Section: New Results

Frequency domain methods for the analysis and control of systems governed by PDE's

In [21] and [20] , we propose an asymptotic analysis for the simple layer potential for multiple scattering at low frequencies.

In [19] we propose some strategies to solve numerically the difficult problem of multiple scattering by a large number of disks at high frequency. To achieve this, we combine a Fourier series decomposition with the EFIE integral equation. Numerical examples will be presented to show the efficiency of our method.

In [32] , we are concerned with the convergence analysis of the iterative algorithm for solving initial data inverse problems from partial observations that has been recently proposed in Ramdani et al. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed).

In [23] , we propose a strategy to determine the Dirichlet-to-Neumann (DtN) operator for infinite, lossy and locally perturbed hexagonal periodic media, using a factorization of this operator involving two non local operators. The first one is a DtN type operator and corresponds to a half-space problem, while the second one is a Dirichlet-to-Dirichlet (DtD) type operator related to the symmetry properties of the problem.

In [18] , we investigate absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential.