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Center for Nonlinear Studies |
We present and discuss efficient variance-reduced Monte Carlo methods for solving the Boltzmann equation in the limit of small deviation from equilibrium; in this limit, traditional particle methods, such as direct simulation Monte Carlo (DSMC), become very inefficient due to the slow convergence associated with the statistical sampling of hydrodynamic properties. The limit of small deviation from equilibrium has recently received significant attention in connection to small-scale science and engineering applications.
Variance reduction is achieved using the method of control variates, which in this case translates to considering only the deviation from equilibrium. In this talk, two methods will be discussed, compared and contrasted. Both methods are able to resolve arbitrarily small deviations from equilibrium, and thus provide significant variance reduction in the limit of small deviation from equilibrium.
Host: Frank Alexander