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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

The lightest plane structures of a bounded stress level transmitting a point load to a circular support

Cezary Graczykowski, Tomasz Lewiński (2005)

Control and Cybernetics

The Obstacle Problem Revisited.

L.A. Caffarelli (1998)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

The optimal shape of a dendrite sealed at both ends

Yannick Privat (2009)

Annales de l'I.H.P. Analyse non linéaire

The problem of the body of revolution of minimal resistance

Alexander Plakhov, Alena Aleksenko (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of convex axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class of axially symmetric but generally nonconvex bodies. The infimum in this problem is not attained. We construct a sequence of bodies minimizing the resistance. This sequence approximates a convex body with smooth front surface, while the surface of approximating bodies...

The surface evolver.

Brakke, Kenneth A. (1992)

Experimental Mathematics

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

The topological asymptotic for the Navier-Stokes equations

Samuel Amstutz (2005)

ESAIM: Control, Optimisation and Calculus of Variations

The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples of cost functional...

The topological asymptotic for the Navier-Stokes equations

Samuel Amstutz (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The uniqueness as a generic property for some one-dimensional segmentation problems

Micol Amar, Virginia De Cicco (1992)

Rendiconti del Seminario Matematico della Università di Padova

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

Topological derivative for linear elastic plate bending problems

A. Novotny, R. Feijóo, C. Padra, E. Taroco (2005)

Control and Cybernetics

Topological derivatives for semilinear elliptic equations

Mohamed Iguernane, Serguei A. Nazarov, Jean-Rodolphe Roche, Jan Sokolowski, Katarzyna Szulc (2009)

International Journal of Applied Mathematics and Computer Science

The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L∞ norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.

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