engleski

Variants of optimality criteria method for optimal design problems

We consider multiple state optimal design problems, aiming to find the best arrangement of two given isotropic materials, such that the obtained body has some optimal properties regarding m different regimes. Speaking in terms of thermal conductivity, the cost function is an integral functional taking into account temperatures u_1, ..., u_m (state functions) of the body, obtained for different right hand sides (given source terms) f_1, ..., f_m. Using the homogenisation method as the relaxation tool, the standard variational techniques lead to necessary conditions of optimality. These conditions give the basis for the optimality criteria method, a commonly used numerical (iterative) method for optimal design problems. We study two variants of this method. The explicit calculation of the design update is possible for both of them, making the implementation much simpler and similar to the case of one state equation.

optimal design; optimality criteria method

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