Two-step acceleration method for transport problems

In recent years, much effort has been focused on understanding and improving the convergence properties of iteration methods for solving transport problems. The comparative advantages and disadvantages of the source iteration (SI), Chebyschev-acceleration, rebalance, diffusion-synthetic acceleration (DSA), and projected acceleration methods are documented in the literature and will not be discussed here except to note that no one single method has proven to be best in all situations. Here we describe a new acceleration method that is more computationally efficient than SI, extremely simple to implement, linear (hence can be theoretically treated by a Fourier analysis), and does not contain any spatial differencing difficulties of the sort that have confronted DSA. However, this method is not as efficient as DSA because its performance degrades as the scattering ratio c approaches 1.0