High-order semi-Lagrangian WENO schemes based on non-polynomial space for the Vlasov equation

DOI10.1007/s42967-021-00150-5OpenAlexW3196171907MaRDI QIDQ2692146

Andrew J. Christlieb, Ruimeng Chang, Hyoseon Yang, Matthew Link

Publication date: 21 March 2023

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42967-021-00150-5

zbMATH Keywords

Vlasov equationVlasov-Poisson systemsemi-Lagrangian methodsWENO schemesnon-polynomial basishigh-order splitting methods

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical interpolation (65D05) Algorithms for approximation of functions (65D15) Vlasov equations (35Q83) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Uses Software

• XFEM
• Vador

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
• Arbitrarily high order convected scheme solution of the Vlasov-Poisson system
• Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system
• A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations
• An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm
• The energy conserving particle-in-cell method
• Comparison of Eulerian Vlasov solvers
• Eulerian Vlasov codes
• High order maximum principle preserving semi-Lagrangian finite difference WENO schemes for the Vlasov equation
• Energy-conserving discontinuous Galerkin methods for the Vlasov-Maxwell system
• Extended finite element method on polygonal and quadtree meshes
• A conservative high order semi-Lagrangian WENO method for the Vlasov equation
• A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system
• An efficient scheme for convection-dominated transport
• The semi-Lagrangian method for the numerical resolution of the Vlasov equation
• Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods
• Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space
• A sixth-order weighted essentially non-oscillatory schemes based on exponential polynomials for Hamilton-Jacobi equations
• A particle-in-cell method for the simulation of plasmas based on an unconditionally stable field solver
• A high order multi-dimensional characteristic tracing strategy for the Vlasov-Poisson system
• Efficient implementation of weighted ENO schemes
• WENO schemes and their application as limiters for RKDG methods based on trigonometric approximation spaces
• A moving mesh WENO method based on exponential polynomials for one-dimensional conservation laws
• A truly forward semi-Lagrangian WENO scheme for the Vlasov-Poisson system
• Conservative multi-dimensional semi-Lagrangian finite difference scheme: stability and applications to the kinetic and fluid simulations
• A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm
• Vlasov-Poisson: the waterbag method revisited
• A conservative semi-Lagrangian HWENO method for the Vlasov equation
• A Particle-in-cell Method with Adaptive Phase-space Remapping for Kinetic Plasmas
• Nonoscillatory Interpolation Methods Applied to Vlasov-Based Models
• An extended finite element library
• Conservative Semi-Lagrangian Finite Difference WENO Formulations with Applications to the Vlasov Equation
• A finite element method for crack growth without remeshing
• Improving Accuracy of the Fifth-Order WENO Scheme by Using the Exponential Approximation Space
• Trigonometric WENO Schemes for Hyperbolic Conservation Laws and Highly Oscillatory Problems
• Vlasov and Drift Kinetic Simulation Methods Based on the Symplectic Integrator
• High-order extended finite element method for cracked domains
• Sixth-order Weighted Essentially Nonoscillatory Schemes Based on Exponential Polynomials
• Conservative numerical schemes for the Vlasov equation

This page was built for publication: High-order semi-Lagrangian WENO schemes based on non-polynomial space for the Vlasov equation