$textbf{Background}$ More than half of all the elements heavier than iron are made by the rapid neutron capture process (or r process). For very neutron-rich astrophysical conditions, such at those found in the tidal ejecta of neutron stars, nuclear fission determines the r-process endpoint, and the fission fragment yields shape the final abundances of $110le A le 170$ nuclei. The knowledge of fission fragment yields of hundreds of nuclei inhabiting very neutron-rich regions of the nuclear landscape is thus crucial for the modeling of heavy-element nucleosynthesis. $textbf{Purpose}$ In this study, we propose a model for the fast calculation of fission fragment yields based on the concept of shell-stabilized prefragments defined with help of the nucleonic localization functions. $textbf{Methods}$ To generate realistic potential energy surfaces and nucleonic localizations, we apply Skyrme Density Functional Theory. The distribution of the neck nucleons among the two prefragments is obtained by means of a statistical model. $textbf{Results}$ We benchmark the method by studying the fission yields of $^{178}$Pt, $^{240}$Pu, $^{254}$Cf, and $^{254,256,258}$Fm and show that it satisfactorily explains the experimental data. We then make predictions for $^{254}$Pu and $^{290}$Fm as two representative cases of fissioning nuclei that are expected to significantly contribute during the r-process nucleosynthesis occurring in neutron star mergers. $textbf{Conclusions}$ The proposed framework provides an efficient alternative to microscopic approaches based on the evolution of the system in a space of collective coordinates all the way to scission. It can be used to carry out global calculations of fission fragment distributions across the r-process region.
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