Principal fields of interest: they come from the mathematical analysis and numerical solution of Partial Differential Equations.

Applications come from the mathematical physics (wave equations, compressible fluids) for various problems.

Specific applications in Plasma Physics (ICF-Inertial Confinement Fusion and MCF-Magnetic Confinement Fusion) are considered.

Long term interests in the construction of new numerical algorithms started in my PhD thesis.

It materialized recently in 2 directions

ANR MUFFIN 2019/2023 here : ITER oriented project

ANR CHROME 2012/2016 completed : ITER oriented project

Groupe de travail

Recent 2019/2020 papers or preprints

- A projection algorithm on the set of polynomials with two bounds, with M. Campos-Pinto, F. Charles, Herda Numer. Algo. 2020
- Iterative Calculation of Sum Of Squares, with Maxime Herda HAL 2018, accepted in SIAM J. Numerical Analysis 2020
- Polynomials with bounds and numerical approximation, Numerical Algorithms 2017 and Erratum (with M. Herda).
- Algorithms for positive polynomial approximation, with F. Charles and M. Campos-Pinto, Siam Numer. Anal. 2019
- A functional equation with polynomial solutions and application to Neural Networks, with Matthieu Ancellin HAL 2020

- Machine Learning design of Volume of Fluid schemes for compressible flows, with H. Jourdren, HAL 2020, accepted in JCP
- TDG method for Friedrichs systems and the P N model in 2D, with G. Morel and C. Buet, HAL 2019
- Trefftz Discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport, with G. Morel and C. Buet, to appear in ACOMP
- High-order staggered schemes for compressible hydrodynamics. Weak consistency and numerical validation, with G. Dakin and S. Jaouen, JCP 2019
- Sensitivity equation method for the Navier-Stokes equations applied to uncertainty propagation, with C. Fiorina and A. Puscas HAL 2020

- Degenerate elliptic equations for resonant wave problems,
with A. Nicolopoulos, P. Ciarlet Jr. and M. Campos-Pinto,
accepted in IMA Journal of Applied Mathematics 2019

- A Stable Formulation of Resonant Maxwell's Equations in Cold Plasma,
with A. Nicolopoulos and M. Campos-Pinto,
Journal of Computational and Applied Mathematics 2019

- Scattering structure and Landau damping for linearized Vlasov equations with inhomogeneous Boltzmannian states,
published in AHP 2019

- Trace class properties of the non homogeneous linear Vlasov-Poisson equation in dimension 1+1,
accepted in J. Spectral theory, 2019

- The Vlasov-Ampere system and the Bernstein-Landau paradox, with F. Charles, A. Rege and R. Weder,
Hal 2020 ,
Arxiv 2020

- Corners and stable optimized domain decomposition methods for the Helmholtz problem,
with Anouk Nicolopoulos and Bertrand Thierry,
HAL 2020

Le poly (incomplet) est au lien ici .

Les transparents du 21/01 ont au lien ici .