  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.
