Non-LTE line-blanketed model atmospheres of hot stars. I. Hybrid complete linearization/accelerated lambda iteration method

A new numerical method for computing sophisticated non-LTE model stellar atmospheres is presented. The method called the hybrid complete linearization/accelerated lambda iteration (CL/ALI) method, combines advantages of both its constituents. Its rate of convergence is virtually as high as for the standard CL method, while the computer time per iteration is almost as low as for the standard ALI method. The method is formulated as the standard complete linearization, the only difference being that the radiation intensity at selected frequency points is not explicitly linearized; instead, it is treated by means of the ALI approach. The scheme offers a wide spectrum of options, ranging from the full CL to the full ALI method. We demonstrate that the method works optimally if the majority of frequency points are treated in the ALI mode, while the radiation intensity at a few (typically two to 30) frequency points is explicitly linearized. We show how this method can be applied to calculate metal line-blanketed non-LTE model atmospheres, by using the idea of "superlevels" and "superlines" introduced originally by Anderson (1989). We calculate several illustrative models taking into account several tens of thousand of lines of Fe III to Fe VI and show that the hybrid CL/ALI method provides a robust method for calculating non-LTE line-blanketed model atmospheres for a wide range of stellar parameters. The results for individiual stellar types will be presented in subsequent papers in this series.