Microlocal approach to the numerical solution of the Helmholtz equation (Victorita Dolean, University of Strathclyde and Université Côte d'Azur)

08.03.2022 14:00 – 15:00

The numerical solution of the Helmholtz equation is a real challenge when the frequency k is high. Indeed, the usual discretisation methods (finite elements, finite differences, etc.) involve meshing the domain with elements whose diameter is $o(k^{-1})$, and therefore dealing with a discrete problem having a number of degrees of freedom >> k^d. We will present a new approach to the numerical solution of the Helmholtz equation, inspired by harmonic analysis considerations. By taking into account the microlocal properties of the solution, we manage to deal only with discrete problems having $o(k^d)$ degrees of freedom. This presentation is at the interface between numerical analysis, harmonic analysis and semiclassical analysis; no knowledge of any of the topics will be assumed on the part of the audience.
This work is in collaboration with T. Chaumont-Frélet and M. Ingremeau.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre