Séminaire du pôle Analyse

11h30, salle de séminaire du CMAP.

Abstract: We are interested in the scattering of time-harmonic waves in infinite complex media. The complexity of the media comes from the nature of the equations (Maxwell's or elasticity equations), its physical characteristics (periodic, stratified, or anisotropic coefficients) and/or even its geometry (infinite 2D or 3D media or 3D plates). Solving time harmonic scalar waves equations in infinite homogeneous media is an old topic and there exist several methods. They are all based on the natural idea of reducing the pure numerical computations to a bounded domain containing the perturbations (achieved using for instance Finite Element methods), coupled with, for example, integral equation techniques, transparent boundary conditions involving Dirichlet-to-Neumann operators or the Perfectly Matched Layer techniques. However it seems that all these methods either do not extend to complex media or do extend but with a tremendous computational cost.

By contrast, our method is based on a simple and quite general idea: the solution of halfspace problems can be expressed thanks to its trace on the edge of the half-space, via the Fourier transform in the transverse direction in the homogeneous case or via the Floquet-Bloch Transform in the periodic case. The system of equations to solve couples the traces of the solution on the edges of the half-spaces with the restriction of the solution in a square.