Abstract:
The gradient of the cost functional in a discrete optimal control problem for metal solidification in metal casting is exactly calculated. In contrast to previous studies, the object under analysis has a complex geometric shape. The mathematical model for describing the solidification process is based on a three-dimensional two-phase initial–boundary value problem of the Stefan type. Formulas for exact gradient evaluation are derived using the fast automatic differentiation technique.
Key words:heat equation, metal solidification, Stefan problem, optimal control problem, fast automatic differentiation, adjoint optimal control problem.
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