Displaying similar documents to “A moving mesh fictitious domain approach for shape optimization problems”

Boundary integral representations of second derivatives in shape optimization

Karsten Eppler (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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For a shape optimization problem second derivatives are investigated, obtained by a special approach for the description of the boundary variation and the use of a potential ansatz for the state. The natural embedding of the problem in a Banach space allows the application of a standard differential calculus in order to get second derivatives by a straight forward "repetition of differentiation". Moreover, by using boundary value characerizations for more regular data, a complete boundary...

An Optimum Design Problem in Magnetostatics

Antoine Henrot, Grégory Villemin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.