L²(H¹γ) finite element convergence for degenerate isotropic Hamilton–Jacobi–Bellman equations

In this paper we study the convergence of monotone P1 finite element methods for fully nonlinear Hamilton–Jacobi–Bellman equations with degenerate, isotropic diffusions. The main result is strong convergence of the numerical solutions in a weighted Sobolev space L²(H¹γ(Ω)) to the viscosity solution without assuming uniform parabolicity of the HJB operator

Numerical study of acoustic multiperforated plates

International audienceIt is rather classical to model multiperforated plates by approximate impedance boundary conditions. In this article we would like to compare an instance of such boundary conditions obtained through a matched asymptotic expansions technique to direct numerical computations based on a boundary element formulation in the case of linear acoustic

Lower and upper bounds for the Rayleigh conductivity of a perforated plate

International audienceLower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for inclined perforations. The main techniques are a proper use of the variational principles of Dirichlet and Kelvin in the context of Beppo-Levi spaces. The derivations are validated by numerical experiments in the two-dimensional axisymmetric case and the full three-dimensional one

Sur l'approximation rationnelle de fonctions de la variable complexe au sens de la norme de Hardy

Université : Université scientifique et médicale de Grenobl

Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems

International audienceWe present in this study some three-dimensional numerical results that validate the use of the linear sampling method as an inverse solver in electromagnetic scattering problems. We recall that this method allows the reconstruction of the shape of an obstacle from the knowledge of multi-static radar data at a fixed frequency. It does not require any a priori knowledge of the physical properties of the scatterer nor any nonlinear optimization scheme. This study also contains some analytical results in the simplified case of a spherical scatterer that somehow make the link between known abstract theoretical results and the numerical scheme. Special attention has been given to pointing out the influence of the frequency on the inversion accuracy

A New Formulation for Scattering by Impedant 3D Bodies

International audienceA new integral equation formulation is introduced for solving, in the frequency domain, the problem of electromagnetic scattering by an impedant (IBC) or perfect electric/magnetic (PEC/PMC) 3D body of arbitrary shape. It is based firstly, on a special application of the equivalence principle [2] where the 0-field exterior domain is filled with another impedant medium and, secondly, on the widely used PMCHW (Poggio, Miller, Chang, Harrington and Wu) formulation which forces field continuity through the scatterer surface [3]. Unlike other IBC formulations such as [4], this one also applies to PEC/PMC. Furthermore, in this last case, it appears to stabilize the numerical scheme in the vicinity of eigen frequencies. We will provide proofs and conditions of the wellposedness of the problem for impedant as well as for PEC/PMC bodies

Analysis of two linear sampling methods applied to electromagnetic imaging of buried objects

International audienc

On the validation of the linear sampling method in electromagnetic inverse scattering problems

International audienc