Close Search Advanced
Journals
Resources
About Us
Open Access

Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field

Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field
Preview
Add to basket

Year:    2015

Author:    Emmanuel Frénod, Sever A. Hirstoaga, Mathieu Lutz, Eric Sonnendrücker

Communications in Computational Physics, Vol. 18 (2015), Iss. 2 : pp. 263–296

Abstract

With the aim of solving in a four dimensional phase space a multi-scale Vlasov-Poisson system, we propose in a Particle-In-Cell framework a robust time-stepping method that works uniformly when the small parameter vanishes. As an exponential integrator, the scheme is able to use large time steps with respect to the typical size of the solution's fast oscillations. In addition, we show numerically that the method has accurate long time behaviour and that it is asymptotic preserving with respect to the limiting Guiding Center system.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.070214.160115a

Communications in Computational Physics, Vol. 18 (2015), Iss. 2 : pp. 263–296

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:   

Author Details

Emmanuel Frénod

Sever A. Hirstoaga

Mathieu Lutz

Eric Sonnendrücker

  1. An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields

    Chen, G. | Chacón, L.

    Journal of Computational Physics, Vol. 487 (2023), Iss. P.112160

    https://doi.org/10.1016/j.jcp.2023.112160 [Citations: 5]

  2. Uniformly Accurate Forward Semi-Lagrangian Methods for Highly Oscillatory Vlasov--Poisson Equations

    Crouseilles, Nicolas | Lemou, Mohammed | Méhats, Florian | Zhao, Xiaofei

    Multiscale Modeling & Simulation, Vol. 15 (2017), Iss. 2 P.723

    https://doi.org/10.1137/16M1059497 [Citations: 10]

  3. A High Order Semi-Lagrangian Discontinuous Galerkin Method for the Two-Dimensional Incompressible Euler Equations and the Guiding Center Vlasov Model Without Operator Splitting

    Cai, Xiaofeng | Guo, Wei | Qiu, Jing-Mei

    Journal of Scientific Computing, Vol. 79 (2019), Iss. 2 P.1111

    https://doi.org/10.1007/s10915-018-0889-1 [Citations: 14]

  4. Homogenization-based numerical methods

    Frénod, Emmanuel

    Discrete and Continuous Dynamical Systems - Series S, Vol. 9 (2016), Iss. 5 P.i

    https://doi.org/10.3934/dcdss.201605i [Citations: 0]

  5. Continuous-stage adapted exponential methods for charged-particle dynamics with arbitrary magnetic fields

    Li, Ting | Wang, Bin

    Advances in Computational Mathematics, Vol. 49 (2023), Iss. 6

    https://doi.org/10.1007/s10444-023-10093-5 [Citations: 0]

  6. LeXInt: Package for exponential integrators employing Leja interpolation

    Deka, Pranab J. | Einkemmer, Lukas | Tokman, Mayya

    SoftwareX, Vol. 21 (2023), Iss. P.101302

    https://doi.org/10.1016/j.softx.2022.101302 [Citations: 2]

  7. Uniformly Accurate Methods for Three Dimensional Vlasov Equations under Strong Magnetic Field with Varying Direction

    Chartier, Philippe | Crouseilles, Nicolas | Lemou, Mohammed | Méhats, Florian | Zhao, Xiaofei

    SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 2 P.B520

    https://doi.org/10.1137/19M127402X [Citations: 21]

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

    Chartier, Philippe | Crouseilles, Nicolas | Zhao, Xiaofei

    Journal of Computational Physics, Vol. 375 (2018), Iss. P.619

    https://doi.org/10.1016/j.jcp.2018.09.007 [Citations: 11]

  9. Asymptotically Preserving Particle-in-Cell Methods for Inhomogeneous Strongly Magnetized Plasmas

    Filbet, Francis | Rodrigues, Luis Miguel

    SIAM Journal on Numerical Analysis, Vol. 55 (2017), Iss. 5 P.2416

    https://doi.org/10.1137/17M1113229 [Citations: 22]

  10. Conservative Multi-dimensional Semi-Lagrangian Finite Difference Scheme: Stability and Applications to the Kinetic and Fluid Simulations

    Xiong, Tao | Russo, Giovanni | Qiu, Jing-Mei

    Journal of Scientific Computing, Vol. 79 (2019), Iss. 2 P.1241

    https://doi.org/10.1007/s10915-018-0892-6 [Citations: 8]

  11. Optimal Convergence and Long-Time conservation of Exponential Integration for Schrödinger Equations in a Normal or Highly Oscillatory Regime

    Wang, Bin | Jiang, Yaolin

    Journal of Scientific Computing, Vol. 90 (2022), Iss. 3

    https://doi.org/10.1007/s10915-022-01774-2 [Citations: 4]

  12. Geometric continuous-stage exponential energy-preserving integrators for charged-particle dynamics in a magnetic field from normal to strong regimes

    Li, Ting | Wang, Bin

    Applied Numerical Mathematics, Vol. 181 (2022), Iss. P.1

    https://doi.org/10.1016/j.apnum.2022.05.013 [Citations: 2]

  13. Semi-discretization and full-discretization with improved accuracy for charged-particle dynamics in a strong nonuniform magnetic field

    Wang, Bin | Jiang, Yaolin

    ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 57 (2023), Iss. 4 P.2427

    https://doi.org/10.1051/m2an/2023058 [Citations: 1]

  14. Convergence analysis of asymptotic preserving schemes for strongly magnetized plasmas

    Filbet, Francis | Rodrigues, L. Miguel | Zakerzadeh, Hamed

    Numerische Mathematik, Vol. 149 (2021), Iss. 3 P.549

    https://doi.org/10.1007/s00211-021-01248-x [Citations: 7]

  15. SHARP DECAY ESTIMATES FOR SMALL DATA SOLUTIONS TO THE MAGNETIZED VLASOV-POISSON SYSTEM AND MAGNETIZED VLASOV-YUKAWA SYSTEM

    Hu, Xianghong | Zhang, Xianwen

    Journal of Applied Analysis & Computation, Vol. 14 (2024), Iss. 3 P.1648

    https://doi.org/10.11948/20230332 [Citations: 0]

  16. Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov–Poisson equation with strong magnetic field

    Crouseilles, Nicolas | Hirstoaga, Sever A. | Zhao, Xiaofei

    Computer Physics Communications, Vol. 222 (2018), Iss. P.136

    https://doi.org/10.1016/j.cpc.2017.09.027 [Citations: 8]

  17. Uniformly accurate Particle-in-Cell method for the long time solution of the two-dimensional Vlasov–Poisson equation with uniform strong magnetic field

    Crouseilles, Nicolas | Lemou, Mohammed | Méhats, Florian | Zhao, Xiaofei

    Journal of Computational Physics, Vol. 346 (2017), Iss. P.172

    https://doi.org/10.1016/j.jcp.2017.06.011 [Citations: 25]

  18. Fourth-Order Conservative Non-splitting Semi-Lagrangian Hermite WENO Schemes for Kinetic and Fluid Simulations

    Zheng, Nanyi | Cai, Xiaofeng | Qiu, Jing-Mei | Qiu, Jianxian

    Journal of Scientific Computing, Vol. 99 (2024), Iss. 3

    https://doi.org/10.1007/s10915-024-02520-6 [Citations: 0]

  19. The Vlasov--Poisson System with a Uniform Magnetic Field: Propagation of Moments and Regularity

    Rege, Alexandre

    SIAM Journal on Mathematical Analysis, Vol. 53 (2021), Iss. 2 P.2452

    https://doi.org/10.1137/20M1376133 [Citations: 2]

  20. On the Vlasov--Maxwell System with a Strong Magnetic Field

    Filbet, Francis | Xiong, Tao | Sonnendrücker, Eric

    SIAM Journal on Applied Mathematics, Vol. 78 (2018), Iss. 2 P.1030

    https://doi.org/10.1137/17M1112030 [Citations: 9]
  21. Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations

    Introduction

    Frénod, Emmanuel

    2017

    https://doi.org/10.1007/978-3-319-64668-8_1 [Citations: 0]

  22. Long term analysis of splitting methods for charged-particle dynamics

    Li, Xicui | Wang, Bin

    Applied Mathematics and Computation, Vol. 441 (2023), Iss. P.127682

    https://doi.org/10.1016/j.amc.2022.127682 [Citations: 1]

  23. Asymptotic-preserving schemes for multiscale physical problems

    Jin, Shi

    Acta Numerica, Vol. 31 (2022), Iss. P.415

    https://doi.org/10.1017/S0962492922000010 [Citations: 30]

  24. Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations

    Cai, Xiaofeng | Guo, Wei | Qiu, Jing-Mei

    Communications on Applied Mathematics and Computation, Vol. 4 (2022), Iss. 1 P.3

    https://doi.org/10.1007/s42967-020-00088-0 [Citations: 1]

  25. Error Estimates of Some Splitting Schemes for Charged-Particle Dynamics under Strong Magnetic Field

    Wang, Bin | Zhao, Xiaofei

    SIAM Journal on Numerical Analysis, Vol. 59 (2021), Iss. 4 P.2075

    https://doi.org/10.1137/20M1340101 [Citations: 32]

  26. Geometric Two-Scale Integrators for Highly Oscillatory System: Uniform Accuracy and Near Conservations

    Wang, Bin | Zhao, Xiaofei

    SIAM Journal on Numerical Analysis, Vol. 61 (2023), Iss. 3 P.1246

    https://doi.org/10.1137/21M1462908 [Citations: 10]

  27. Accurate particle time integration for solving Vlasov-Fokker-Planck equations with specified electromagnetic fields

    Jenny, Patrick | Gorji, Hossein

    Journal of Computational Physics, Vol. 387 (2019), Iss. P.430

    https://doi.org/10.1016/j.jcp.2019.02.040 [Citations: 4]

  28. Asymptotically Stable Particle-In-Cell Methods for the Vlasov--Poisson System with a Strong External Magnetic Field

    Filbet, Francis | Rodrigues, Luis Miguel

    SIAM Journal on Numerical Analysis, Vol. 54 (2016), Iss. 2 P.1120

    https://doi.org/10.1137/15M104952X [Citations: 36]