For several years, the POEMS team has been developing a C ++ finite element library (XLiFE ++) for processing both FEM and BEM methods. This library makes it possible in particular to easily couple various numerical methods. When propagation phenomena are very high frequency (small wavelength compared to the characteristic size of the obstacles), the FEM-BEM methods show their limits in terms of efficiency. This is why we want to develop specific modules for high-frequency approximations. The work will consist on the one hand to establish various high-frequency approximations based on the geometric theory of the diffraction, first for canonical obstacles (sphere, cylinder, ...) then for any obstacles. It will then implement these approximations in the XLiFE ++ library and develop geometric tools (computation of geodesics in particular). Required skills: scientific computation, finite elements, C ++ language Duration: 30 months, from January 1, 2018 to June 30, 2020