  New high-resolution spectropolarimetric observations of solar prominences
require improved radiative modelling capabilities in order to take into account
both multi-dimensional - at least 2D - geometry and complex atomic models. This
makes necessary the use of very fast numerical schemes for the resolution of 2D
non-LTE radiative transfer problems considering freestanding and illuminated
slabs. The implementation of Gauss-Seidel and successive over-relaxation
iterative schemes in 2D, together with a multi-grid algorithm, is thoroughly
described in the frame of the short characteristics method for the computation
of the formal solution of the radiative transfer equation in cartesian
geometry. We propose a new test for multidimensional radiative transfer codes
and we also provide original benchmark results for simple 2D multilevel atom
cases which should be helpful for the further development of such radiative
transfer codes, in general.
