Skip to main content
SpringerLink
Log in

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

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

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.

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

References

  1. A. F. Albu and V. I. Zubov, “Mathematical modeling and study of the process of solidification in metal casting,” Comput. Math. Math. Phys. 47, 843–862 (2007).

    Article  MathSciNet  Google Scholar 

  2. A. F. Albu and V. I. Zubov, “Optimal control of the solidification process in metal casting,” Comput. Math. Math. Phys. 48, 805–815 (2008).

    Article  MathSciNet  Google Scholar 

  3. A. F. Albu and V. I. Zubov, “Determination of functional gradient in an optimal control problem related to metal solidification,” Comput. Math. Math. Phys. 49, 47–70 (2009).

    Article  MathSciNet  Google Scholar 

  4. A. V. Albu and V. I. Zubov, “Choosing a cost functional and a difference scheme in the optimal control of metal solidification,” Comput. Math. Math. Phys. 51(1), 24–38 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  5. A. V. Albu, A. F. Albu, and V. I. Zubov, “Functional gradient evaluation in the optimal control of a complex dynamical system,” Comput. Math. Math. Phys. 51, 762–780 (2011).

    Article  MathSciNet  Google Scholar 

  6. A. V. Albu, A. F. Albu, and V. I. Zubov, “Control of substance solidification in a complex-geometry mold,” Comput. Math. Math. Phys. 52, 1612–1623 (2012).

    Article  MathSciNet  Google Scholar 

  7. A. F. Albu and V. I. Zubov, “On the influence of setup parameters on the control of solidification in metal casting,” Comput. Math. Math. Phys. 53, 170–179 (2013).

    Article  Google Scholar 

  8. A. Albu and V. Zubov, “On the controlling of liquid metal solidification in foundry practice,” Operations Research Proceedings 2011: Selected Papers of the International Conference on Operations Research (OR 2011), August 30–September 2, 2011, Zurich, Switzerland, Ed. by D. Klatte, H.-J. Lüthi, and K. Schmedders (Springer, Berlin, 2012), pp. 3–8.

    Chapter  Google Scholar 

  9. A. V. Albu and V. I. Zubov, “Investigation of the optimal control problem for metal solidification in a new formulation,” Comput. Math. Math. Phys. 54, 756–766 (2014).

    Article  MathSciNet  Google Scholar 

  10. Yu. G. Evtushenko, “Computation of exact gradients in distributed dynamic systems,” Optim. Methods Software, No. 9, 45–75 (1998).

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    A. F. Albu & V. I. Zubov

  2. Moscow Institute of Physics and Technology, Technical University, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    V. I. Zubov

Authors
  1. A. F. Albu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Zubov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Zubov.

Additional information

Original Russian Text © A.F. Albu, V.I. Zubov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 12, pp. 1879–1893.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Albu, A.F., Zubov, V.I. Investigation of the optimal control of metal solidification for a complex-geometry object in a new formulation. Comput. Math. and Math. Phys. 54, 1804–1816 (2014). https://doi.org/10.1134/S0965542514120057

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542514120057

Keywords

Search

Navigation