[1] Zhou T, Guo Y, Shu C W. Numerical study on Landau damping. Physica D: Nonlinear Phenomena, 2001, 157(4): 322-333. [2] Filbet F, Sonnendrücker E. Comparison of Eulerian Vlasov solvers. Computer Physics Communications, 2003, 150(3): 247-266. [3] Cheng Y, Gamba I M, Morrison P J. Study of conservation and recurrence of Runge-Kutta discontinuous Galerkin schemes for Vlasov-Poisson systems. Journal of Scientific Computing, 2013, 56, 319-349. [4] Cheng Y, Christlieb A J, Zhong X. Numerical study of the two-species Vlasov-Ampère system: Energy-conserving schemes and the current-driven ion-acoustic instability. Journal of Computational Physics, 2015, 288: 66-85. [5] Cai X, Guo W, Qiu J M. A high order semi-Lagrangian discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting. Journal of Computational Physics, 2018, 354: 529-551. [6] Begue M, Ghizzo A, Bertrand P. Two-dimensional Vlasov simulation of Raman scattering and plasma beatwave acceleration on parallel computers. Journal of Computational Physics,1999, 151(2): 458-478. [7] Besse N, Segré J, Sonnendrücker E. Semi-Lagrangian schemes for the two-dimensional Vlasov-Poisson system on unstructured meshes. Transport Theory and Statistical Physics, 2005, 34(3-5): 311-332. [8] Cheng C, Knorr G. The integration of the Vlasov equation in configuration space. Journal of Computational Physics, 1976, 22(3): 330-351. [9] Christlieb A, Guo W, Morton M, et al. A high order time splitting method based on integral deferred correction for semi-Lagrangian Vlasov simulations. Journal of Computational Physics, 2014, 267: 7-27. [10] Crouseilles N, Mehrenberger M, Sonnendrücker E. Conservative semi-Lagrangian schemes for Vlasov equations. Journal of Computational Physics, 2010, 229(6): 1927-1953. [11] Crouseilles N, Respaud T, Sonnendrücker E. A forward semi-Lagrangian method for the numerical solution of the Vlasov equation. Computer Physics Communications, 2009, 180(10): 1730-1745. [12] Filbet F, Sonnendrücker E, Bertrand P. Conservative numerical schemes for the Vlasov equation. Journal of Computational Physics, 2001, 172(1): 166-187. [13] Guo W, Qiu J M. Hybrid semi-Lagrangian finite element-finite difference methods for the Vlasov equation. Journal of Computational Physics, 2013, 234: 108-132. [14] Parker G J, Hitchon W N G. Convected scheme simulations of the electron distribution function in a positive column plasma. Japanese Journal of Applied Physics, 1997, 36(7S): 4799. [15] Qiu J M, Shu C W. Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov-Poisson system. Journal of Computational Physics, 2011, 230(23): 8386-8409. [16] Rossmanith J, Seal D. A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov-Poisson equations. Journal of Computational Physics, 2011, 230(16): 6203-6232. [17] Sonnendrücker E, Roche J, Bertrand P, et al. The semi-Lagrangian method for the numerical resolution of the Vlasov equation. Journal of Computational Physics, 1999, 149(2): 201-220. [18] Birdsall C K, Langdon A B. Plasma Physics Via Computer Simulaition. Boca Raton, FL: CRC Press, 2005. [19] Verboncoeur J P. Particle simulation of plasmas: Review and advances. Plasma Physics and Controlled Fusion, 2005, 47(5A): A231-A260. [20] Hockney R W, Eastwood J W. Computer Simulation Using Particles. Boca Raton, FL: CRC Press, 2010. [21] Barnes J, Hut P. A hierarchical O(N log N) force-calculation algorithm. Nature,1986,324: 446-449. [22] Evstatiev E G, Shadwick B A. Variational formulation of particle algorithms for kinetic plasma simulations. Journal of Computational Physics, 2013, 245: 376-398. [23] Christlieb A, Guo W, Jiang Y. A WENO-based method of lines transpose approach for Vlasov simulations. Journal of Computational Physics, 2016, 327: 337-367. [24] Schemann M, Bornemann F. An adaptive Rothe method for the wave equation. Computing and Visualization in Science, 1998, 1(3): 137-144. [25] Salazar A J, Raydan M, Campo A. Theoretical analysis of the exponential transversal method of lines for the diffusion equation. Numerical Methods for Partial Differential Equations, 2000, 16(1): 30-41. [26] Causley M F, Cho H, Christlieb A J, et al. Method of lines transpose: High order L-stable O(N) schemes for parabolic equations using successive convolution. SIAM Journal on Numerical Analysis, 2016, 54(3): 1635-1652. [27] Cheng Y, Christlieb A J, Guo W, et al. An asymptotic preserving Maxwell solver resulting in the Darwin limit of electrodynamics. Journal of Scientific Computing, 2017, 71(3): 959-993. [28] Liu H, Qiu J. Finite difference Hermite WENO schemes for hyperbolic conservation laws. Journal of Scientific Computing, 2015, 63(2): 548-572. [29] Liu H, Qiu J. Finite difference Hermite WENO schemes for conservation laws, II: An alternative approach. Journal of Scientific Computing, 2016, 66(2): 598-624. [30] Zhao Z, Zhu J, Chen Y, et al. A new hybrid WENO scheme for hyperbolic conservation laws. Computers & Fluids, 2019, 179: 422-436. [31] Qiu J, Shu C W. Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case. Journal of Computational Physics, 2004, 193(1): 115-135. [32] Zhao Z, Chen Y, Qiu J. A hybrid Hermite WENO scheme for hyperbolic conservation laws. Journal of Computational Physics, 2020, 405: 109175. [33] Zhu J, Qiu J. Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method, III: Unstructured meshes. Journal of Scientific Computing, 2009, 39(2): 293-321. [34] Qiu J, Shu C W. Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method II: Two dimensional case. Computers & Fluids, 2005, 34(6): 642-663. [35] Zhu J, Qiu J. A new type of modified WENO schemes for solving hyperbolic conservation laws. SIAM Journal on Scientific Computing,2017, 39(3): A1089-A1113. [36] Zhu J, Shu C W. A new type of multi-resolution WENO schemes with increasingly higher order of accuracy. Journal of Computational Physics, 2018, 375: 659-683. |