Séminaire du CERAMATHS - DMATHS : exposé d'Antoine Tonnoir

Le séminaire du département de mathématiques du CÉRAMATHS accueillera à 14h Antoine Tonnoir (INSA Rouen), jeudi 19 février 2026, pour l'exposé suivant :

Computation of half space solutions in elastic anisotropic media

This work is motivated by the numerical computation of half-space solutions of (time-harmonic) waves problems in homogeneous anisotropic elastic media. Anisotropic elastic media occur in several applications such as geophysics or non-destructive evaluation (to model for instance composite materials) and it is necessary to be able to accurately compute the waves field. Although it is quite easy to obtain an integral representation of the solution (solving via Fourier transform the equations), the difficulty is to evaluate it accurately. Indeed, this leads to evaluate highly oscillatory integrals. This issue is well-known, in particular in the context of boundary elements methods for high frequency problems. In our case, an additional difficulty comes from the anisotropy of the medium.     

In this talk, the purpose will be to present some classical methods to evaluate oscillatory integrals and see the difficulties to apply them in our situation. We will also present the numerical approach we are currently implementing to solve this problem.

This is an ongoing joint work with S. Nicaise and S. Dupont from the Polytechnique University of Hauts de France, and S. Fliss and A.-S. Bonnet-Ben Dhia from ENSTA.