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What is Multigrid Methods for Polarized Radiative Transfer about?

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.

Author

Stepan, Jiri

Published

2006

Language

EN