Upgrading the Accelerated Lambda Iteration technique by means of 'least change secant methods'

Details Upgrading the Accelerated Lambda Iteration technique by means of 'least change secant methods' Upgrading the Accelerated Lambda Iteration technique by means of 'least change secant methods'

Feb 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992a%26a...255..490k&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 255, no. 1-2, p. 490-494.

Mathematics

27

Algorithms, Iterative Solution, Nonlinear Equations, Radiative Transfer, Stellar Atmospheres, Approximation, Equilibrium Equations, Matrices (Mathematics), Reaction Kinetics

Scientific paper

Non-LTE radiation transfer calculations can be made much more efficient and powerful, when the Iteration with Approximate Lambda Operators (ALI) is combined with a modern method for solving the nonlinear rate equations which occur within that framework. We explain in detail how Broyden's method from the class of so-called 'least change secant methods' can be applied for that purpose, replacing the conventional Newton iteration. Very positive experiences were collected when we implemented Broyden's method into our non-LTE code for modeling spherically expanding stellar atmospheres (Wolf-Rayet stars). Compared to the conventional Newton algorithm, the new technique offers a twofold advantage. First, the computational effort to solve the equations of statistical equilibrium is greatly reduced (e.g., by a factor of eight in our case), and, second, the number of atomic levels which can be accounted for is increased far beyond the usual limit of 100 where the Newton algorithm becomes numerically unstable.

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