Optimal Control of Glass Cooling Using Simplified PN Theory

This paper summarizes work that the authors were involved in on the optimal control of cooling processes in industrial glass manufacturing. The problem is formulated as the minimization of a functional constrained by equations for the temperature and the radiation field. In an optimization algorithm, this system of constraints has to be solved tens of times. The problem becomes numerically tractable if we substitute the radiative transfer equation for the photons by its SPN approximation. We derive steady and time-dependent SPN approximations for radiative transfer in glass using an asymptotic analysis. An optimization algorithm using adjoint information from the forward problem is designed using an abstract Newton's method. We show the results of one sample cooling problem.