  In the time-dependent simulation of pure states dealing with transport in
open quantum systems, the initial state is located outside of the active region
of interest. Using the superposition principle and the analytical knowledge of
the free time-evolution of such state outside the active region, together with
absorbing layers and remapping, a model for a very significant reduction of the
computational burden associated to the numerical simulation of open
time-dependent quantum systems is presented. The model is specially suited to
study (many-particle and high-frequency effects) quantum transport, but it can
also be applied to any other research field where the initial time-dependent
pure state is located outside of the active region. From numerical simulations
of open quantum systems described by the (effective mass) Schr\"{o}dinger and
(atomistic) tight-binding equations, a reduction of the computational burden of
about two orders of magnitude for each spatial dimension of the domain with a
negligible error is presented.
