Global iteration scheme

As the first step in our outermost iteration loop (the ``model iteration'') we use the current best guess of $\{T,n_i\}$ as function of radius to solve the hydrostatic or hydrodynamic equations to calculate an improved run of $\hbox{$P_{\rm gas}$}$ with radius. Simultaneously, the population numbers are updated to account for changes in $\hbox{$P_{\rm gas}$}$. The next major step is the computation of the radiation field for each wavelength point (the ``wavelength loop''), which has the prerequisite of a spectral line selection procedure for LTE background lines. Immediately after the radiation field at any given wavelength is known, the radiative rates and the rate operators are updated so that their calculation is finished after the last wavelength point. In the next steps, the population numbers are updated by solving the rate equations for each NLTE species and new electron densities are computed, this gives improved estimates for $\{n_i\}$. The last part of the model iteration is the temperature correction scheme outlined above (using opacity averages etc. that were computed in the wavelength loop) which delivers an improved temperature structure. If the errors in the constraint equations are larger than a prescribed accuracy, the improved $\{T,n_i\}$ are used in another model iteration. Using this scheme, about 10-20 model iterations are typically required to reach convergence to better than about 1% relative errors, depending on the quality of the initial guess of the independent variables and the complexity of the model.