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Optimal shapes for the control of nonlinear heat conduction

✍ Scribed by R. Butt; J.E. Rubio

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
655 KB
Volume
327
Category
Article
ISSN
0016-0032

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✦ Synopsis

The material derivative method is developed here for the optimal shape design in the control of a nonlinear heat conduction system in steady state described by a variational inequality. It is known that this method can be used for the optimal shape design for systems described by partial dtyerential equations ; it is used here for dtj$erential inequalities by taking limits of the expressions resulting from an approximation scheme. The computations are done by the finite element method; the gradient of the criteria as a function of the coordinates nodes is computed, and the performance criterion is then minimized by the material derivative method.

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## Abstract A new numerical method is developed for the boundary optimal control problems of the heat conduction equation in the present paper. When the boundary optimal control problem is solved by minimizing the objective function employing a conjugate‐gradient method, the most crucial step is th