| 초록 |
The goal of this work is to propose a better methodology for optimization of the spatial distribution of a certain variable such as the crystal surface temperature distribution in CZ process. We formulate a simple optimization problem by both considering the thermal stress distribution inside the crystal and the crystal growth rate. Based on calculus of variations and the method of Lagrange multiplier, we derive and solve Euler-Lagrange equations. Also we solve the same problem by using the conjugate direction method, which is among the techniques of nonlinear programming. Then we compare the histories of convergence during iterations between two methods. From this work, we can see that the numerical algorithm based on the calculus of variations has a strong point for the optimization problem in distributed parameter systems, at least in the view point of solution convergency.
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