Computational Experiments with Direct Simulation Quasi-Random Monte Carlo

The equations derived in kinetic theory express a desired quantity in terms of a probability density. The solution to these equations often requires computational techniques. For example, the Direct Simulation Monte Carlo (DSMC) method is a well-known powerful technique for computational rarefied gas dynamics. DSMC uses an algorithm that evolves an initial distribution in time using random sampling. The sampling is achieved classically through the use of a pseudo-random number generator. Alternatively, QuasiMonte Carlo methods (QMCMs) can replace calls to a pseudo-random number generator by calls to a quasi-random number generator. QMCMs are known to have better convergence rates than Monte Carlo methods for high-dimensional integration, but it is not trivial to make QMCM work well in contexts outside of Monte Carlo integration, such as