  We demonstrate the capabilities of time-dependent density functional theory
(TDDFT) for strong-field, short wavelength (soft X-ray) physics, as compared to
a formalism based on rate equations. We find that TDDFT provides a very good
description of the total and individual ionization yields for Ne and Ar atoms
exposed to strong laser pulses. We assess the reliability of different
adiabatic density functionals and conclude that an accurate description of
long-range interactions by the exchange and correlation potential is crucial
for obtaining the correct ionization yield over a wide range of intensities
($10^{13}$ -- $5 \times 10^{15}$ W/cm$^2$). Our TDDFT calculations disentangle
the contribution from each ionization channel based on the Kohn-Sham
wavefunctions.
