  We propose a scheme of the exact fast-forwarding of standard quantum dynamics
for a charged particle. The present idea allows the acceleration of both the
amplitude and phase of the wave function throughout the fast-forward time range
and is distinct from that of Masuda-Nakamura (e.g., Proc. R. Soc. A {\bf 466},
1135 (2010)) which enabled acceleration of only the amplitude of the wave
function on the way. We shall apply the proposed method to the quantum
tunneling phenomena and obtain the electro-magnetic field to ensure the rapid
penetration of wave functions through a tunneling barrier. Typical examples
described here are: 1) an exponential wave packet passing through the
delta-function barrier; 2) the opened Moshinsky shutter with a delta-function
barrier just behind the shutter. We elucidate the tunneling current in the
vicinity of the barrier and find the remarkable enhancement of the tunneling
rate (: tunneling power) due to the fast-forwarding. In the case of a very high
barrier, in particular, we present the asymptotic analysis and exhibit a
suitable driving force to recover a recognizable tunneling current. The
analysis is also carried out on the exact acceleration of macroscopic quantum
tunneling with use of the nonlinear Schr\"odinger equation which accommodates a
tunneling barrier.
