Ivan Hlaváček, Jan Chleboun (1996)
Applications of Mathematics
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A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
Dalibor Lukáš (2004)
Applications of Mathematics
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In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization...
Ivan Hlaváček, Raino Mäkinen (1991)
Applications of Mathematics
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An axisymmetric second order elliptic problem with mixed boundarz conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The numerical realization is presented in detail. The convergence of piecewise linear approximations is proved. Several numerical examples are given.
Jaroslav Haslinger, Raino Mäkinen (1997)
Applications of Mathematics
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Optimal shape design problem for a deformable body in contact with a rigid foundation is studied. The body is made from material obeying a nonlinear Hooke’s law. We study the existence of an optimal shape as well as its approximation with the finite element method. Practical realization with nonlinear programming is discussed. A numerical example is included.