Displaying similar documents to “On the ersatz material approximation in level-set methods”

Multi-phase structural optimization via a level set method

G. Allaire, C. Dapogny, G. Delgado, G. Michailidis (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves...

On solution to an optimal shape design problem in 3-dimensional linear magnetostatics

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...