Displaying similar documents to “Removing holes in topological shape optimization”

The topological asymptotic expansion for the Quasi-Stokes problem

Maatoug Hassine, Mohamed Masmoudi (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

A penalty method for topology optimization subject to a pointwise state constraint

Samuel Amstutz (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.

The topological asymptotic for the Navier-Stokes equations

Samuel Amstutz (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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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...