62 citations · 263 across the 12 of their papers we have counts for
9 papers · 1 filter
Beyond the analytic solution manufacturing for anisotropic elliptic equations
Fabrice Deluzet, Valdimir Latocha, Frédéric Robert
This article is aimed at introducing a new procedure to define reference solutions to which the numerical approximations of anisotropic problems arising in plasma physics may be co…
An Asymptotic-Preserving Micro--Macro Scheme for Plasma Simulations in Quasi-Neutral and Low-Mach-Number Regimes with Kinetic Upgrades
Zeyu Liu, Fabrice Deluzet, Chang Yang
We propose an asymptotic-preserving micro--macro method bridging a kinetic description of electrons and a low-frequency reduced model in which the electrons are a massless, quasi-n…
A hierarchical sparse-grid particle method for the Vlasov--Poisson system
Fabrice Deluzet, Clément Guillet, Jacek Narski
We introduce a hierarchical sparse-grid (HSG) particle method for the numerical solution of the Vlasov--Poisson system. Sparse-grid PIC methods have so far been formulated within f…
Preserving the accuracy of numerical methods discretizing anisotropic elliptic problems
Chang Yang, Fabrice Deluzet, Jacek Narski
In this paper we study the loss of precision of numerical methods discretizing anisotropic problems and propose alternative approaches free from this drawback. The deterioration of…
A hybrid method for anisotropic elliptic problems based on the coupling of an Asymptotic-Preserving method with the Asymptotic-Limit model
Anais Crestetto, Fabrice Deluzet, Claudia Negulescu
This paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems. The anisotropy is aligned with one coordinate-axis and its stren…
Numerical resolution of an anisotropic non-linear diffusion problem
Stéphane Brull, Fabrice Deluzet, Alexandre Mouton
This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter \varepsilon, defined as the anisotropy strength recipro…
Degenerate anisotropic elliptic problems and magnetized plasma simulations
Stéphane Brull, Pierre Degond, Fabrice Deluzet
This paper is devoted to the numerical approximation of a degenerate anisotropic elliptic problem. The numerical method is designed for arbitrary space-dependent anisotropy directi…
Duality-based Asymptotic-Preserving method for highly anisotropic diffusion equations
Pierre Degond, Fabrice Deluzet, Alexei Lozinski +2
The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variab…
An asymptotic preserving scheme for strongly anisotropic elliptic problems
Pierre Degond, Fabrice Deluzet, Claudia Negulescu
In this article we introduce an asymptotic preserving scheme designed to compute the solution of a two dimensional elliptic equation presenting large anisotropies. We focus on an a…