  We study the problem of dimension reduction for the three dimensional
Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate confined
in a strongly anisotropic harmonic trap. Since the gas is assumed to be in a
strong interaction regime, we have to analyze two combined singular limits: a
semi-classical limit in the transport direction and the strong partial
confinement limit in the transversal direction. We prove that both limits
commute together and we provide convergence rates. The by-products of this work
are approximated models in reduced dimension for the GPE, with a priori
estimates of the approximation errors.
