engleski

Some advances in optimality criteria method

The optimality criteria method appears to be the most popular numerical method for optimal design problems. We shall present how this method can be applied in some more complicated situations: multiple state optimal design problem for stationary diffusion, optimal design for wave equation and inverse problem for stationary diffusion equation (in connection with the Dirichlet to Neumann map). In each case we work in three-dimensional space setting, looking for the arrangement of two given isotropic materials. The homogenisation method, as a relaxation tool, enables us to use standard variational techniques for obtaining necessary conditions of optimality, the starting point for the optimality criteria method. More precisely, in this iterative method the following design is calculated from the assumption that preceding design satisfies necessary conditions of optimality. For this purpose we use explicit calculations of optimal microstructures in some modification of energy bounds of Hashin-Shtrikman type. In the presented algorithms, this result enables us to calculate explicitly the next iteration, similarly as it was done in the case of one state optimal design for stationary diffusion, where all iterations correspond to simple laminates.

optimal design; optimality criteria method

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