Fast 2D non–LTE radiative modelling of prominences I. Numerical methods and benchmark results

Context. 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. Aims. 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. Methods. 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. Results. 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.