Geodesic
Application of explicit iterative schemes for solution of kinetic problems
Matematičeskoe modelirovanie, Tome 16 (2004) no. 3, pp. 13-21 
F. S. Zaitsev; D. P. Kostomarov; I. I. Kurbet. Application of explicit iterative schemes for solution of kinetic problems. Matematičeskoe modelirovanie, Tome 16 (2004) no. 3, pp. 13-21. http://geodesic.mathdoc.fr/item/MM_2004_16_3_a1/
@article{MM_2004_16_3_a1,
     author = {F. S. Zaitsev and D. P. Kostomarov and I. I. Kurbet},
     title = {Application of explicit iterative schemes for solution of kinetic problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {13--21},
     year = {2004},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_3_a1/}
}
TY  - JOUR
AU  - F. S. Zaitsev
AU  - D. P. Kostomarov
AU  - I. I. Kurbet
TI  - Application of explicit iterative schemes for solution of kinetic problems
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 13
EP  - 21
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_3_a1/
LA  - ru
ID  - MM_2004_16_3_a1
ER  - 
%0 Journal Article
%A F. S. Zaitsev
%A D. P. Kostomarov
%A I. I. Kurbet
%T Application of explicit iterative schemes for solution of kinetic problems
%J Matematičeskoe modelirovanie
%D 2004
%P 13-21
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/MM_2004_16_3_a1/
%G ru
%F MM_2004_16_3_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper studies a possibility of application of explicit iterative schemes for solution of multidimensional kinetic problems. Properties of modified local iterative scheme LI-M are analyzed. The results of calculations with the scheme are compared with the implicit splitting scheme. Parallel MPI algorithms for explicit iterative scheme and implicit scheme are proposed. The advantages and disadvantages of explicit iterative and implicit schemes are analyzed. Investigations showed that in some cases scheme LI-M has advantages in respect to implicit schemes. Use of scheme LI-M in combination with splitting scheme allows performing stable calculations with the second order of approximation over time.

[1] Yu. N. Dnestrovskii, D. P. Kostomarov, Matematicheskoe modelirovanie plazmy, Nauka, M., 1993

[2] J. Killeen, G. D. Kerbel, M. G. McCoy, A. A. Mirin, Computational Methods for Kinetic Models of Magnetically Confined Plasmas, Springer, New York, 1986 | MR

[3] F. S. Zaitsev, M. R. O'Brien, M. Cox, “Three Dimensional Neoclassical Non-linear Kinetic Equation for Low Collisionality Axisymmetric Tokamak Plasmas”, Physics of Fluids B, 5:2 (1993), 509–519 | DOI

[4] M. R. O'Brien, M. Cox, C. A. Gardner and F. S. Zaitsev, “$3D$ Fokker-Planck Calculation of Alpha-Particle Distributions: a TFTR Simulation”, Nucl. Fusion, 35:12 (1995), 1537–1541 | DOI

[5] F. S. Zaitsev, R. J. Akers and M. R. O'Brien, “Perturbations to deuterium and tritium distributions caused by close collisions with high-energy alpha-particles”, Nucl. Fusion, 42 (2002), 1340–1347 | DOI

[6] F. S. Zaitsev, V. V. Longinov, M. R. O'Brien and R. Tanner, “Difference Schemes for the Time Evolution of Three-Dimensional Kinetic Equations”, J. Comput. Phys., 147 (1998), 239–264 | DOI | MR | Zbl

[7] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1983 | MR

[8] V. T. Zhukov, “Yavno iteratsionnye skhemy dlya parabolicheskikh uravnenii”, Voprosy atomnoi nauki i tekhniki. Seriya: Matematicheskoe modelirovanie fizicheskikh protsessov, 1993, no. 4, 40–46

[9] A. S. Shvedov, V. T. Zhukov, “Yavnye iteratsionnye raznostnye skhemy dlya parabolicheskikh uravnenii”, Zhurnal chislennogo analiza i matematicheskogo modelirovaniya, 1998, 133–148 | MR | Zbl

[10] G. I. Marchuk, Metody vychislitelnoi matematiki, Nauka, M., 1989 | MR

[11] V. T. Zhukov, Raznostnye skhemy lokalnykh iteratsii dlya parabolicheskikh uravnenii, Preprint, In-ta Prikladnoi matematiki im. M. V. Keldysha, 1986 | MR