241 citations
- Université de RennesFR519 papers
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- Laboratoire de Mathématiques Jean LerayFR25 papers
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97 papers · 1 filter
Machine Learning for highly oscillatory differential equations
Maxime Bouchereau
Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been d…
Convergence analysis of a Crank-Nicolson scheme for strongly magnetized plasmas
Francis Filbet, L Miguel Rodrigues, Kim Han Trinh
The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for t…
Numerical analysis of the large deviation regime of a kinetic equation with a nonlocal Hamilton-Jacobi limit
Hélène Hivert, Tino Laidin
We develop and study an asymptotic-preserving (AP) numerical scheme for a linear kinetic equation in a large deviation regime. After applying a Hopf-Cole transform to the distribut…
A modified Crank-Nicolson scheme for the Vlasov-Poisson system with a strong external magnetic field
Francis Filbet, L Miguel Rodrigues, Kim Han Trinh
We propose and study a Particle-In-Cell (PIC) method based on the Crank-Nicolson time discretization for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic…
An asymptotic preserving scheme for the M1model of non-local thermal transport for two-dimensional structured and unstructured meshes
Jean-Luc Feugeas, Julien Mathiaud, Luc Mieussens +1
The M1 moment model for electronic transport is commonly used to describe non-local thermal transport effects in laser-plasma simulations. In this article, we propose a new asympto…
Discrete stability estimates for the pressureless Euler-Poisson-Boltzmann equations in the Quasi-Neutral limit
Mehdi Badsi, Nicolas Crouseilles
We propose and study a fully implicit finite volume scheme for the pressureless Euler-Poisson-Boltzmann equations on the one dimensional torus. Especially, we design a consistent a…