A new stochastic acceleration scheme for the Monte Carlo method

Abstract

A novel scheme to accelerate the Monte Carlo (MC) simulation is described. The method is based on a newly-devised parameter for solution estimation, the average-of-average (AOA). The AOA basically stems from the probability theory, and takes the advantage of stochastic nature of the method itself. Because the concept is simple and utilizes the same random variables as the conventional Monte Carlo method, it can be easily implemented after a minor modification without compromising the computing time. The main purpose of this study is to investigate the feasibility of the AOA method and to identify its numerical performance with regard to the solution estimation. First of all, the mathematical background of the AOA method is described in detail. The definition and the variance of the AOA is derived and the variance of the AOA is compared with that of the standard mean. Furthermore, two additional schemes for variance reduction of the AOA are also introduced, one is a non-uniform weighting scheme and the other one is cut-off strategy of the sampled information. The weighting scheme and cut-off strategy are optimized by sensitivity tests to minimize the variance of the AOA. Conceptually, any kind of random variables can be used for the AOA calculation. In this work, two stochastic reactor parameters, the neutron multiplication factor and the neutron flux, are considered. Several Monte Carlo simulation codes are utilized in this work for the study of the AOA method. MCNP and McCARD are used to check the feasibility of the AOA and to provide the reference solution. In addition, an in-house MC code developed in this work is also adopted for various Monte Carlo simulations in the AOA analysis. The in-house MC code is verified by comparing with the MCNP code for several benchmarks. For the AOA performance analysis, various test problems are considered in this study, which include multi-group energy, continuous energy, simple lattice problem and large scale of reactor problem. The first test problem is C5G7 benchmark problem, which is to test the ability of the method on a basis of multi-group energy structure. The second test problem is an infinite lattice of 17 by 17 fuel assembly problem. The final benchmark problem is APR1400 quarter core problem based on continuous energy physics. For each test problem, the AOA method has been characterized in view of 4 different estimators for the multiplication factor, which are ‘absorption’, ‘collision’, ‘track length’, and ‘combined’ one. The numerical tests have been done for various Monte Carlo calculational conditions, e.g., the number of histories per cycle and the number of active cycles.