Geodesic
Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 2110-2121 
M. A. Korotchenko; G. A. Mikhailov; S. V. Rogazinskii. Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 2110-2121. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a11/
@article{ZVMMF_2007_47_12_a11,
     author = {M. A. Korotchenko and G. A. Mikhailov and S. V. Rogazinskii},
     title = {Modifications of weighted {Monte} {Carlo} algorithms for nonlinear kinetic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2110--2121},
     year = {2007},
     volume = {47},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a11/}
}
TY  - JOUR
AU  - M. A. Korotchenko
AU  - G. A. Mikhailov
AU  - S. V. Rogazinskii
TI  - Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 2110
EP  - 2121
VL  - 47
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a11/
LA  - ru
ID  - ZVMMF_2007_47_12_a11
ER  - 
%0 Journal Article
%A M. A. Korotchenko
%A G. A. Mikhailov
%A S. V. Rogazinskii
%T Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 2110-2121
%V 47
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a11/
%G ru
%F ZVMMF_2007_47_12_a11

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

Test problems for the nonlinear Boltzmann and Smoluchowski kinetic equations are used to analyze the efficiency of various versions of weighted importance modeling as applied to the evolution of multiparticle ensembles. For coagulation problems, a considerable gain in computational costs is achieved via the approximate importance modeling of the “free path” of the ensemble combined with the importance modeling of the index of a pair of interacting particles. A weighted modification of the modeling of the initial velocity distribution was found to be the most efficient for model solutions to the Boltzmann equation. The technique developed can be useful as applied to real-life coagulation and relaxation problems for which the model problems considered give approximate solutions.

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

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

[3] Mikhailov G. A., Rogazinskii C. B., Ureva N. M., “Vesovoi metod Monte-Karlo dlya priblizhennogo resheniya nelineinogo uravneniya koagulyatsii”, Zh. vychisl. matem. i matem. fiz., 46:4 (2006), 715–726 | MR | Zbl

[4] Mikhailov G. A., Voitishek A. B., Chislennoe statisticheskoe modelirovanie (metod Monte-Karlo), Izdat. tsentr “Akademiya”, M., 2006

[5] Vladimirov B. C., Marchuk G. I., “Ob opredelenii sopryazhennogo operatora dlya nelineinykh zadach”, Dokl. RAN, 372:2 (2000), 165–168 | MR | Zbl

[6] Mikhailov G. A., “Postroenie vesovykh metodov Monte-Karlo na osnove uvelicheniya razmernosti fazovogo prostranstva”, Dokl. RAN, 389:4 (2003), 461–464 | MR | Zbl

[7] Voloschuk V. M., Kineticheskaya teoriya koagulyatsii, Gidrometeoizdat, Leningrad, 1984

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

[9] Ivanov M. S., Korotchenko M. L., Mikhailov G. A., Rogazinskii S. V., “Globalno-vesovoi metod Monte-Karlo dlya nelineinogo uravneniya Boltsmana”, Zh. vychisl. matem. i matem. fiz., 45:10 (2005), 1860–1870 | MR | Zbl

[10] Marchenko M. A., Mikhailov G. A., “Raspredelennye vychisleniya po metodu Monte-Karlo”, Avtomatika i telemekhan., 2007, no. 5 | MR