Modelling control of crystal growth processes

The goal of this paper is to describe an efficient cost-effective mathematical modelfor controlling the Czochralski crystal growth process. We first consider the governing equations for a class of MHD problems. We then choose the use of an externally applied magnetic field as a control mechanism. We examine theoretical and numerical results applicable to the optimal control of evolutionary magnetically conducted flows. The appropriate state equations are derived. First-order necessary conditions are examined. Next, we develop numerical methods for solving the necessary conditions of optimality, and alternative cost-efficient algorithms are discussed. Finally, these results are used to design a control strategy for the Czochralski crystal growth process.