Numerical methods for the two-dimensional Vlasov-Poisson equation in the finite Larmor radius approximation regime

DOI10.1016/j.jcp.2018.09.007zbMath1416.65388OpenAlexW2889645775MaRDI QIDQ2002275

Xiaofei Zhao, Nicolas Crouseilles, Philippe Chartier

Publication date: 11 July 2019

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2018.09.007

zbMATH Keywords

particle-in-cell methodtwo-scale formulationVlasov-Poisson equationuniform accuracyfinite Larmor radiusmultirevolution composition

Mathematics Subject Classification ID

Applications to the sciences (65Z05) Vlasov equations (35Q83) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (8)

Semi-discretization and full-discretization with improved accuracy for charged-particle dynamics in a strong nonuniform magnetic field ⋮ Multiscale Numerical Schemes for the Collisional Vlasov Equation in the Finite Larmor Radius Approximation Regime ⋮ Numerical methods for some nonlinear Schrödinger equations in soliton management ⋮ Uniformly Accurate Methods for Three Dimensional Vlasov Equations under Strong Magnetic Field with Varying Direction ⋮ On the Rotating Nonlinear Klein--Gordon Equation: NonRelativistic Limit and Numerical Methods ⋮ Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime ⋮ Convergence analysis of asymptotic preserving schemes for strongly magnetized plasmas ⋮ Error Estimates of Some Splitting Schemes for Charged-Particle Dynamics under Strong Magnetic Field

Cites Work

• Unnamed Item
• Asymptotic preserving schemes for highly oscillatory Vlasov-Poisson equations
• Implicit-explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning
• Solving highly-oscillatory NLS with SAM: numerical efficiency and long-time behavior
• Multi-revolution composition methods for highly oscillatory differential equations
• Two-scale semi-Lagrangian simulation of a charged particle beam in a periodic focusing channel
• Gyrokinetic particle simulation model
• Uniformly accurate particle-in-cell method for the long time solution of the two-dimensional Vlasov-Poisson equation with uniform strong magnetic field
• Stroboscopic averaging for the nonlinear Schrödinger equation
• Uniformly accurate numerical schemes for the nonlinear Dirac equation in the nonrelativistic limit regime
• Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime
• Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
• The Finite Larmor Radius Approximation
• Asymptotically Stable Particle-In-Cell Methods for the Vlasov--Poisson System with a Strong External Magnetic Field
• MultiScale Analysis for Linear First Order PDEs. The Finite Larmor Radius Regime
• ON THE PARAXIAL APPROXIMATION OF THE STATIONARY VLASOV-MAXWELL SYSTEM
• The heterogeneous multiscale method
• Nonlinear gyrokinetic equations
• The three-dimensional finite Larmor radius approximation
• Two-Scale Convergence
• LONG TIME SIMULATION OF A BEAM IN A PERIODIC FOCUSING CHANNEL VIA A TWO-SCALE PIC-METHOD
• Gyrokinetic approach in particle simulation
• Homogenization and Two-Scale Convergence
• Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type
• On the Vlasov--Maxwell System with a Strong Magnetic Field
• Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
• LONG TIME BEHAVIOR OF THE TWO-DIMENSIONAL VLASOV EQUATION WITH A STRONG EXTERNAL MAGNETIC FIELD
• The Effective Vlasov--Poisson System for the Finite Larmor Radius Regime
• Asymptotically Preserving Particle-in-Cell Methods for Inhomogeneous Strongly Magnetized Plasmas
• Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field
• Uniformly Accurate Forward Semi-Lagrangian Methods for Highly Oscillatory Vlasov--Poisson Equations
• Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations
• Stochastic homogenization of quasilinear PDEs with a spatial degeneracy
• Multiscale particle-in-cell methods and comparisons for the long-time two-dimensional Vlasov-Poisson equation with strong magnetic field

This page was built for publication: Numerical methods for the two-dimensional Vlasov-Poisson equation in the finite Larmor radius approximation regime