Francis Filbet
Professor of Applied Mathematics, Institut de Mathématiques de Toulouse
Scientific director of the LabEx CIMI
Research
I design and analyse numerical methods for kinetic equations — the mathematical description of many-particle systems, from plasmas and rarefied gases to quantum systems and neuron networks.
My work focuses on schemes that preserve the structure of the continuous problem (conservation laws, entropy, long-time behaviour) and remain accurate across scales, in particular asymptotic-preserving methods for stiff regimes such as strong magnetic fields or small mean free paths. I combine rigorous convergence analysis with large-scale simulation.
Themes
Plasma physics
Vlasov–Poisson with strong magnetic fields, particle-in-cell methods, Landau and Fokker–Planck collisions.
Rarefied gases
Boltzmann, BGK and ES-BGK equations, fast spectral solvers, hybrid multiscale methods.
Quantum mechanics
Quantum Boltzmann and von Neumann equations, semi-classical limit.
Life sciences
Chemotaxis, coagulation–fragmentation, mean-field models in neuroscience.
Numerical analysis
Entropy methods, discrete hypocoercivity, discrete functional inequalities.
News
- Co-organiser of the thematic trimester Interacting particles, PDEs and applications, Toulouse.
- Master 2 course An introduction to nonlinear PDEs — kinetic theory, mean-field limits, numerical methods.
- Numerical analysis of the homogeneous Landau equation accepted in Numerische Mathematik (with Y. Gui and L.-B. He).
- New preprint: Discrete hypocoercive estimates for discontinuous Galerkin methods (with Y. Cai, A. Blaustein and T. Xiong).
Selected papers
- On the approximation of the von Neumann equation in the semi-classical limit Quantum
- On a discrete framework of hypocoercivity for kinetic equations Analysis
- Asymptotically preserving particle-in-cell methods for inhomogeneous strongly magnetized plasmas Plasmas
- A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources Rarefied gases
- Solving the Boltzmann equation in N log N with deterministic methods Rarefied gases
- Conservative numerical schemes for the Vlasov equation Plasmas
Software
HOPE — High Order Program for kinetic Equations. A C++ library implementing structure- and asymptotic-preserving methods (particle-in-cell, semi-Lagrangian, WENO, Hermite spectral) for plasma physics, including 3D toroidal geometries close to tokamaks.
Positions & grants
- 2010–2014ERC Starting Grant NuSiKiMo
- 2015–2020Junior member, Institut Universitaire de France
- 2021–Associate editor, SIAM J. Sci. Comput.
- 2021–Scientific director, LabEx CIMI
Supervision
8 PhD students supervised, several now permanent researchers at CNRS, Inria and Université Côte d’Azur. Current: Kim Han Trinh (2023–), particle-in-cell methods for the Vlasov–Poisson system. Full list →