Advancement of functional expansion capabilities: Implementation and optimization in Serpent 2

Functional expansions (FEs) are a promising and mathematically-sound tool for representing distributions where meshes or tallies might otherwise be used. This study is based on a prior implementation of functional expansion tallies (FETs) into Serpent, and includes methods developed to improve performance. The Legendre and Zernike polynomial series, both of which can be used to construct an FE's function basis, are studied. A hybrid evaluation method, combining both direct calculations and recurrence relations, is developed for each. Subsequently, a vector-based version of the hybrid evaluation method is presented. The different evaluation methods are then benchmarked and compared. The migration of FETs into Serpent version 2.1.29 as a detector option is then presented. This new detector feature is benchmarked for speed and compared against the conventional mesh-based tallies. The fidelity of each tally type is also briefly discussed. This work is an elaboration and expansion on Advancement of Functional Expansion Tallies Capabilities in Serpent 2 (Wendt et al., 2017), presented in 2017 at both the ANS Student and ANS Annual meetings.