Displaying similar documents to “Adaptive finite element method for shape optimization”

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...

Shape and topology optimization of the robust compliance the level set method

Frédéric de Gournay, Grégoire Allaire, François Jouve (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this paper is to study the so-called worst-case or robust optimal design problem for minimal compliance. In the context of linear elasticity we seek an optimal shape which minimizes the largest, or worst, compliance when the loads are subject to some unknown perturbations. We first prove that, for a fixed shape, there exists indeed a worst perturbation (possibly non unique) that we characterize as the maximizer of a nonlinear energy. We also propose a stable algorithm...

A priori error estimates for finite element discretizations of a shape optimization problem

Bernhard Kiniger, Boris Vexler (2013)

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

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In this paper we consider a model shape optimization problem. The state variable solves an elliptic equation on a domain with one part of the boundary described as the graph of a control function. We prove higher regularity of the control and develop error analysis for the finite element discretization of the shape optimization problem under consideration. The derived error estimates are illustrated on two numerical examples.