357 citations · 864 across the 37 of their papers we have counts for
43 papers
A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model
Alain Blaustein, Francis Filbet
We propose a numerical method for the Vlasov-Poisson-Fokker-Planck model written as an hyperbolic system thanks to a spectral decomposition in the basis of Hermite functions with r…
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…
Asymptotically preserving particle methods for strongly magnetizedplasmas in a torus
Francis Filbet, Luis Miguel Miguel Rodrigues
We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subj…
On the convergence of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system
Marianne Bessemoulin-Chatard, Francis Filbet
We prove the convergence of discontinuous Galerkin approximations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials in velocity. To obtain sta…
Fokker-planck Multi-species Equations In The Adiabatic Asymptotics
Francis Filbet, Claudia Negulescu
The main concern of the present paper is the study of the multi-scale dynamics of thermonuclear fusion plasmas via a multi-species Fokker-Planck kinetic model. One of the goals is…
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…
On the stability of conservative discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system
Marianne Bessemoulin-Chatard, Francis Filbet
We study a class of spatial discretizations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials. In particular, we focus on spectral methods and…
A spectral collocation method for the Landau equation in plasma physics
Francis Filbet
In this paper we present a spectral collocation method for the fast evaluation of the Landau collision operator for plasma physics, which allows us to obtain spectrally accurate nu…
Conservative discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System
Francis Filbet, Tao Xiong
We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Poisson system written as a hyperbolic system using Hermite polynomials in the velocity variable. T…
Convergence Analysis of Asymptotic Preserving Schemes for Strongly Magnetized plasmas
Francis Filbet, Luis Miguel Rodrigues, Hamed Zakerzadeh
The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes [Filbet \& Rodrigues, SIAM J. Numer. Anal., 54 (2) (2016)] for the Vla…
Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions
Joachim Crevat, Francis Filbet
This paper is devoted to the numerical approximation of the spatially-extended FitzHugh-Nagumo transport equation with strong local interactions based on a particle method. In this…
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…
Numerical Simulations to the Vlasov-Poisson System with a Strong Magnetic Field
Francis Filbet, Chang Yang
In this paper, we present an efficient Particle-In-Cell algorithm for the simulation of the three dimensional Vlasov-Poisson system in the presence of a strong external magnetic fi…
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…
Convergence of a Finite Volume Scheme for a System of Interacting Species with Cross-Diffusion
José A. Carrillo, Francis Filbet, Markus Schmidtchen
In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cros…
A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations
Francis Filbet, Tao Xiong
We develop a multi-dimensional hybrid discontinuous Galerkin method for multi-scale kinetic equations. This method is based on moment realizability matrices, a concept introduced b…
Discontinuous-galerkin methods for a kinetic model of self-organized dynamics
Francis Filbet, Chi-Wang Shu
This paper deals with the numerical resolution of kinetic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. We focus on the…
On a three dimensional vision based collision avoidance model
Céline Parzani, Francis Filbet
This paper presents a three dimensional collision avoidance approach for aerial vehicles inspired by coordinated behaviors in biological groups. The proposed strategy aims to enabl…
Asymptotically preserving particle-in-cell methods for inhomogenous strongly magnetized plasmas
Francis Filbet, Luis Rodrigues
We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on t…
A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure
Francis Filbet, Maxime Herda
We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy function…
A p-adaptive local discontinuous galerkin level set method for Willmore flow
Ruihan Guo, Francis Filbet
The level set method is often used to capture interface behavior in two or three dimensions. In this paper, we present a combination of local discontinuous Galerkin (LDG) method an…
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…
Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field
Francis Filbet, Luis Miguel Rodrigues
This paper deals with the numerical resolution of the Vlasov-Poissonsystem with a strong external magnetic field by Particle-In-Cell(PIC) methods. In this regime, classical PIC met…
Mixed semi-Lagrangian/finite difference methods for plasma simulations
Francis Filbet, Chang Yang
In this paper, we present an efficient algorithm for the long time behavior of plasma simulations. We will focus on 4D drift-kinetic model, where the plasma's motion occurs in the…