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Aims. This paper deals with multidimensional NLTE polarized radiative transfer in the case of two level atom in the absence of lower level polarization. We aim to develop an efficient and robust method for 2D cylindrical geometry and to apply it to various axi-symmetrical astrophysical objects such as rings, disks, rotating stars, and solar prominences. Methods. We review the methods of short characteristics and Jacobi iteration applied to axisymmetric geometry. Then we demonstrate how to use a reduced basis for polarized intensity and polarized source function to self-consistently solve the coupled equations of radiative transfer and statistical equilibrium for linearly polarized radiation. We discuss some peculiarities that do not appear in Cartesian geometry, such as angular interpolation in performing the formal solution. We also show how to account for two different types of illuminating radiation. Results. The proposed method is tested on homogeneous, self-emitting cylinders to compare the results with those in 1D geometries. We demonstrate a possible astrophysical application on a very simple model of circumstellar ring illuminated by a host star where we show that such a disk can introduce a significant amount of scattering polarization in the system. Conclusions. This method is found to converge properly and, apparently, to allow for substantial time saving compared to 3D Cartesian geometry. We also discuss the advantages and disadvantages of this approach in multidimensional radiative transfer modeling.

Transfer of polarized line radiation in 2D cylindrical geometry