A numerical method for the accurate solution of the Fokker-Planck-Landau equation in the nonhomogeneous case

Journal of Computational Physics

Volumn 179, Issue 1, 2002, Pages 1-26

  Filbet, Francis ^a   Pareschi, Lorenzo ^b,c  

^a IECN INRIA Project NumathUniversité de Nancy i   (France)

^b UNIVERSITY OF FERRARA   (Italy)

^c UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Fokker Planck Landau equation; Spectral methods; Splitting algorithms; Vlasov Poisson system

Indexed keywords

EQUATIONS OF MOTION; FOKKER PLANCK EQUATION; POISSON EQUATION; RUNGE KUTTA METHODS; VLASOV EQUATION;

COLLISION OPERATORS; COLLISION PHASE; FOKKE-PLANCK-LANDAU EQUATION; FOKKER PLANCK; LANDAU EQUATION; NEW APPROACHES; NON-HOMOGENEOUS; SPECTRAL METHODS; SPLITTING ALGORITHMS; VLASOV-POISSON SYSTEMS;

NUMERICAL METHODS;

EID: 0037054256     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7010     Document Type: Article

References (47)

1. On the connection between a solution of the Boltzmann equation and a solution of the Fokker-Planck-Landau equation
2. Conservative finite difference schemes for the Fokker-Planck equation not violating the law of an increasing entropy
3. Exact solutions of the Boltzmann equation
4. Theory of collision algorithms for gases and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation
5. Completely conservative difference schemes for nonlinear kinetic equation of Landau (Fokker-Planck) type
6. Difference scheme for the Boltzmann equation based on the Fast Fourier Transform
7. Numerical analysis of conservatives and entropy schemes for the Fokker-Planck-Landau equation
8. Conservative and entropy decaying numerical scheme for the isotropic Fokker-Planck-Landau equation
9. Fast algorithms for numerical, conservative, and entropy approximations of the Fokker-Planck equation
10. Comparison of numerical schemes for Fokker-Planck-Landau equation
11. Simulation of the collisional plasma kinetics under the action of laser and particle beams
12. A practical differences scheme for Fokker-Planck equations
13. The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case
14. An entropy scheme for the Fokker-Planck collision operator of plasma kinetic theory
15. On asymptotics of the Boltzmann equation when the collisions become grazing
16. On the spatially homogeneous Landau equation for hard potentials. Part I: Existence, uniqueness and smoothness; Part II: H-theorem and applications
17. Implicit and conservative difference schemes for the Fokker-Planck equation
18. A numerical solution to the Vlasov equation
19. The spectral collocation method for the kinetic equation with the nonlinear two-dimensional coulomb collisional operator
20. Die kinetische gleichung für den fall Coulombscher vechselwirkung
21. Multipole expansions for the Fokker-Planck-Landau operator
22. Discretization methods for one dimensional Fokker-Planck operators
23. Discrétization de l'opérateur de Fokker-Planck dans le cas homogène
24. High order explicit methods for parabolic equations
25. Fully Implicit Kinetic Solution of Collisional Plasmas
26. Weighted particles in Coulomb collision simulations based on the theory of a cumulative scattering angle
27. Higher order approximation methods for the Boltzmann equation
28. A Fourier spectral method for homogeneous Boltzmann equations
29. Numerical solution of the Boltzmann equation. I: Spectrally accurate approximation of the collision operator
30. On the stability of spectral methods for the homogeneous Boltzmann equation
31. Méthode spéctrale rapide pour l'equation de Fokker-Planck-Landau
32. Fast spectral methods for the Fokker-Planck-Landau collision operator
33. Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit
34. Conservative difference schemes for the Fokker-Planck equation
35. The completely conservative difference schemes for the nonlinear Landau-Fokker-Planck equation
36. Self-consisten Langevin simulation of Coulomb collisions in charged particle beams
37. Fokker-Planck equation for an inverse square force
38. The semi-Lagrangian method for the numerical resolution of Vlasov equations
39. On the construction and comparison of difference schemes
40. Difference schemes for the time evolution of three-dimensional kinetic equations
41. A review of mathematical topics in collisional kinetic theory