Practical Monte Carlo simulation using modified power method with preconditioning

The authors developed the modified power method (MPM) in previous publications to obtain multiple eigenmodes of an eigenvalue problem at the same time by employing a generalized eigenvalue problem (GEP) of the form of WX = VXK. Special attention has been paid to the Monte Carlo (MC) implementation of the MPM because it always suffers from the inherent statistical noises. In this paper, a preconditioning method for the GEP has been developed for the MC MPM, so that the performance is more stable and robust to the MC statistical noises. This preconditioning method is crucial for MC solving of problems with degenerated eigenmodes, which requires the accumulation of a so-called transfer matrix and the division of the system space into multiple sub-regions, the number of sub-regions being greater than the number of eigenmodes to be solved. The preconditioning method solves the issues arising from the mismatch between the number of sub-regions and the target number of eigenmodes to be calculated. The numerical results for a model cube problem and BEAVRS whole core neutron transport eigenvalue problem successfully demonstrate the validity of the preconditioning method and the extended applicability of the MC MPM for practical problems.