Gauss-Seidel and Successive Overrelaxation Methods for Radiative Transfer with Partial Frequency Redistribution

The linearly-polarized solar limb spectrum that is produced by scattering processes contains a wealth of information on the physical conditions and magnetic fields of the solar outer atmosphere, but the modeling of many of its strongest spectral lines requires solving an involved non-LTE radiative transfer problem accounting for partial redistribution (PRD) effects. Fast radiative transfer methods for the numerical solution of PRD problems are also needed for a proper treatment of hydrogen lines when aiming at realistic time-dependent magnetohydrodynamic simulations of the solar chromosphere. Here we show how the two-level atom PRD problem with and without polarization can be solved accurately and efficiently via the application of highly convergent iterative schemes based on the Gauss-Seidel (GS) and Successive Overrelaxation (SOR) radiative transfer methods that had been previously developed for the complete redistribution (CRD) case. Of particular interest is the Symmetric SOR method, which allows us to reach the fully converged solution with an order of magnitude of improvement in the total computational time with respect to the Jacobi-based local ALI (Accelerated Lambda Iteration) method.