  In this paper, we propose and analyze a new semi-implicit stochastic
multiscale method for the radiative heat transfer problem with additive noise
fluctuation in composite materials. In the proposed method, the strong
nonlinearity term induced by heat radiation is first approximated, by a
semi-implicit predictor-corrected numerical scheme, for each fixed time step,
resulting in a spatially random multiscale heat transfer equation. Then, the
infinite-dimensional stochastic processes are modeled and truncated using a
complete orthogonal system, facilitating the reduction of the model's
dimensionality in the random space. The resulting low-rank random multiscale
heat transfer equation is approximated and computed by using efficient spatial
basis functions based multiscale method. The main advantage of the proposed
method is that it separates the computational difficulty caused by the spatial
multiscale properties, the high-dimensional randomness and the strong
nonlinearity of the solution, so they can be overcome separately using
different strategies. The convergence analysis is carried out, and the optimal
rate of convergence is also obtained for the proposed semi-implicit stochastic
multiscale method. Numerical experiments on several test problems for composite
materials with various microstructures are also presented to gauge the
efficiency and accuracy of the proposed semi-implicit stochastic multiscale
method.
