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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.
colloquim talk on Scattering theory (Lax, Kato, ...) interpretation of linearized Landau damping:
recently given at IAMP
Long term interests in the construction of new numerical algorithms started in my
PhD thesis.
It
materialized recently in 2 directions
new approach to polynomials with sign:
Recent Results In Positivity Preserving Polynomials
here
Machine Learning
and Scientific Computing:
Machine Learning design of Volume of Fluid schemes for compressible flows, with H. Jourdren,
HAL 2020, JCP 2020
colloquim talk on ML:
recently given at LJLL/SU
Play with both polynomials and Machine Learning:
A functional equation with polynomial solutions and application to Neural Networks,
with Matthieu Ancellin
HAL 2020
ANR MUFFIN 2019/2023 here
: ITER oriented project
ANR CHROME 2012/2016 completed
: ITER oriented project
Groupe de travail
Stability and boundary interactions for fusion plasmas
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Recent 2019/2020 papers or preprints
Polynomials (positive, with Machine Learning, ...)
Numerical methods/scientific computing
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Machine Learning design of Volume of Fluid schemes for compressible flows,
with H. Jourdren,
HAL 2020, accepted in JCP
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TDG method for Friedrichs systems and the P N model in 2D,
with G. Morel and C. Buet,
HAL 2019
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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
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High-order staggered schemes for compressible hydrodynamics. Weak consistency and numerical validation,
with G. Dakin and S. Jaouen,
JCP 2019
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Sensitivity equation method for the Navier-Stokes equations applied to uncertainty propagation,
with C. Fiorina and A. Puscas
HAL 2020
Mathematical modeling in applied physics for fusion
- 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
Master M2A: Analyse numerique et Neural Networks
Le poly (incomplet) est
au lien ici .
Les transparents du 21/01 ont
au lien ici .