Multigrid Methods for Polarized Radiative Transfer
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.
- Publication:
-
Solar Polarization 4
- Pub Date:
- December 2006
- DOI:
- 10.48550/arXiv.astro-ph/0611112
- arXiv:
- arXiv:astro-ph/0611112
- Bibcode:
- 2006ASPC..358..148S
- Keywords:
-
- Astrophysics
- E-Print:
- 4 pages, 1 figure