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

TL;DR

This paper introduces efficient iterative schemes based on Gauss-Seidel and Successive Overrelaxation methods to solve complex non-LTE radiative transfer problems involving partial redistribution effects in solar spectral line modeling.

Contribution

It adapts and demonstrates the effectiveness of GS and SOR iterative schemes for polarized and unpolarized PRD problems, significantly improving computational efficiency.

Findings

Symmetric SOR achieves faster convergence than Jacobi-based ALI.

The methods accurately solve PRD problems with reduced computational time.

Applicable to time-dependent magnetohydrodynamic simulations of the solar chromosphere.

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.