Regularity analysis of metamaterial Maxwell's equations with random coefficients and initial conditions

In this paper we develop and analyze the stochastic collocation method for solving the time-dependent metamaterial Maxwell's equations subject to random coefficients and random initial conditions. We provide a rigorous regularity analysis of the solution with respect to the random variables. To our best knowledge, this is the first theoretical results derived for the stochastic metamaterial Maxwell equations. The rate of convergence is proved depending on the regularity of the solution. Numerical results are presented to confirm the theoretical analysis. We also demonstrate that the backward wave propagation phenomenon still exists in random metamaterial.