Recent book with colleagues on "Transport et Diffusion". Recent book on "Neural Networks and Numerical Analysis"

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
- A functional equation with polynomial solutions and application to Neural Networks, with Matthieu Ancellin HAL 2020

- Implicit discretization of Lagrangian gas dynamics, with A. Plessier and S. del Pino, HAL 2021
- Quadratic stability of flux limiters HAL 2021
- Approximation with vectorial exponential functions of solutions of the P N model for the transport of particles with G. Morel and C. Buet, HAL 2021
- 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
- Sensitivity equation method for the Navier-Stokes equations applied to uncertainty propagation, with C. Fiorina and A. Puscas HAL 2020

- Trace class properties of the non homogeneous linear Vlasov-Poisson equation in dimension 1+1,
to appear in J. Spectral theory, 2021

- 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

- A variational sheath model for gyrokinetic Vlasov-Poisson equations,
with Mehdi Badsi, Martin Campos-Pinto and Ludov Godard-Cadillac,
HAL 2021

- On Domain Decomposition Methods with optimized transmission conditions and cross-points,
with Anouk Nicolopoulos and Bertrand Thierry,
HAL 2021

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