  This paper develops an efficient Monte Carlo interior penalty discontinuous
Galerkin method for electromagnetic wave propagation in random media. This
method is based on a multi-modes expansion of the solution to the time-harmonic
random Maxwell equations. It is shown that each mode function satisfies a
Maxwell system with random sources defined recursively. An unconditionally
stable IP-DG method is employed to discretize the nearly deterministic Maxwell
system and the Monte Carlo method combined with an efficient acceleration
strategy is proposed for computing the mode functions and the statistics of the
electromagnetic wave. A complete error analysis is established for the proposed
multi-modes Monte Carlo IP-DG method. It is proved that the proposed method
converges with an optimal order for each of three levels of approximations.
Numerical experiments are provided to validate the theoretical results and to
gauge the performance of the proposed numerical method and approach.
