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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 12, Pages 2149–2162 (Mi zvmmf9806)  
This article is cited in 8 scientific papers (total in 8 papers)

Control of substance solidification in a complex-geometry mold

A. V. Albu, A. F. Albu, V. I. Zubov

Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
Full-text PDF (609 kB) Citations (8)
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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.
Key words: heat equation, solidification of metal, Stefan problem, optimal control, fast automatic differentiation, adjoint problem.
Received: 15.06.2012
English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 12, Pages 1612–1623
DOI: https://doi.org/10.1134/S0965542512120020
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: A. V. Albu, A. F. Albu, V. I. Zubov, “Control of substance solidification in a complex-geometry mold”, Zh. Vychisl. Mat. Mat. Fiz., 52:12 (2012), 2149–2162; Comput. Math. Math. Phys., 52:12 (2012), 1612–1623
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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