Open Access
Issue |
ESAIM: M2AN
Volume 57, Number 6, November-December 2023
|
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Page(s) | 3637 - 3668 | |
DOI | https://doi.org/10.1051/m2an/2023091 | |
Published online | 22 December 2023 |
- R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Vol. 140. Elsevier (2003). [Google Scholar]
- 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]
- 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]
- 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]
- C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation. CRC Press, Boca Raton (1998). [Google Scholar]
- 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]
- C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods: Fundamentals in Single Domains. Springer (2006). [CrossRef] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- R.W. Hockney and J.W. Eastwood, Computer Simulation Using Particles. CRC Press, Boca Raton (1988). [CrossRef] [Google Scholar]
- J.P. Holloway, Spectral velocity discretizations for the Vlasov-Maxwell equations. Transp. Theory Stat. Phys. 25 (1996) 1–32. [CrossRef] [Google Scholar]
- K. Kormann, A semi-Lagrangian Vlasov solver in tensor train format. SIAM J. Sci. Comput. 37 (2015) B613–B632. [CrossRef] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- J. Shen, T. Tang and L.L. Wang, Spectral Methods: Algorithms, Analysis and Applications. Vol. 41. Springer Science & Business Media (2011). [CrossRef] [Google Scholar]
- G. Szegö, Orthogonal Polynomials, 4th edition. Amer. Math. Soc, Providence, RI (1975). [Google Scholar]
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