Numerical Algorithms for Axisymmetric Fokker-Planck-Landau Operators

Journal of Computational Physics

Volumn 157, Issue 2, 2000, Pages 762-786

  Lemou, M ^a  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

AXISYMMETRIC; CONSERVATION PROPERTIES; CYLINDRICAL GEOMETRY; DISCRETE LEVELS; FAST NUMERICAL ALGORITHM; FOKKER PLANCK; NUMERICAL ALGORITHMS; NUMERICAL SCHEME; NUMERICAL TESTS; WEAK FORMULATION;

EID: 0034687903     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6401     Document Type: Article

References (25)

1. Arsene'v Pa. A., Buryac O. E. Math. USSR Sb. 69:1991;465.
2. Berezin Y. A., Khudick V. N., Pekker M. S. J. Comput. Phys. 69:1987;163.
3. Bobylev A. V., Potapenko I. F., Chuyanov V. A. USSR Comput. Math. Math. Phys. 20:1981;190.
4. Buet C., Cordier S. J. Comput. Phys. 145:1998;228.
5. Buet C., Cordier S., Degond P., Lemou M. Fast algorithms for numerical, conservative and entropy approximations of the Fokker-Planck-Landau equation. J. Comput. Phys. 133:1997;310.
6. Degond P., Lucquin-Desreux B. An entropy scheme for the Fokker-Planck collision of plasma kinetic theory. Numer. Math. 68:1994;239.
7. Degond P., Lucquin-Desreux B. The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case. Math. Models Methods Appl. Sci. 2:1992;167.
8. Dellacherie S. Contribution à l'analyse et àla simulation numérique des équations cinétiques décrivant un plasma chaud. 1998.
9. Desvillettes L. On asymptotics of the Boltzmann equation when the collisions become grazing. Trans. Theor. Stat. Phys. 21:1992;259.
10. Epperlein E. M. Implicit and conservative difference scheme for the Fokker-Planck equation. J. Comput. Phys. 112:1994;291.
11. 2AN, 33, 307, 1998.
12. Greengard L., Rokhlin V. A fast algorithm for a particle simulation. J. Comput. Phys. 73:1987.
13. Krall N. A., Trivelpiece A. W. Principles of Plasmas Physics. 1973.
14. Larroche O. Kinetic simulations of a plasma collision experiment. Phys. Fluids B. 5:1993.
15. Lemou M. Multipole expansions for the Fokker-Planck-Landau equation. Numer. Math. 78:1998;597.
16. Lemou M. Exact solutions of the Fokker-Planck equation. C.R. Acad. Sci. Ser. I. 319:1994;579.
17. Lifchitz E. M., Petaevski L. P. Kinetic Theory. 10:1979.
18. MacDonald W. M., Rosenbluth M. N., Chuck W. Relaxation of a system of particles with Coulomb interactions. Phys. Rev. 107:1957.
19. Pekker M. S., Khudick V. N. Conservative difference schemes for the Fokker-Planck equation. USSR Comput. Math. Math. Phys. 24:1984;206.
20. Potapenko I. F., Chuyanov V. A. A completely conservative difference scheme for the two-dimensional Landau equation. USSR Comput. Math. Math. Phys. 20:1980;249.
21. Ray P. S. Energy loss of relativistic electrons in plasmas in accordance with covariant Fokker-Planck formalism. J. Plasma Phys. 24:1980;75.
22. Rosenbluth N., MacDonald W. M., Judd D. L. Fokker-Planck equation for an inverse-square force. Phys. Rev. 107:1957.
23. Schaeffer J. Convergence of a difference scheme for the Vlasov-Poisson-Fokker-Planck system in one dimension. SIAM J. Numer. Anal. 35:1998;1149.
24. Villani C. Contribution à l'étude mathématique des équations de Boltzmann et de Landau en théorie cinétique des gaz et des plasmas. 1998.
25. Whitney J. C. Finite difference methods for the Fokker-Planck equation. J. Comput. Phys. 6:1970;483.