engleski

Second order shape derivatives - numerical applications for optimal design problems

We consider optimal design problems for stationary diffusion equation, seeking for an arrangement of two isotropic materials, with prescribed amounts, which maximizes a given functional. We presented some classes of optimal design problems on an annulus with classical solutions. First and second order shape derivatives for the considered problem are derived for numerical implementations. Descent methods based on distributed first and second order shape derivatives are implemented and tested. We observe a stable convergence of both descent methods with a novel Newton-like method converging in half as many steps.

optimal design ; homogenization ; shape derivative ; gradient method

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