  We revisit optimization of functional renormalization group flows by
analyzing regularized loop integrals. This leads us to a principle, the
Principle of Strongest Singularity, and a corresponding order relation which
allows to order existing regularization schemes with respect to the stability
of renormalization group flows. Moreover, the order relation can be used to
construct new regulators in a systematic fashion. For studies of critical
behavior, which require to follow renormalization group flows down to the deep
infrared regime, such new regulators may turn out to be particularly useful.
The general application of this principle is demonstrated with the aid of a
scalar field theory which is solved over a wide range of scales with novel
methods borrowed from numerical fluid dynamics.
