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Displaying similar documents to “Relating phase field and sharp interface approaches to structural topology optimization”

Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset  of a reference domain, and the complement of is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure , which is the total work of...

Global minimizer of the ground state for two phase conductors in low contrast regime

Antoine Laurain (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to and to small geometric perturbations of the optimal shape, that the global minimum of the...

Convex shape optimization for the least biharmonic Steklov eigenvalue

Pedro Ricardo Simão Antunes, Filippo Gazzola (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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The least Steklov eigenvalue for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the -norm of harmonic functions. These applications suggest to address the problem of minimizing in suitable classes of domains. We survey the existing results and conjectures about this topic;...

On shape optimization problems involving the fractional laplacian

Anne-Laure Dalibard, David Gérard-Varet (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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Our concern is the computation of optimal shapes in problems involving (−). We focus on the energy (Ω) associated to the solution of the basic Dirichlet problem ( − )  = 1 in Ω,  = 0 in Ω. We show that regular minimizers Ω of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the...

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.

Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini

Slim Chaabane, Mohamed Jaoua (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This work deals with a non linear inverse problem of reconstructing an unknown boundary , the boundary conditions prescribed on being of Signorini type, by using boundary measurements. The problem is turned into an optimal shape design one, by constructing a Kohn & Vogelius-like cost function, the only minimum of which is proved to be the unknown boundary. Furthermore, we prove that the derivative of this cost function with respect to a direction depends only on the state ...

Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Alfredo Candia-Véjar, Eduardo Álvarez-Miranda, Nelson Maculan (2011)

RAIRO - Operations Research

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Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90's and broadly studied in the past years. This approach named (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, , where uncertainty...