  This article introduces a new numerical method for the minimization under
constraints of a discrete energy modeling multicomponents rotating
Bose-Einstein condensates in the regime of strong confinement and with
rotation. Moreover, we consider both segregation and coexistence regimes
between the components. The method includes a discretization of a continuous
energy in space dimension 2 and a gradient algorithm with adaptive time step
and projection for the minimization. It is well known that, depending on the
regime, the minimizers may display different structures, sometimes with
vorticity (from singly quantized vortices, to vortex sheets and giant holes).
In order to study numerically the structures of the minimizers, we introduce in
this paper a numerical algorithm for the computation of the indices of the
vortices, as well as an algorithm for the computation of the indices of vortex
sheets. Several computations are carried out, to illustrate the efficiency of
the method, to cover different physical cases, to validate recent theoretical
results as well as to support conjectures. Moreover, we compare this method
with an alternative method from the literature.
