Skip to main content
SpringerLink
Log in

Control of substance solidification in a complex-geometry mold

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

Abstract

The control of metal solidification in a mold of complex geometry is studied. The underlying mathematical model is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. The mathematical formulation of the optimal control problem for the solidification process is presented. This problem was solved numerically using gradient optimization methods. The gradient of the cost function was computed by applying the fast automatic differentiation technique, which yields the exact value of the cost function gradient for the chosen discrete version of the optimal control problem. The results of the study are described and analyzed. Some of the results are illustrated as plots.

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. 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, 24–38 (2011).

    MathSciNet  MATH  Google Scholar 

  3. 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 

  4. Y. G. Evtushenko, “Computation of Exact Gradients in Distributed Dynamic Systems,” Optimizat. Methods Software, No. 9, 45–75 (1998).

  5. 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 

Download references

Author information

Authors and Affiliations

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

    A. V. Albu, A. F. Albu & V. I. Zubov

Authors
  1. A. V. Albu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. F. Albu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. 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.V. Albu, A.F. Albu, V.I. Zubov, 2012, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2012, Vol. 52, No. 12, pp. 2149–2162.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Albu, A.V., Albu, A.F. & Zubov, V.I. Control of substance solidification in a complex-geometry mold. Comput. Math. and Math. Phys. 52, 1612–1623 (2012). https://doi.org/10.1134/S0965542512120020

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542512120020

Keywords

Search

Navigation