Investigation of the optimal control problem for metal solidification in a new formulation

被引：5

作者：

Albu, A. F. ^{[1
]}

Zubov, V. I. ^{[2
]}

机构：

[1] Russian Acad Sci, Dorodnicyn Comp Ctr, Moscow 119333, Russia

[2] Tech Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2014年 / 54卷 / 05期

基金：

俄罗斯基础研究基金会;

关键词：

heat equation; metal solidification; Stefan problem; optimal control; fast automatic differentiation; FUNCTIONAL GRADIENT;

D O I：

10.1134/S0965542514050042

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

New formulations of the optimal control problem for metal solidification in a furnace are proposed and studied. The underlying mathematical model of the process 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 computed by applying the fast automatic differentiation technique, which yields the exact value of the cost function gradient for a chosen discrete version of the optimal control problem. The research results are described and analyzed. Some of the results are illustrated.

引用

页码：756 / 766

页数：11

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