Monte Carlo methods are the most popular methods for solving problems in kinetic theory. In this short remark we emphasize some of the side effects due to the use of conservative methods over a finite number of statistical samples (particles) in the simulation. The most relevant aspect is that the steady states of the system are compactly supported and thus they cannot be Maxwellian (or any other non compactly supported statistics) unless the number of particles goes to infinity. These aspects are studied numerically with the help of a simple one-dimensional space homogeneous kinetic model.
A remark on the finite number of particles effect in Monte Carlo methods for kinetic equations
DIMARCO, Giacomo;PARESCHI, Lorenzo
2007
Abstract
Monte Carlo methods are the most popular methods for solving problems in kinetic theory. In this short remark we emphasize some of the side effects due to the use of conservative methods over a finite number of statistical samples (particles) in the simulation. The most relevant aspect is that the steady states of the system are compactly supported and thus they cannot be Maxwellian (or any other non compactly supported statistics) unless the number of particles goes to infinity. These aspects are studied numerically with the help of a simple one-dimensional space homogeneous kinetic model.File in questo prodotto:
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