[mesa-users] Convergence

Bill Paxton paxton at kitp.ucsb.edu
Fri May 20 12:24:16 EDT 2016

On May 20, 2016, at 9:05 AM, Kenny Van wrote:

> One question I had was that does tol_max_correction guarantee that conversion is always no worse than that? Also is there a way to figure out after the runs have completed to determine how well the convergence was in reality?


First we need to be careful about the meaning of "convergence"

1) we speak of the newton iterations converging to a solution for the new model at the end of a timestep


2) we also use convergence to mean the final results of a run converging to (roughly) the same values as the tolerances are tightened forcing more timesteps and more zones.  

the 1st kind is done at each timestep, the 2nd is done before publishing (or sooner!) by expert users to check the chance that their results are numerical artifacts of inadequate time or space resolution.   there is of course the danger that by reducing timesteps, you'll open up new physics that you would rather stayed hidden (surface pulsations for example).   so this process cannot be pushed too far, but it also should not be neglected.

for newton iterations, i try to avoid the term "convergence" and talk about "acceptance" instead.  the newton generates a series of trial solutions.  each is checked for how well it satisfies the equations ("residuals") and how small the difference is from the previous trial sotution ("corrections").

acceptance must happen within a specified number of trials, or the effort is stopped and the system must do a retry with a smaller timestep.

both the residuals and the corrections can be considered in deciding whether or not to accept a trial solution.

in many cases, it is desirable to stop checking residuals after a specified number of iterations and just use corrections to decide acceptance.

these options are given in controls.defaults, so that's where you need to go next.  search for "solver controls" and read on.


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