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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
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     volume = {47},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a11/}
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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/

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