  We derive a novel computational scheme for functional Renormalization Group
(fRG) calculations for interacting fermions on 2D lattices. The scheme is based
on the exchange parametrization fRG for the two-fermion interaction, with
additional insertions of truncated partitions of unity. These insertions
decouple the fermionic propagators from the exchange propagators and lead to a
separation of the underlying equations. We demonstrate that this separation is
numerically advantageous and may pave the way for refined, large-scale
computational investigations even in the case of complex multiband systems.
Furthermore, on the basis of speedup data gained from our implementation, it is
shown that this new variant facilitates efficient calculations on a large
number of multi-core CPUs. We apply the scheme to the $t$,$t'$ Hubbard model on
a square lattice to analyze the convergence of the results with the bond length
of the truncation of the partition of unity. In most parameter areas, a fast
convergence can be observed. Finally, we compare to previous results in order
to relate our approach to other fRG studies.
