Numerical solutions to linear transfer problems of polarized radiation

Abstract

Context. The polarization signals produced by the scattering of anistropic radiation in strong resonance lines encode important information about the elusive magnetic fields in the outer layers of the solar atmosphere. An accurate modeling of these signals is a very challenging problem from the computational point of view, in particular when partial frequency redistribution (PRD) effects in scattering processes are accounted for with a general angle-dependent treatment. Aims. We aim at solving the radiative transfer problem for polarized radiation in nonlocal thermodynamic equilibrium conditions, taking angle-dependent PRD effects into account. The problem is formulated for a two-level atomic model in the presence of arbitrary magnetic and bulk velocity fields. The polarization produced by scattering processes and the Zeeman effect is considered. Methods. The proposed solution strategy is based on an algebraic formulation of the problem and relies on a convenient physical assumption, which allows its linearization. We applied a nested matrix-free GMRES iterative method. Effective preconditioning is obtained in a multifidelity framework by considering the light-weight description of scattering processes in the limit of complete frequency redistribution (CRD). Results. Numerical experiments for a one-dimensional (1D) atmospheric model show near optimal strong and weak scaling of the proposed CRD-preconditioned GMRES method, which converges in few iterations, independently of the discretization parameters. A suitable parallelization strategy and high-performance computing tools lead to competitive run times, providing accurate solutions in a few minutes. Conclusions. The proposed solution strategy allows the fast systematic modeling of the scattering polarization signals of strong resonance lines, taking angle-dependent PRD effects into account together with the impact of arbitrary magnetic and bulk velocity fields. Almost optimal strong and weak scaling results suggest that this strategy is applicable to realistic 3D models. Moreover, the proposed strategy is general, and applications to more complex atomic models are possible.

The Impact of Angle-dependent Partial Frequency Redistribution on the Scattering Polarization of the Solar Na i D Lines

“…As far as III  is concerned, a widely used approximation is to assume that the scattering processes described by this matrix are also totally incoherent in the observer's frame (e.g., Mihalas 1978;Bommier 1997;Alsina Ballester et al 2017;Benedusi et al 2022). This assumption is also applied in this work.…”

“…Following the works by Janett et al (2021b) and Benedusi et al (2021Benedusi et al ( , 2022, we first present an algebraic formulation of the considered linearized RT problem for polarized radiation. Starting from this formulation, we then apply a parallel solution strategy based on Krylov iterative methods with physics-based preconditioning.…”

“…After introducing the collocation vectors Î I N  and Î N   (N = 4N r N ν N θ N χ ), which contain the numerical approximations of the Stokes vector and the emission vector, respectively, at all N nodes, the whole discrete RT problem can then be formulated in the compact form given by (see Janett et al 2021a;Benedusi et al 2022)…”

“…The proposed iterative solver consists of two nested GMRES iterations (see Benedusi et al 2022). We use no restart and the same threshold tolerance, tol, for both GMRES iterations.…”

“…The preconditioned GMRES solvers outperform the unpreconditioned one, strongly reducing the number of iterations to convergence. The reader is referred to Benedusi et al (2022) for more details on this solution strategy.…”