Displaying similar documents to “On solution to an optimal shape design problem in 3-dimensional linear magnetostatics”

On the ersatz material approximation in level-set methods

Marc Dambrine, Djalil Kateb (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire , (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...

Numerical analysis for optimal shape design in elliptic boundary value problems

Zdeněk Kestřánek (1988)

Aplikace matematiky

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Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system...

Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls

Jana Daňková, Jaroslav Haslinger (1996)

Applications of Mathematics

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We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.