Marc Dambrine

Interactions between moderately close inclusions for the Laplace equation

The presence of small inclusions modifies the solution of the Laplace equation posed in a reference domain Ω0. This question has been studied extensively for a single inclusion or well-separated inclusions. In two-dimensional situations, we investigate the case where the distance between the holes tends to zero but remains large with respect to their characteristic size. We first consider two perfectly insulated inclusions. In this configuration we give a complete multiscale asymptotic expansion of the solution to the Laplace equation. We also address the situation of a single inclusion close to a singular perturbation of the boundary ∂Ω0. We also present numerical experiments implementing a multiscale superposition method based on our first order expansion.

On Second Order Shape Optimization Methods for Electrical Impedance Tomography

This paper is devoted to the analysis of a second order method for recovering the a priori unknown shape of an inclusion

Shape Methods for the Transmission Problem with a Single Measurement

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On Generalized Ventcel's Type Boundary Conditions for Laplace Operator in a Bounded Domain

inside a body

DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS

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Interactions between moderately close circular inclusions: the Dirichlet-Laplace equation in the plane

from boundary measurement. This inverse problem—known as electrical impedance tomography—has many important practical applications and hence has been the focus of much attention during the past few years. However, to the best of our knowledge, no work has yet considered a second order approach for this problem. This paper aims to fill that void: We investigate the existence of second order derivative of the state

Shape optimization for quadratic functionals and states with random right-hand sides

u

Localization of small obstacles in Stokes flow

with respect to perturbations of the shape of the interface

Effect of surface defects on structure failure: A two-scale approach

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Shape optimization methods for the inverse obstacle problem with generalized impedance boundary conditions

. Then we choose a cost function in order to recover the geometry of