  We present the numerical operator method designed for the real time dynamics
of currents through nanostructures beyond the linear response regime. We apply
this method to the transient and stationary currents through nanostructures
with different topologies, e.g., the flakes of square and honeycomb lattices.
We find a quasi-stationary stage with a life proportional to the flake size in
the transient currents through the square flakes, but this quasi-stationary
stage is destroyed in the presence of disorder. However, there is no
quasi-stationary stage in the transient currents through the honeycomb flakes,
showing that the transient current depends strongly upon the topologies of the
nanostructures. We also study the stationary current by taking the limit of the
current at long times. We find that the stationary current through a square
flake increases smoothly as the voltage bias increasing. In contrast, we find a
threshold voltage in the current-voltage curve through a honeycomb flake,
indicating a gap at the Fermi energy of a honeycomb flake.
