This article is cited in 16 papers

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

A. F. Albu^a, V. I. Zubov<sup>ba

a</sup> 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.

UDC: 519.626

Received: 26.06.2014

DOI: 10.7868/S0044466914120059

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

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