A Functional expansion tally method with numerical basis sets generated by singular value decomposition for one-dimensional Monte Carlo calculations

Kondo, Ryoichi   ; Nagaya, Yasunobu  

A functional expansion tally (FET) method with numerical basis functions generated by singular value decomposition (SVD) is newly proposed. Traditionally, analytical functions were used for the FET calculations, e.g., Legendre polynomials for a one-dimensional distribution. However, the expansion terms could increase to reconstruct steep or complex distributions with these functions. A basis set that can well represent the target distribution with lower order expansion is desired to achieve high accuracy with the small computational resource. In the present study, a numerical basis set is generated from snapshot data by using SVD. This approach is based on the reduced order modeling (ROM). We applied ROM to the FET method in Monte Carlo calculations. The numerical result showed the applicability of the proposed method, on the other hand, some issues were revealed, e.g., discretization of the snapshot data.