A Novel Source Convergence Acceleration Scheme for Monte Carlo Criticality Calculations, Part I: Theory

A novel technique for accelerating the convergence rate of the iterative power method for solving eigenvalue problems is presented. Smoothed Residual Acceleration (SRA) is based on a modification to the well known fixed-parameter extrapolation method for power iterations. In SRA the residual vector is passed through a low-pass filter before the extrapolation step. Filtering limits the extrapolation to the lower order eigenmodes, improving the stability of the method and allowing the use of larger extrapolation parameters. In simple tests SRA demonstrates superior convergence acceleration when compared with an optimal fixed-parameter extrapolation scheme. The primary advantage of SRA is that it can be easily applied to Monte Carlo criticality calculations in order to reduce the number of discard cycles required before a stationary fission source distribution is reached. A simple algorithm for applying SRA to Monte Carlo criticality problems is described.