Michael Scheffler
Schedae Informaticae, Volume 21, 2012, pp. 81-105
https://doi.org/10.4467/20838476SI.12.006.0816The paper deals with the numerical treatment of the optimal control of drying of materials which may lead to cracks. The drying process is controlled by temperature, velocity and humidity of the surrounding air. The state equations define the humidity and temperature distribution within a simplified wood specimen for given controls. The elasticity equation describes the internal stresses under humidity and temperature changes. To avoid cracks these internal stresses have to be limited. The related constraints are treated by smoothed exact barrier-penalty techniques. The objective functional of the optimal control problem is of tracking type. Further it contains a quadratic regularization by an energy term for the control variables (surrounding air) and barrier-penalty terms.
The necessary optimality conditions of the auxiliary problem form a coupled system of nonlinear equations in appropriate function spaces. This optimality system is given by the state equations and the related adjoint equations, but also by an approximate projection onto the admissible set of controls by means of barrier-penalty terms. This system is discretized by finite elements and treated iteratively for given controls. The optimal control itself is performed by quasi-Newton techniques.