RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Zh. Vychisl. Mat. Mat. Fiz.: Year: Volume: Issue: Page: Find

 Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 12, Pages 1879–1893 (Mi zvmmf10122)

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

A. F. Albua, V. I. Zubovba

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
b Moscow Institute of Physics and Technology, Technical University, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

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.

Key words: heat equation, metal solidification, Stefan problem, optimal control, fast automatic differentiation.

DOI: https://doi.org/10.7868/S0044466914120059

Full text: PDF file (643 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2014, 54:12, 1804–1816

Bibliographic databases:

UDC: 519.626

Citation: A. F. Albu, V. I. Zubov, “Investigation of the optimal control of metal solidification for a complex-geometry object in a new formulation”, Zh. Vychisl. Mat. Mat. Fiz., 54:12 (2014), 1879–1893; Comput. Math. Math. Phys., 54:12 (2014), 1804–1816

Citation in format AMSBIB
\Bibitem{AlbZub14} \by A.~F.~Albu, V.~I.~Zubov \paper Investigation of the optimal control of metal solidification for a complex-geometry object in a new formulation \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2014 \vol 54 \issue 12 \pages 1879--1893 \mathnet{http://mi.mathnet.ru/zvmmf10122} \crossref{https://doi.org/10.7868/S0044466914120059} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3291547} \elib{http://elibrary.ru/item.asp?id=22453415} \transl \jour Comput. Math. Math. Phys. \yr 2014 \vol 54 \issue 12 \pages 1804--1816 \crossref{https://doi.org/10.1134/S0965542514120057} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000346411700005} \elib{http://elibrary.ru/item.asp?id=24022007} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919710732} 

• http://mi.mathnet.ru/eng/zvmmf10122
• http://mi.mathnet.ru/eng/zvmmf/v54/i12/p1879

 SHARE:

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. A. Albu, V. Zubov, “An approach to solving control problems of heat processes with phase transitions”, 2017 International Conference on Control, Artificial Intelligence, Robotics & Optimization, ICCAIRO 2017, IEEE, 147–153
2. A. F. Albu, V. I. Zubov, “On the efficiency of solving optimal control problems by means of Fast Automatic Differentiation technique”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 1–10
3. 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
4. V. I. Zubov, “Application of fast automatic differentiation for solving the inverse coefficient problem for the heat equation”, Comput. Math. Math. Phys., 56:10 (2016), 1743–1757
5. S. A. Nekrasov, V. S. Volkov, “Optimalnoe upravlenie v probleme Stefana i metody ego vychisleniya”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2016, no. 2, 87–100
6. Yu. G. Evtushenko, V. I. Zubov, “Generalized fast automatic differentiation technique”, Comput. Math. Math. Phys., 56:11 (2016), 1819–1833
7. A. F. Albu, V. I. Zubov, “Identification of thermal conductivity coefficient using a given temperature field”, Comput. Math. Math. Phys., 58:10 (2018), 1585–1599
8. V. I. Zubov, A. F. Albu, “Identification of the thermal conductivity coefficient using a given surface heat flux”, Comput. Math. Math. Phys., 58:12 (2018), 2031–2042
•  Number of views: This page: 166 Full text: 24 References: 22 First page: 15