|
[1] A. Grill, "Cold Plasma in Materials Fabrication - from Fundamentals to Applications," IEEE Press (1993). [2] T. P. Armstrong, "Numerical Studies of the Nonlinear Vlasov Equation," Physics Fluids 10, 1269 (1967). [3] YU. A. Berezin, V. N. Khudick and M. S. Pekker, "Conservative Finite-Difference Schemes for the Fokker-Planck Equation not Violating the Law of an Increasing Entropy," Journal of Computational Physics 69,163 (1987). [4] J. E. Broadwell, "Shock Structure in a Simple Discrete Velocity Gas," Physics of Fluids 7(8), 1243 (1964). [5] J. E. Broadwell, "Study of Rarefied Shear Flow by the Discrete Velocity Method, "Fluid Mech. 19, 401(1967). [6] H. Cabannes, "New Analytic Solutions for the Broadwell Equations on Discrete Kinetic Theory," European Journal of Mechanics, B/Fluids, 16(1), 1 (1997). [7] R. E. Caflisch, S. Jin and G. Russo, "Uniformly Accurate Schemes for Hyperbolic System with Relaxation," SIAM Journal on Numerical Analysis 34(1), 246 (1997). [8] M. M. Cecchi, M. Redivo-Zaglia and G. Russo, "Extrapolation Methods for Hyperbolic Systems with Relaxation," Journal of Computational and Applied Mathematics 66, 359 (1996). [9] J. S. Chang and G. Cooper, "A Practical Difference Scheme for Fokker-Planck Equations," Journal of Computational Physics 6, 1 (1970). [10] F. F. Chen, "Introduction to Plasma Physics and Controlled Fusion, Volume 1: Plasma Physics," Plenum Press (1974). [11] C. Z. Cheng and G. Knorr, "The Intergration of the Vlasov Equation in Configuration Space," Journal of Computational Physics 22, 330 (1976). [12] J. Denavit, B. W. Doyle and R. H. Hirsch, "Nonlinear and Collisional Effects on Landau Damping," Physics Fluids 11, 2241 (1968). [13] J. A. Elliott, "Plasma Kinetic Theory,Plasma Physics: an Introductory Course, " R. O. Dendy ed., Cambridge University Press (1993). [14] E. M. Epperlein, "Implicit and Conservation Difference Scheme for the Fokker-Planck Equation," Journal of Computational Physics 112, 291 (1994). [15] E. Gabetta, L. Pareschi and G. Toscani, "Relaxation Schemes for Nonlinear Kinetic Equations," SIAM Journal on Numerical Analysis 34(6), 2168 (1997). [16] R. R. J. Gagne and M. M. Shoucri, "A Splitting Scheme for the Numerical Solution of a One-Dimensional Vlasov Equation," Journal of Computational Physics 24, 445 (1977). [17] L. R. T. Gardner, G. A. Gardner and S. I. Zaki, "Collisional Effects in Plasma Modelled by a Simplified Fokker-Planck Equation," Journal of Computational Physics 107,40 (1993). [18] A. Ghizzo, B. Izrar, and P. Bertrand, "Stability of Bernstein-Greene-Kruskal Plasma Equilibria. Numerical Experiments over Long Time," Physics Fluids 31 (1), 72 (1988). [19] A. Ghizzo, P. Bertrand, M. M. Shoucri, T. W. Johnston, E. Fijalkow and M. R. Feix, "A Vlasov Code for the Numerical Simulation of Stimulated Raman Scattering," Journal of Computational Physics 90,431 (1990). [20] F. C. Grant and M. R. Feix, "Fourier-Hermite Solutions of the Vlasov Equations in the Linear Limit," Physics Fluids 10, 10. (1967). [21] A. Harten, "High Resolution Schemes for Hyperbolic Conservation Law," Journal of Computational Physics 49,357 (1983). [22] A. Harten and S. Osher, "Uniformly High-order Accurate Non-oscillatory Schemes Ⅰ," SIAM Journal on Numerical Analysis, 24(2), 279 (1987). [23] C. A. Hsu, "High Resolution Non-oscillatory Schemes for Hyperbolic Conservation Laws with Applications to Aerodynamics," Ph.D. Dissertation, Institute of Applied Mechanics, National Taiwan University (1993). [24] G. S. Jiang and C. W. Shu, "Efficient Implementation of Weighted ENO Schemes," Journal of Computational Physics 126, 202 (1996). [25] Shi Jin, "Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms," Journal of Computational Physics 122, 51(1995). [26] G. Joyce, G. Knorr and H. K. Meier, "Numerical Integration Methods of the Vlasov Equation," Journal of Computational Physics 8, 53 (1979). [27] N. V. Karetkina, "An Unconditionally Stable Difference Scheme for Parabolic Equations Containing First Derivatives," U.S.S.R. Computational Mathematics and Mathematical Physics 20(1),257 (1980). [28] T. H. Kho, "Relaxation of a System of Charged Particles," Physical Review A 32(1), 666 (1985). [29] A. J. Klimas and W. M. Farrell, "A Splitting Algorithm for Vlasov Simulation with Filamentation Filtration," Journal of Computational Physics 110, 150 (1994). [30] A. J. Klimas, "A Numerical Method Based on the Fourier Transform Approach for Modeling 1-D Electron Plasma Evolution," Journal of Computational Physics 50, 270 (1983). [31] G. Knorr, "Plasma Simulation with Few Particles," Journal of Computational Physics 13, 165 (1973). [32] E. W. Larsen, C. D. Levermore, G. C. Pomraning and J.G. Sanderson, "Discretization Methods for One-dimensional Fokker-Planck Operators," Journal of Computational Physics 61, 359 (1985). [33] X. D. Liu, S. Osher and T. Chan, "Weighted Essentially Non-oscillatory Schemes," Journal of Computational Physics 115, 200 (1994) [34] W. M. Manheimer, M. Lampe, and G. Joyce, "Langevin Representation of Coulomb Collisions in PIC Simulations," Journal of Computational Physics 138, 563 (1997). [35] N. Marushchenko, U, Gasparino, H. Maaβberg and M. Rome, "Bounce-averaged Fokker-Planck Code for the Description of ECRH in a Periodic Magnetic Field," Computer Physics Communications 103,145 (1997). [36] R. Monaco and L. Preziosi, "Fluid Dynamics Applications of the Discrete Boltzmann Equation," World Scinetific Publishing Co. Pte. Ltd.,(1991). [37] D. C. Montgomery and D. A. Tidman, "Plasma Kinetic Theory," McGraw-Hill Book Company (1964). [38] V. A. Mousseau and D. A. Knoll, "Fully Implicit Kinetic Solution of Collisional Plasma," Journal of Computational Physics 136, 308 (1997). [39] C. E. Rathman and J. Denavit, "Simulation of Collisional Effects in Plasmas," Journal of Computational Physics 18, 165 (1975). [40] J. L. Schwarzmeier, H. R. Lewis, B. B. Shrauner and K.R. Symon, "Stability of Bernstein-Greene-Kruskal Equilibria," Physics Fliuds 22(9), 1747 (1979). [41] M. M. Shoucri and G. Knorr, "Numerical Integration of the Vlasov Equation," Journal of Computational Physics 14, 84(1974). [42] M. M. Shoucri, "Numerical Solution of the Two-dimensional Vlasov Equation," IEEE Transactions of Plasma Science, PS-7(2), 69 (1979). [43] M. M. Shoucri and R.R.J. Ganne, A Multistep, "Technique for the Numerical Solution of a Two-dimensional Vlasov Equation," Journal of Computational Physics 23, 242 (1977). [44] C. W. Shu, Preface to the Republication of "Uniformly High Order Essentially Non-oscillatory Schemes,Ⅲ," by Harten, Engquist, Osher, and Chakravarthy, Journal of Computational Physics 131,1 (1997). [45] B. S. Tanenbaum, "Plasma Physics," McGraw-Hill Book Company (1967). [46] J. Y. Yang and C. A. Hsu, "High-resolution Nonoscillatory Schemes for Unsteady Compressible Flows," AIAA Journal 30(6), 1570(1992).
|