Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aspc..288..215k&link_type=abstract
Stellar Atmosphere Modeling, ASP Conference Proceedings, Vol. 288. Abstracts from a conference held 8-12 April 2002 in Tuebingen
Astronomy and Astrophysics
Astronomy
Scientific paper
One of the kernels of the widely applied Accelerated Lambda Iteration (ALI) for the construction of non-LTE model atmospheres is the solution of the rate equations, i.e. the calculation of level population numbers from a given radiation field. Due to the so-called ``acceleration'', which is vital for the overall convergence, this set of equations is usually non-linear. In my talk I will discuss the Newton iteration which is the prototype of all fast and reliable methods for the solution of non-linear equations, and its derivatives, namely the Broyden and the Kantorovich method. I will show that the attributes fast and reliable are aligned, which also means that slow methods are virtually of no use. This is demonstrated by means of the slow Unsöld-Lucy temperature correction scheme.
I will also show how the non-linear equations can be transformed into linear equations by two techniques named preconditioning and linearization, respectively.
At last I will focus on the construction of the Λ-operator, i.e. the ``accelerating'' term. In static atmospheres the operator can be easily derived from the solution of the radiation transfer while in moving atmospheres life is much more difficult.
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