Open Access
Volume 57, Number 6, November-December 2023
Page(s) 3637 - 3668
Published online 22 December 2023
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Vol. 140. Elsevier (2003). [Google Scholar]
  2. T.P. Armstrong, R.C. Harding, G. Knorr and D. Montgomery, Solution of Vlasov’s equation by transform methods. Methods Comput. Phys. 9 (1970) 29–86. [Google Scholar]
  3. N. Besse and E. Sonnendrücker, Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. J. Comput. Phys. 191 (2003) 341–376. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Bessemoulin-Chatard and F. Filbet, On the stability of conservative discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system. J. Comput. Phys. 451 (2022) 110881. [CrossRef] [Google Scholar]
  5. C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation. CRC Press, Boca Raton (1998). [Google Scholar]
  6. E. Camporeale, G.L. Delzanno, B.K. Bergen and J.D. Moulton, On the velocity space discretization for the Vlasov-Poisson system: comparison between implicit Hermite spectral and Particle-in-Cell methods. Comput. Phys. Commun. 198 (2016) 47–58. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods: Fundamentals in Single Domains. Springer (2006). [CrossRef] [Google Scholar]
  8. C.Z. Cheng and G. Knorr, The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22 (1976) 330–351. [NASA ADS] [CrossRef] [Google Scholar]
  9. N. Crouseilles, G. Latu and E. Sonnendrücker, A parallel Vlasov solver based on local cubic spline interpolation on patches. J. Comput. Phys. 228 (2009) 1429–1446. [CrossRef] [MathSciNet] [Google Scholar]
  10. G.L. Delzanno, Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form. J. Comput. Phys. 301 (2015) 338–356. [CrossRef] [MathSciNet] [Google Scholar]
  11. L. Einkemmer and C. Lubich, A quasi-conservative dynamical low-rank algorithm for the Vlasov equation. SIAM J. Sci. Comput. 41 (2019) B1061–B1081. [CrossRef] [Google Scholar]
  12. L. Fatone, D. Funaro and G. Manzini, A Semi-Lagrangian spectral method for the Vlasov-Poisson system based on Fourier, Legendre and Hermite polynomials. Commun. Appl. Math. Comput. 1 (2019) 333–360. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Filbet and T. Xiong, Conservative discontinuous Galerkin/Hermite spectral method for the Vlasov-Poisson system. Commun. Appl. Math. Comput. 4 (2022) 34–59. [CrossRef] [MathSciNet] [Google Scholar]
  14. F. Filbet, E. Sonnendrücker and P. Bertrand, Conservative numerical schemes for the Vlasov equation. J. Comput. Phys. 172 (2001) 166–187. [CrossRef] [MathSciNet] [Google Scholar]
  15. D. Funaro and G. Manzini, Stability and conservation properties of Hermite-based approximations of the Vlasov-Poisson system. J. Sci. Comput. 88 (2021) 29. [CrossRef] [Google Scholar]
  16. I.S. Gradshteyn, I.M. Ryzhik, D. Zwillinger and V. Moll, Table of Integrals, Series, and Products, 8th edition. Academic Press, Amsterdam (2015). [Google Scholar]
  17. R.W. Hockney and J.W. Eastwood, Computer Simulation Using Particles. CRC Press, Boca Raton (1988). [CrossRef] [Google Scholar]
  18. J.P. Holloway, Spectral velocity discretizations for the Vlasov-Maxwell equations. Transp. Theory Stat. Phys. 25 (1996) 1–32. [CrossRef] [Google Scholar]
  19. K. Kormann, A semi-Lagrangian Vlasov solver in tensor train format. SIAM J. Sci. Comput. 37 (2015) B613–B632. [CrossRef] [Google Scholar]
  20. W. Liu, L.-L. Wang and B. Wu, Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation. Adv. Comput. Math. 47 (2021) 1–32. [CrossRef] [Google Scholar]
  21. N.F. Loureiro, A.A. Schekochihin and A. Zocco, Fast collisionless reconnection and electron heating in strongly magnetized plasmas. Phys. Rev. Lett. 111 (2013) 025002. [CrossRef] [PubMed] [Google Scholar]
  22. N.F. Loureiro, W. Dorland, L. Fazendeiro, A. Kanekar, A. Mallet, M.S. Vilelas and A. Zocco, Viriato: a Fourier-Hermite spectral code for strongly magnetized fluid-kinetic plasma dynamics. Comput. Phys. Commun. 206 (2016) 45–63. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Manzini, G.L. Delzanno, J. Vencels and S. Markidis, A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system. J. Comput. Phys. 317 (2016) 82–107. [CrossRef] [MathSciNet] [Google Scholar]
  24. G. Manzini, D. Funaro and G.L. Delzanno, Convergence of spectral discretizations of the Vlasov-Poisson system. SIAM J. Numer. Anal. 55 (2017) 2312–2335. [CrossRef] [MathSciNet] [Google Scholar]
  25. J.T. Parker and P.J. Dellar, Fourier-Hermite spectral representation for the Vlasov-Poisson system in the weakly collisional limit. J. Plasma Phys. 81 (2015) 305810203. [CrossRef] [Google Scholar]
  26. M. Pulvirenti and J. Wick, Convergence of Galerkin approximation for two-dimensional Vlasov-Poisson equation. Z. Angew. Math. Phys. 35 (1984) 790–801. [CrossRef] [MathSciNet] [Google Scholar]
  27. J.M. Qiu and C.W. Shu, Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov-Poisson system. J. Comput. Phys. 230 (2011) 8386–8409. [CrossRef] [MathSciNet] [Google Scholar]
  28. J. Shen, T. Tang and L.L. Wang, Spectral Methods: Algorithms, Analysis and Applications. Vol. 41. Springer Science & Business Media (2011). [CrossRef] [Google Scholar]
  29. G. Szegö, Orthogonal Polynomials, 4th edition. Amer. Math. Soc, Providence, RI (1975). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you