Transport error estimation using residual Monte Carlo

The residual Monte Carlo (RMC) method is also known in the literature as sequential Monte Carlo and reduced-source Monte Carlo. Given a Monte Carlo method for solving a linear equation and an approximate solution to that system, the residual method enables use of essentially the same Monte Carlo algorithm to directly compute the additive error or “defect” associated with the approximate solution. As the size of the defect decreases relative to the size of the solution, the residual Monte Carlo method becomes increasingly efficient relative to the standard Monte Carlo (SMC) method. Here we present a new RMC algorithm for evaluating the space-angle error in Sn radiation transport solutions, and provide computational examples demonstrating that it can be far more efficient than SMC for this purpose. We also describe a particular pitfall that must be avoided if RMC is to be efficient, and explain why the performance of RMC can significantly differ between different transport problems and different quantities of interest for the same problem.