Kernel Density Estimation Method for Monte Carlo Global Flux Tallies

The kernel density estimator (KDE) is used to represent Monte Carlo tallies. Two new neutron flux estimators and their variances are developed, namely the KDE collision and KDE track-length tallies. These new estimators are capable of estimating the flux and its variance at any point within a given domain without any bin structure. The strength of these two estimators is illustrated with numerical examples in one- and two-dimensional geometries. Convergence properties of the KDE estimators are discussed and the KDE estimators are compared with the functional expansion tally (FET) and the conventional histogram tally. The results show that the KDE tallies compare favorably with the FET and histogram tallies with respect to accuracy and convergence rate. Disadvantages of KDE estimators are also discussed, and some future research scopes in this area are identified.