Francis Filbet

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.

• On the approximation of the von Neumann equation in the semi-classical limit with F. Golse — J. Comput. Phys. 2025 & Math. Comp. 2026 Quantum
• On a discrete framework of hypocoercivity for kinetic equations with A. Blaustein — Math. Comp. 93 (2024) Analysis
• Asymptotically preserving particle-in-cell methods for inhomogeneous strongly magnetized plasmas with L. M. Rodrigues — SIAM J. Numer. Anal. 55 (2017) Plasmas
• A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources with S. Jin — J. Comput. Phys. 229 (2010) Rarefied gases
• Solving the Boltzmann equation in N log N with deterministic methods with C. Mouhot and L. Pareschi — SIAM J. Sci. Comput. 28 (2006) Rarefied gases
• Conservative numerical schemes for the Vlasov equation with E. Sonnendrücker and P. Bertrand — J. Comput. Phys. 172 (2001) Plasmas

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.