. F. H. Muldoon, “Numerical study of hydrothermal wave suppression in thermocapillary flow using a predictive control method”, Comput. Math. Math. Phys., 58:4 (2018), 493–507  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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