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- Virginie Bonnaillie-Noël, Marc Dambrine
- Asymptotic Analysis
- 2013

The presence of small inclusions or of a surface defect modifies the solution of the Laplace equation posed in a reference domain Ω 0. If the characteristic size of the perturbation is small, then one can expect that the solution of the problem posed on the perturbed geometry is close to the solution of the reference shape. Asymptotic expansion with respect… (More)

- Virginie Bonnaillie-Noël, Marc Dambrine, Frédéric Hérau, Grégory Vial
- SIAM J. Math. Analysis
- 2010

Ventcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to wellposed varia-tional problems under a sign condition of a coefficient. Nevertheless situations where this condition is violated appeared in several works. The wellposedness of such problems was still open.… (More)

- M. Dambrine, G. Vial
- 2008

We consider some singular perturbations of the boundary of a smooth domain. Such domain variations are not differen-tiable within the classical theory of shape calculus. We mimic the topological asymptotic and we derive an asymptotic expansion of the shape function in terms of a size parameter. The two-dimensional case of the Dirichlet energy is treated in… (More)

We study the stability of some critical (or equilibrium) shapes in the minimization problem of the energy dissipated by a fluid (i.e. the drag minimization problem) governed by the Stokes equations. We first compute the shape derivative up to the second order, then provide a sufficient condition for the shape Hessian of the energy functional to be coercive… (More)

- Virginie Bonnaillie-Noël, Marc Dambrine, Frédéric Hérau, Grégory Vial
- Math. Comput.
- 2015

In this paper, we consider the equations of linear elasticity in an exterior domain. We exhibit artificial boundary conditions on a circle, which lead to a non-coercive second order boundary value problem. In the particular case of an axisymmetric geometry, explicit computations can be performed in Fourier series proving the well-posedness except for a… (More)

- A. Henrot, Gregoire Allaire, +8 authors SOKO LOWSKI
- 2008

Activities of the CNRS programme GDR Shape optimization are described. Recent developments in shape optimization for eingenvalues and drag minimization are presented.

- M. Dambrine, J. Soko, A. Żochowski
- 2005

The stability issue of critical shapes for shape optimization problems with the state function given by a solution to the Neumann problem for the Laplace equation is considered. To this end, the properties of the shape Hessian evaluated at critical shapes are analysed. First, it is proved that the stability cannot be expected for the model problem. Then,… (More)

- Q. V. Dang, A. Dequidt, L. Vermeiren, M. Dambrine
- 2014 IEEE/ASME International Conference on…
- 2014

Stability of force feedback haptic systems under variable time delays remains a major challenge. This paper presents a theoretical and experimental approach for studying the stability of a haptic interface in interaction with a virtual environment. A novel approach based on Lyapunov theory for assuring the stability of haptic systems under constant and… (More)

- MARC DAMBRINE
- 2008

The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a weak material approximation [4], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied… (More)

- Marc Dambrine, Isabelle Greff, Helmut Harbrecht, Bénédicte Puig
- J. Comput. Physics
- 2017