  We propose a surface hopping Gaussian beam method to numerically solve a
class of high frequency linear transport systems in high spatial dimensions,
based on asymptotic analysis. The stochastic surface hopping is combined with
Gaussian beam method to deal with the multiple characteristic directions of the
transport system in high dimensions. The Monte Carlo nature of the proposed
algorithm makes it easy for parallel implementations. We validate the
performance of the algorithms for applications on the quantum-classical
Liouville equations.
