  We study nonadiabatic effects of geometric pumping. With arbitrary choices of
periodic control parameters, we go beyond the adiabatic approximation to obtain
the exact pumping current. We find that a geometrical interpretation for the
nontrivial part of the current is possible even in the nonadiabatic regime. The
exact result allows us to find a smooth connection between the adiabatic Berry
phase theory at low frequencies and the Floquet theory at high frequencies. We
also study how to control the geometric current. Using the method of shortcuts
to adiabaticity with the aid of an assisting field, we illustrate that it
enhances the current.
