  The nonlinear response of a material to a large electric field (steady or
pulsed) often determines the ultimate performance of the material for
electronics applications. The formalism for understanding nonlinear effects in
conventional semiconductors is well understood. The formalism is less well
developed for so-called ``smart'' materials that are tuned to lie close to the
metal-insulator transition. Here we show that the nonlinear response of a
strongly correlated electronic material can be calculated with a massively
parallel algorithm by discretizing a continuous matrix operator on the
Kadanoff-Baym contour in real time. We benchmark the technique by examining the
solutions when the field vanishes and comparing the results to exact results
from an equilibrium formalism. We briefly discuss the numerical issues
associated with the case of a large electric field and present results that
show how the Bloch oscillations become damped as the scattering due to electron
correlations increases.
