Krylov iterative methods and synthetic acceleration for transport in binary statistical media

Iterative solution of the Levermore-Pomraning equations for transport in binary statistical mixtures can be extremely slow in certain limits. We propose an iterative method that improves convergence by utilizing a combination of inner iterations, synthetic acceleration schemes and Krylov iterative methods. Spectral analysis and numerical results show that our new scheme outperforms simpler iterative methods for problems in either the diffusion or the atomic mix regimes, or both. (authors)