Equations derived from kinetic theory often express a desired quantity in terms of a probability density. For example, the Direct Simulation Monte Carlo (DSMC) method is a well-known powerful technique for computational rarefied gas dynamics. It uses an algorithm that begins with an initial distribution and, through random sampling, converges to a stationary distribution. Random sampling is achieved using random numbers obtained with pseudo-random number generators. Quasi-Monte Carlo methods (QMCMs) replace calls to a pseudo-random number generator by calls to a quasi-random number generator. QMCMs are known to have a better convergence rates than Monte Carlo methods for multidimensional integration, but it is not trivial to make QMCM work well in contexts outside of Monte Carlo integration, such as DSMC.
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