Abstract
In this paper the optimal design of a vertical reactor for growing crystals and epitaxial layers by physical vapor transport technique is discussed. The transport phenomena involved in the deposition process is modeled by the gasdynamics equations and chemical kinematics. The problem is formulated as a shape optimization with respect to the geometry of the reactor and an optimal control problem by controlling the wall temperature. The material and shape derivatives of solutions to the so-called Boussinesq approximation are derived. Optimality condition and a numerical optimization method based on the augmented Lagrangian method are discussed for the boundary control of the Boussinesq flow. A numerical approximation based on the Jacobi polynomials for the axi-symmetric flow is developed along with a discussion of an iterative method based on GMRES for solving the resulting system of nonlinear equations.
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Ito, K., Tran, H.T., Scroggs, J.S. (1995). Mathematical Issues in Optimal Design of a Vapor Transport Reactor. In: Gunzburger, M.D. (eds) Flow Control. The IMA Volumes in Mathematics and its Applications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2526-3_9
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DOI: https://doi.org/10.1007/978-1-4612-2526-3_9
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