Multilevel line formation in the comoving frame - Accurate solution using an approximate Newton-Raphson operator

Details Multilevel line formation in the comoving frame - Accurate solution using an approximate Newton-Raphson operator Multilevel line formation in the comoving frame - Accurate solution using an approximate Newton-Raphson operator

Jul 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986a%26a...163..151s&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 163, no. 1-2, July 1986, p. 151-158.

Statistics

Computation

23

Computational Astrophysics, Newton-Raphson Method, Radiative Transfer, Stellar Envelopes, Convergence, Early Stars, Late Stars, Scattering Functions, Stellar Models

Scientific paper

In this paper, the approximate Newton-Raphson (ANR) operator technique that has been developed by Hempe and Schoenberg (1986) for two-level problems is extended to multilevel problems in expanding envelopes. It is shown that the exact Newton-Raphson method leads to quite complex equations that inhibit the application of the exact technique. These equations can be considerablly simplified by assuming that the operator acts mainly locally. Only a simple matrix has to be calculated and inverted for the ANR-technique. The matrix elements contain the usual transition rates from level i to level j as well as the scattering integral and its derivative with respect to the occupation numbers. The derivatives are calculated from the formal solution of the equation of radiative transfer in the comoving frame. However, the ANR-technique is not restricted to comoving frame calculations, but is a general method for problems involving velocity fields. Test calculations representative for early type as well as for late type stars were performed which show that the ANR-method is a simple, efficient and fast technique. The decrease of the corrections is monoton and linear. No stabilizing occurs. Convergence was found for the early type models within 8-11 iterations and for the late type models within 11-20 iterations.

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