Convergence Check

The program starts by calculating the new emissivity function (using equation 4.22) and storing the old value of the emissivity function. The convergence check is then done by comparing the old and new values of the emissivity function using

$$DIF=\left\vert\frac{\left(E_{k,i,j}\right)_{\rm new}-\left(E_... ...ight)_{\rm old}} {\left(E_{k,i,j}\right)_{\rm new}}\right\vert$$ (4.37)

for all shells $k$ and all transitions $i \rightarrow j$. Where $DIF$ must be less than the convergence criteria specified in the input files for that transition to have converged.

Convergence is defined as having occurred when either all transitions in all shells converge twice in a row or when only 3 or less levels did not converge in 5 iterations (note that these 5 iterations do not necessarily have to be consecutive). This second option is provided to stop convergence never occurring when one or two levels display instability and do not consistently converge even when the rest of the cloud has done so^4.15.

Once convergence has taken place the program moves on to calculate the line profiles.