Section: Application Domains

Electromagnetism

This is a particularly important domain, first because of the very important technological applications but also because the treatment of Maxwell’s equations is much more technically involved from the mathematical point of view that the scalar wave equation. Applied mathematics for electromagnetism during the last ten years have mainly concerned stealth technology, electromagnetic compatibility, design of optoelectronic micro-components or smart materials. Stealth technology relies in particular on the conception and simulation of new absorbing materials (anisotropic, chiral, non-linear...). The simulation of antennas raises delicate questions related to the complexity of the geometry (in particular the presence of edges and corners). In optics, the development of the Mmcro and nano optics has made recently fantastic progress and the thematic of metamaterials (with negative index of refraction) opens new amazing applications. For all these reasons, we are developing an intense research in the following areas

• Highly accurate and hybrid numerical methods in collaboration with CEA (Gramat) and ONERA (Toulouse).

• Electromagmetic wave propagation in periodic media.

• Development of simplified approximate models by asymptotic anslysis for various applications : boundary layers, thin coatings, thin domains, thin wires and cables, ...

• Mathematical and numerical questions linked to the modeling of metamaterials.