activity
20062023
most citedA class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources

357 citations · 864 across the 37 of their papers we have counts for

collaborators
Showing math.APShow all

8 papers · 1 filter

math.AP2022

On a discrete framework of hypocoercivity for kinetic equations

Alain Blaustein, Francis Filbet

We propose and study a fully discrete finite volume scheme for the Vlasov-Fokker-Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This approac…

math.AP2022

Concentration phenomena in Fitzhugh-Nagumo's equations: A mesoscopic approach

Alain Blaustein, Francis Filbet

We consider a spatially extended mesoscopic FitzHugh-Nagumo model with strong local interactions and prove that its asymptotic limit converges towards the classical nonlocal reacti…

math.AP2018

Asymptotics of the three dimensional Vlasov equation in the large magnetic field limit

Francis Filbet, Luis Miguel Rodrigues

We study the asymptotic behavior of solutions to the Vlasov equation in the presence of a strong external magnetic field. In particular we provide a mathematically rigorous derivat…

math.AP2018★ 5 cited

Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system

Joachim Crevat, Grégory Faye, Francis Filbet

We introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlo…

math.AP2016★ 21 cited

On the asymptotic limit of the three dimensional Vlasov-Poisson system for large magnetic field : formal derivation

Pierre Degond, Francis Filbet

This paper establishes the long time asymptotic limit of the three dimensional Vlasov-Poisson equation with strong external magnetic field. The guiding center approximation is inve…

math.AP2012★ 36 cited

A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media

Francis Filbet, Thomas Rey

We present a new numerical algorithm based on a relative energy scaling for collisional kinetic equations allowing to study numerically their long time behavior, without the usual…

math.AP2008

Analysis of spectral methods for the homogeneous Boltzmann equation

Francis Filbet, Clément Mouhot

The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analys…

math.AP2006★ 124 cited

Solving the Boltzmann equation in N log N

Francis Filbet, Clément Mouhot, Lorenzo Pareschi

In [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R. Math. Acad. Sci. Paris, 33…