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The linearly-polarized solar limb spectrum that is produced by scatteringprocesses contains a wealth of information on the physical conditions andmagnetic fields of the solar outer atmosphere, but the modeling of many of itsstrongest spectral lines requires solving an involved non-LTE radiativetransfer problem accounting for partial redistribution (PRD) effects. Fastradiative transfer methods for the numerical solution of PRD problems are alsoneeded for a proper treatment of hydrogen lines when aiming at realistictime-dependent magnetohydrodynamic simulations of the solar chromosphere. Herewe show how the two-level atom PRD problem with and without polarization can besolved accurately and efficiently via the application of highly convergentiterative schemes based on the Gauss-Seidel (GS) and Successive Overrelaxation(SOR) radiative transfer methods that had been previously developed for thecomplete redistribution (CRD) case. Of particular interest is the Symmetric SORmethod, which allows us to reach the fully converged solution with an order ofmagnitude of improvement in the total computational time with respect to theJacobi-based local ALI (Accelerated Lambda Iteration) method.

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