ZOLÉSIO , Jean-Paul

We wish to consider in this paper the numerical approximation of the solution of a wave equation when the boundaries of the spatial domain are moving. This problem has many practical applications in engineering science. One encounters wave systems in evolving domains in widely disseminated situations, such that rolling or unrolling antennas of...

We consider weak eulerian evolution of domains through the convection of a measurable set by a nonsmooth vector field $V$.We introduce the concept of tubes by ``product space'' and we show a closure result leading to existence results in non cylindrical shape evolution and a new shape metric using the tube geodesic

We consider weak eulerian evolution of domains through the convection of a measurable set by a nonsmooth vector field V. The transverse variation leads to derivative of functional associated to the evolutiontube and we propose eulerian variational formulation for several classical problems such as incompressible euler flow ( in \cite{chemnitz},...

We consider the free boundary identification problem in a steady viscoplastic flow. The fluid motion is governed by the incompressible Norton-Hoff model coupled with the heat equation. The viscosity of the fluid is modeled by the Arrhenius law .Our point of view is to treat the problem as a shape sensitivity of a cost functional formulated on...

This report deals with problems arising in the optimal control for fluid-struc- ture interaction systems. Our model consists of a fluid described by the incompressible Navier-Stokes equations interacting with an elastically supported rigid solid. We characterize the structure of the gradient of a cost function to be minimized using a new...

We propose a variational formulation of a macroscopic model for crowd motion involving a conservation law describing mass conservation coupled with an eikonal equation giving the flow direction. To get a self contain paper we recall many results concerning flow mapping and convection process associated with non smooth vector field V.

Le but de ce rapport est de donner l'expression de la derivée de forme de fonctionnelles associées à des problmes d'évolution non-cylindrique. Le point clé de ce travail réside dans la définition des perturbations d'un domaine non-cylindrique [appelé aussi tube] en utilisant des champs de vecteurs transverses. Sous des hypothèses de...

This paper deals with a dynamical shape control problem. The state equations are the non-cylindrical Navier-Stokes equations with a non-homogenous Dirichlet condition. The goal is to compute a necessary optimality condition for the considered functional (kinetic energy). Our work is based on the "transformation" of the domain functional on a...

We are interested in the study of a quasistatic visco-plastic flow with thermal effects. The fluid motion is governed by the incompressible Norton-Hof- f model coupled with the dynamic heat equation whose the dissipation mecanicha- l power is the source term. The viscosity of the fluid is modeled by the Arrhenuis law.One of the principal aims...

Nous considérons un nouveau problème de type optimisation et contrôle optimale pour le calcul des regimes harmoniques en électromagnétisme 3D. Cette approche est robuste dans le sens que les coefficients du milieu peuvent être variable et même varier lentement avec le temps. Etant donnée une fréquence $\omega$ on approche la solution $E$...

The paper provides shape derivative analysis for the wave equation with mixed boundary conditions on a moving domain Ωs in the case of non smooth neumann boundary datum. The key ideas in the paper are (i) bypassing the classical sensitivity analysis of the state by using parameter differentiability of a functional expressed in the form of...

Ce rapport s'insère dans le cadre d'études en conception optimale de forme aérodynamique pour lequelles on cherche des paramétrisations géométriques adaptées à l'écoulement . On présente ici une méthode pour identifier un ensemble de fonctions de forme visant à capter la sensibilité de l'écoulement à la géométrie. On modélise la perturbation du...

This report deals with recent progress in the study of shape optimization problems in case of a moving domain. We may restrict ourself to the case of newtonian viscous incompressible fluids described by the Navier-Stokes equations. We suggest three strategies in order to solve an optimal control problem involving the shape variable,...

Novel developments of the so-called controlled evolution of level sets [ Ramananjaona et al., 2001b ], which is devoted to shape identification of homogeneous scattering obstacles buried in a known space from time-harmonic wave field data, are considered herein. The emphasis is twofold: regularization of the geometry of the sought...