The application of FAD-methodology to optimal control of melting process
by
A.F. Albou
Computing Center of Russian Academy of Sciences, Vavilova, 40, 117967, GSP-1, Moscow, Russia
Coauthors: Yu.G.Evtushenko, Computing Center of Russian Academy of Sciences, Moscow, Russia, V.I. Zubov, Computing Center of Russian Academy of Sciences, Moscow, Russia

Based on FAD new methodology for calculating the gradient in controlled systems governed by a partial differential equations is applied to optimization of melting process. In this problem it is necessary to melt the certain part of the metallic sample using the minimal heat consumption. The time depending heat energy supply was considered as a distributed control function. We investigated the cases of space distributed source as well as the point ones. The unsteady melting process was considered. The temperature field and line separating the phases were found using Stephan equation, which was discretized by finite different approximation scheme. Nonuniform computation grid was used. Using canonical equations we found the corresponding discretization of adjoint equations and gradient with respect to control variables. The variation problem was solved numerically with the help of gradient methods. A lot of calculations were made. It was found that if there were no restrictions on source power from the top then the optimal control was delta function; if there are restrictions from the top then the optimal control consists of two parts coinciding with the boundary. The calculations also showed that the best results can be received if the space width of the source was a little bit larger the melting area.

http://homepages.feis.herts.ac.uk/~comqun/AD2000/Ext_Abstracts/Albou.ps

Date received: December 29, 1999