Section: New Results

Maxwell system in strongky absorbing layers

Participants : Hélène Barucq, Mathieu Fontes, Dimitri Komatitsch.

We have develop a model for modeling the propagation of waves in absorbing media. The first study we realize concerns the long-time behavior of the electromagnetic field propagating into a bianisotropic medium. We have proven that there exists an energy which is the combination of the first and second-order electromagnetic energies which is exponentially decreasing if the field propagates into a strictly star-shaped domain bounded by a Silver-Müller boundary. This is a new result because we had to consider the case where both the electric and the magnetic field are not divergence free. The second study consists in extending the first one to the case of PML models. We began by writing a PML version of the model and we have proven that we have to replace the functions tensors by pseudodifferential operators which corresponds to the case of a bianisotropic medium with memory effects. We have then established the problem admits a single solution and we have perform a numerical analysis of the behavior of the electromagnetic energy. Our numerical investigations show that the energy is quickly decreasing.