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

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.