  The simulation of the time-dependent evolution of the resonant tunneling
diode is done by a multiscale algorithm exploiting the existence of resonant
states. After revisiting and improving the algorithm developed in [N. Ben
Abdallah, O. Pinaud, J. Comp. Phys. 213 (2006) 288-310] for the stationary
case, the time-dependent problem is dealt with. The wave function is decomposed
into a non resonant part and a resonant one. The projection method to compute
the resonant part leads to an accurate algorithm thanks to a suitable
interpolation of the non resonant one. The simulation times are largely
reduced.
