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The extended adjoint method

Stanislas Larnier, Mohamed Masmoudi (2013)

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

Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need the fundamental solution of the problem; furthermore...

The extended adjoint method

Stanislas Larnier, Mohamed Masmoudi (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need...

The topological asymptotic expansion for the Quasi-Stokes problem

Maatoug Hassine, Mohamed Masmoudi (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized...

The topological asymptotic expansion for the Quasi-Stokes problem

Maatoug Hassine, Mohamed Masmoudi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized...

Topological asymptotic analysis of the Kirchhoff plate bending problem

Samuel Amstutz, Antonio A. Novotny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation, like the insertion of holes, inclusions, cracks. In this work we present the calculation of the topological derivative for a class of shape functionals associated to the Kirchhoff plate bending problem, when a circular inclusion is introduced at an arbitrary point of the domain. According to the literature, the topological derivative has been fully developed...

Topological asymptotic analysis of the Kirchhoff plate bending problem

Samuel Amstutz, Antonio A. Novotny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation, like the insertion of holes, inclusions, cracks. In this work we present the calculation of the topological derivative for a class of shape functionals associated to the Kirchhoff plate bending problem, when a circular inclusion is introduced at an arbitrary point of the domain. According to the literature, the topological derivative has been fully developed...

Topology optimization of quasistatic contact problems

Andrzej Myśliński (2012)

International Journal of Applied Mathematics and Computer Science

This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the...

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