In a broad sense I am interested in the propagation of time-harmonic waves in variable media. More specifically, my work includes:
- High order Discontinuous Galerkin method with generalized plane waves.
- Theoretical analysis of various wave resonances.
- Fast solver for wave propagation in inhomogeneous media.
- Definition, modeling and simulation of mode conversion.
- Harmonic vector fields on genus 1 surfaces.
- More recently : time-dependent problems for resonances.
My PhD work
During my PhD I studied different aspects of the cold plasma model, aiming at numerical simulation for Reflectometry in fusion plasma. In this context, Maxwell's equations for the electric field can be split into two propagation modes : the Ordinary mode (O-mode) and the eXtraordinary mode (X-mode).
- I developed a numerical method adapted to smooth varying coefficients for the O-mode equation. It is based on the Ultra-Weak Variational Formulation (UWVF) coupled with generalized plane waves (GPW) and designed to fit the varying coefficients. This was a joint work with Bruno Després.
- Thanks to a grant from Fondation Pierre Ledoux, I visited Peter Monk at the University of Delaware, where I implemented a 2D code for the UWVF with GPW.
- Since the X-mode equation is ill-posed in classical function spaces, an important part of my thesis is devoted to its theoretical study. This was a joint work with Bruno Després and Ricardo Weder (UNAM).
My thesis is also here (in English).
I attended CEMRACS 2010 on numerical models for fusion. The CEMRACS is a series of annual six week long meetings that aims at offering participants from academia and industry an interdisciplinary platform for exchanging knowledge.
- 08/2010, EMAFF project, magnetic equations with FreeFem (pdf).
- 08/2010, RESIST project, numerical methods for resistive MHD (pdf).
I also participated in the French math-industry weeks :
- 04/2011, with Alain Fuser from GDF Suez, the French Gas company, on the optimization of benefits from a one year solar energy production (report).
- 11/2011, with Philippe Saadé from PICVIZ labs, on the study of high dimensional data.