Section: New Results

Frequency tools for the analysis of PDE's

Participants : Xavier Antoine, Bruno Pinçon, Karim Ramdani, Bertrand Thierry, Marius Tucsnak.

Our contribution in this direction mainly concerns the numerical approximation of scattering problems.

In [21] 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 [20] , we propose to simulate complex nonlinear physics problems related to the Schrödinger equations by using relaxation techniques coupled with absorbing boundary conditions or PMLs. This shows that these two methods are much more accurate than the usual complex scaling/absorbing potential approaches widely used in physics for domain truncation.

In [19] , complete high order absorbing boundary conditions are proposed, discretize and simulate for one- and two-dimensional nonlinear Schrödinger equations. In [38] , we propose new accurate absorbing boundary condition for computing nonlinear eigenvalue problems related to the Schrödinger equation.

In [57] , we propose a review of how pseudo differential operators theory help in building analytical preconditioners and well-posed integral equations for acoustics scattering. In [26] , we propose a new efficient and robust domain decomposition method for solving large scale three-dimensional acoustic scattering problems.