Geodesic
Global weighted Monte Carlo method for the nonlinear Boltzmann equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 10, pp. 1860-1870 
M. S. Ivanov; M. A. Korotchenko; G. A. Mikhailov; S. V. Rogazinskii. Global weighted Monte Carlo method for the nonlinear Boltzmann equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 10, pp. 1860-1870. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_10_a10/
@article{ZVMMF_2005_45_10_a10,
     author = {M. S. Ivanov and M. A. Korotchenko and G. A. Mikhailov and S. V. Rogazinskii},
     title = {Global weighted {Monte} {Carlo} method for the nonlinear {Boltzmann} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1860--1870},
     year = {2005},
     volume = {45},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_10_a10/}
}
TY  - JOUR
AU  - M. S. Ivanov
AU  - M. A. Korotchenko
AU  - G. A. Mikhailov
AU  - S. V. Rogazinskii
TI  - Global weighted Monte Carlo method for the nonlinear Boltzmann equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 1860
EP  - 1870
VL  - 45
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_10_a10/
LA  - ru
ID  - ZVMMF_2005_45_10_a10
ER  - 
%0 Journal Article
%A M. S. Ivanov
%A M. A. Korotchenko
%A G. A. Mikhailov
%A S. V. Rogazinskii
%T Global weighted Monte Carlo method for the nonlinear Boltzmann equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 1860-1870
%V 45
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_10_a10/
%G ru
%F ZVMMF_2005_45_10_a10

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

New weighted modifications of direct statistical simulation methods as applied to the nonlinear Boltzmann equation are developed on the basis of an original strategy–stratification of the collision distribution in a multiparticle system according to the index of a pair of interacting particles. The weighted algorithms are validated on a model problem with a known solution. It is shown that they effectively estimate variations in the functionals with varying parameters, in particular, with the number of particles in the simulating ensemble.

[1] Berd G., Molekulyarnaya gazovaya dinamika, Mir, M., 1981

[2] Korolev A. E., Yanitskii V. E., “Pryamoe statisticheskoe modelirovanie stolknovitelnoi relaksatsii v smesyakh gazov s bolshim razlichiem v kontsentratsiyakh”, Zh. vychisl. matem. i matem. fiz., 23:3 (1983), 674–680 | Zbl

[3] Rogazinskii S. V., Algoritmy statisticheskogo modelirovaniya dlya resheniya nekotorykh kineticheskikh uravnenii, Dis. ...kand. fiz.-matem. nauk, IVM i MG SO RAN, Novosibirsk, 1989

[4] Rogazinskii S. V., “Ob odnom podkhode k resheniyu odnorodnogo uravneniya Boltsmana”, Zh. vychisl. matem. i matem. fiz., 27:4 (1987), 564–574 | MR

[5] Mikhailov G. A., Rogazinskii S. V., “Vesovye metody Monte-Karlo dlya priblizhennogo resheniya nelineinogo uravneniya Boltsmana”, Sibirskii matem. zhurnal, 43:3 (2002), 620–628 | MR

[6] Mikhailov G. A., Parametric estimates by the Monte-Carlo method, VSP, Utrecht, 1999 | MR | Zbl

[7] Mikhailov G. A., Optimizatsiya vesovykh metodov Monte-Karlo, Izd-vo SO RAN, Novosibirsk, 2000 | MR

[8] Ermakov S. M., Mikhailov G. A., Kurs statisticheskogo modelirovaniya, Nauka, M., 1979 | MR

[9] Ivanov M. S., Rogasinsky S. V., “Analysis of numerical techniques of the direct simulation Monte-Carlo method in the rarefied gas dynamics”, Sov. J. Numer. Analys. Math. Modeling, 3:6 (1988), 453–465 | DOI | MR | Zbl

[10] Denisik S. A., Malama Yu. G., Lebedev C. H., Polak L. S., “Reshenie zadach fizicheskoi i khimicheskoi kinetiki metodom Monte-Karlo”, Primenenie vychisl. matem. v khim. i fiz. kinetike, Nauka, M., 1969, 179–231

[11] Kats M., Veroyatnost i smezhnye voprosy v fizike, Mir, M., 1965 | Zbl

[12] Denisik S. A., Lebedev C. H., Malama Yu. G., “Ob odnoi proverke nelineinoi skhemy metoda Monte-Karlo”, Zh. vychisl. matem. i matem. fiz., 11:3 (1971), 783–785 | Zbl

[13] Ivanov M. S., Rogazinskii S. V., “Ekonomichnye skhemy statisticheskogo modelirovaniya techenii razrezhennogo gaza”, Matematicheskoe modelirovanie, 1:7 (1989), 130–145 | MR | Zbl

[14] Belotserkovskii O. M., Yanitskii V. E., “Statisticheskii metod “chastits v yacheikakh” dlya resheniya zadach dinamiki razrezhennogo gaza”, Zh. vychisl. matem. i matem. fiz., 15:5 (1975), 1195–1208 | MR

[15] Bobylev A. V., “O tochnykh resheniyakh uravneniya Boltsmana”, Dokl. AN SSSR, 225:6 (1975), 1296–1299 | MR | Zbl

[16] Bobylev A. V., “Tochnye resheniya nelineinogo uravneniya Boltsmana i teoriya relaksatsii maksvellovskogo gaza”, Teoreticheskaya i matem. fiz., 60:2 (1984), 280–310 | MR | Zbl