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On the controlling of liquid metal solidification in foundry practice

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Operations Research Proceedings 2011

Part of the book series: Operations Research Proceedings ((ORP))

Abstract

The optimal control problem of metal solidification in casting is considered. The process is modeled by a three dimensional two phase initial-boundary value problem of the Stefan type. The optimal control problem was solved numerically using the gradient method. The gradient of the cost function was found with the help of the conjugate problem. The discreet conjugate problem was posed with the help of the Fast Automatic Differentiation technique.

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References

  1. Albu, A.F., Zubov, V.I.: Mathematical Modeling and Study of the Process of Solidification in Metal Casting. Computational Mathematics and Mathematical Physics 47, 843–862 (2007)

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  2. Albu, A.F., Zubov, V.I.: Functional Gradient Evaluation in an Optimal Control Problem Related to Metal Solidification. Computational Mathematics and Mathematical Physics 49, 47–70 (2009)

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  3. Albu, A.V., Albu, A.F., Zubov, V.I.: Functional Gradient Evaluation in the Optimal Control of a Complex Dynamical System. Computational Mathematics and Mathematical Physics 51, 762–780 (2011)

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  4. Albu, A.V., Zubov, V.I.: Choosing a Cost Functional and a Difference Scheme in the Optimal Control of Metal Solidification. Computational Mathematics and Mathematical Physics 51, 21–34 (2011)

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  5. Evtushenko, Y.G.: Computation of Exact Gradients in Distributed Dynamic Systems. Optimizat. Methods and Software 9, 45–75 (1998)

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Author information

Authors and Affiliations

  1. Computing Center RAS, Vavilov st. 40, 119333, Moscow, Russia

    Andrey Albu & Vladimir Zubov

Authors
  1. Andrey Albu
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  2. Vladimir Zubov
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Corresponding author

Correspondence to Andrey Albu .

Editor information

Editors and Affiliations

  1. Institut für, Betriebswirtschaftslehre, Universität Zürich, Moussonstrasse, Zurich, 8044, Switzerland

    Diethard Klatte

  2. Inst. Operations Research, ETH Zürich, Rämistr. 101, Zürich, 8092, Switzerland

    Hans-Jakob Lüthi

  3. Institut für, Betriebswirtschaftslehre, Universität Zürich, Moussonstrasse 15, Zurich, 8044, Switzerland

    Karl Schmedders

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Albu, A., Zubov, V. (2012). On the controlling of liquid metal solidification in foundry practice. In: Klatte, D., Lüthi, HJ., Schmedders, K. (eds) Operations Research Proceedings 2011. Operations Research Proceedings. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29210-1_1

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