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.