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

Abstract

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.

39 pages, 9 figures, accepted for publication in the Astrophysical Journal (2010), added labels to all the figures to make them more informative for the reader

References in corpus (2)

• Preconditioned Bi-Conjugate Gradient Method for Radiative Transfer in Spherical Media
• A conjugate gradient method for the solution of the non-LTE line radiation transfer problem

Cited by in corpus (6)

• PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers
• The transfer of resonance line polarization with partial frequency redistribution and J-state interference
• On the Sensitivity of Partial Redistribution Scattering Polarization Profiles to Various Atmospheric Parameters
• Numerical solutions to linear transfer problems of polarized radiation I. Algebraic formulation and stationary iterative methods
• Full non-LTE spectral line formation III. The case of a two-level atom with broadened upper level
• Accelerating NLTE radiative transfer by means of the Forth-and-Back Implicit Lambda Iteration: A two-level atom line formation in 2D Cartesian coordinates