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Multigrid Methods for Polarized Radiative Transfer

Jiri Stepan
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Abstract

A new iterative method for non-LTE multilevel polarized radiative transfer in hydrogen lines is presented. Iterative methods (such as the Jacobi method) tend to damp out high-frequency components of the error fast, but converges poorly due to slow reduction of low-frequency components. The idea is to use a set of differently coarsed grids to reduce both the short- and long-period errors. This leads to the so-called multigrid (MG) methods. For the grid of $N$ spatial points, the number of iterations required to solve a non-LTE transfer problem is of the order of O(N). This fact could be of great importance for problems with fine structure and for multi-dimensional models. The efficiency of the so-called standard MG iteration in comparison to Jacobi iteration is shown. The formalism of density matrix is applied to the demonstrative example of 1D, semi-infinite, non-magnetic, 3-principal level hydrogen atmospheric model. The effect of depolarizing collisions with thermal electrons is taken into account as well as general treatment of overlapping profiles.

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Jiri Stepan. 2006-11-03. Multigrid Methods for Polarized Radiative Transfer. https://arxiv.org/abs/astro-ph/0611112

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