Atomic Mix Synthetic Acceleration of Dose Computations in Binary Statistical Media

An iterative solution of coupled standard model equations arising in electron transport in binary statistical mixtures is considered. Convergence degradation is observed in certain energy groups and is attributed to chunk sizes appearing optically thin in the higher energy groups. Fourier analysis shows that the spectral radius approaches unity for the zero wave-number error mode as the chunk sizes become vanishingly small. It is shown that the atomic mix model accurately approximates transport under these circumstances and moreover provides a suitable low-order approximation to the iteration error. Fourier analysis and numerical implementation confirm that atomic mix acceleration is unconditionally effective for the application considered here. Our computations also demonstrate the inaccuracy of the atomic mix model for electron dose, especially for materials with strongly contrasting physical properties.