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

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

International audienc

Matched Asymptotic Expansions of the Eigenvalues of a 3-D boundary-value problem relative to two cavities linked by a hole of small size

International audienc

Mathematical justification of the Rayleigh conductivity model for perforated plates in acoustics

International audienceThis paper is devoted to the mathematical justification of the usual models predicting the effective reflection and transmission of an acoustic wave by a low porosity multiperforated plate. Some previous intuitive approximations require that the wavelength be large compared with the spacing separating two neighboring apertures. In particular, we show that this basic assumption is not mandatory. Actually, it is enough to assume that this distance is less than a half-wavelength. The main tools used are the method of matched asymptotic expansions and lattice sums for the Helmholtz equations. Some numerical experiments illustrate the theoretical derivations

A Symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

International audienceA general symmetric Trefftz Discontinuous Galerkin method is builtfor solving the Helmholtz equation with piecewise constant coefficients.The construction of the corresponding local solutions to the Helmholtzequation is based on a boundary element method. A series of numericalexperiments displays an excellent stability of the method relativelyto the penalty parameters, and more importantly its outstanding abilityto reduce the instabilities known as the pollution effect inthe literature on numerical simulations of long-range wave propagation