### A moving mesh fictitious domain approach for shape optimization problems

Raino A. E. Mäkinen, Tuomo Rossi, Jari Toivanen (2000)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Raino A. E. Mäkinen, Tuomo Rossi, Jari Toivanen (2000)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

Marc Dambrine, Djalil Kateb (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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...

Bijan Mohammadi (2010)

Control and Cybernetics

Similarity:

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

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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...

Antoine Henrot, Grégory Villemin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

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.

Andrzej Myśliński (2006)

Control and Cybernetics

Similarity:

Grégoire Allaire, Frédéric de Gournay, François Jouve, Anca-Maria Toader (2005)

Control and Cybernetics

Similarity:

Karsten Eppler (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

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...

J. Haslinger, P. Neittaanmäki (1987)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity: