科研之友
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摘要
When using standard deterministic particle methods, point values of the computed solutions have to be recovered from their singular particle approximations by using some smoothing procedure. The choice of the smoothing procedure is rather flexible. Moreover, there is always a parameter associated with the smoothing procedure: if this parameter is too large, the numerical solution loses its accuracy; if it is too small, oscillation appears. No explicit formula has been given on how to choose this parameter. In this paper, we develop a particle method for the semiclassical limit of the Schrodinger equation and the Vlasov-Poisson equations, in which we use the property of conservation of charge, which was studied in [D. Wei, Kinetic and Related Models, 3 (2010), pp. 729-754], to construct the density. This method avoids the recovery step of the particle methods; thus it is simpler and more accurate. In particular it gives more accurate field quantities. Consequently, we apply this method to the Vlasov-Poisson equations, which yield more accurate density and electric field in each time step. We carry out numerical experiments in both one and two dimensions for the Schrodinger equation and Vlasov-Poisson equations to verify the method. Some comparisons with other particle methods are also made.
- 出版日期2012
