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...
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...
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...
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 aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical
variational approach without and with a regularization term in order to
smooth the contours of the classified image. Then we present the general
topological asymptotic analysis, and we finally introduce its application to
the grey-level image classification problem.
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