Stability and conservation properties of Hermite-based approximations of the Vlasov-Poisson system

DOI10.1007/s10915-021-01537-5zbMath1486.65193arXiv2103.00691OpenAlexW3167156241WikidataQ114225599 ScholiaQ114225599MaRDI QIDQ2049075

Daniele Funaro, Gianmarco Manzini

Publication date: 24 August 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.00691

zbMATH Keywords

conservation lawsHermite polynomialsVlasov equationspectral methodsVlasov-Poisson system

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) PDEs in connection with optics and electromagnetic theory (35Q60) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Statistical mechanics of plasmas (82D10) Electro- and magnetostatics (78A30) Vlasov equations (35Q83)

Related Items

A decision-making machine learning approach in Hermite spectral approximations of partial differential equations, Error analysis of Fourier–Legendre and Fourier–Hermite spectral-Galerkin methods for the Vlasov–Poisson system

Uses Software

• SpectralPlasmaSolver

Cites Work

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• On the velocity space discretization for the Vlasov-Poisson system: comparison between implicit Hermite spectral and particle-in-cell methods
• On the convergence of the Fourier-Hermite transformation method for the Vlasov equation with an artificial collision term
• Vlasov simulations using velocity-scaled Hermite representations
• Spectral elements for transport-dominated equations
• A Legendre pseudospectral viscosity method
• A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution
• On the use of Hermite functions for the Vlasov-Poisson system
• Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form
• A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system
• Spectral Methods
• Plasma Oscillations with Diffusion in Velocity Space
• Convergence of Spectral Methods for Nonlinear Conservation Laws
• Spectral Vanishing Viscosity Method For Nonlinear Conservation Laws
• Numerical methods for kinetic equations
• Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws
• The Hermite Spectral Method for Gaussian-Type Functions
• Spectral velocity discretizations for the Vlasov-Maxwell equations
• Convergence of Spectral Discretizations of the Vlasov--Poisson System
• Spectral Methods
• Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains
• On the kinetic theory of rarefied gases
• The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations