  An inverse population transfer of the repulsive Bose-Einstein condensate
(BEC) in a weakly bound double-well trap is explored within the 3D
time-dependent Gross-Pitaevskii equation. The model avoids numerous common
approximations (two-mode treatment, time-space factorization, etc) and closely
follows the conditions of Heidelberg experiments, thus providing a realistic
description of BEC dynamics. The transfer is driven by a time-dependent shift
of a barrier separating the left and right wells. It is shown that completeness
and robustness of the process considerably depend on the amplitude and time
profile of the shift velocity. Soft profiles provide the most robust inversion.
The repulsive interaction substantially supports the transfer making it
possible i) in a wide velocity interval and ii) three orders of magnitude
faster than in the ideal BEC.
