you will need to update test results once again

I am ok with merging this to have a test for the bfbt schur complement preconditioner, but just to document this for the future: At the moment the bfbt version requires 159 outer GMRES iterations and the simple inverse viscosity mass matrix requires only 18 outer GMRES iterations. To compute this I used the same parameter file you have here inside the tester docker container, but with set Use weighted BFBT for Schur complement = false. In other words either the method doesnt work very well for this benchmark, or there is something wrong in the method implementation. Did I interpret this correctly?

@gassmoeller

From all the tests I have run, AMG-BFBT can take quite a lot of iterations to converge when the number of initial global refinements is small.

If you start with four initial global refinements, AMG takes 18 iterations and AMG-BFBT takes 73. For five levels,
AMG takes 19 and AMG-BFBT takes 65.

Thanks for confirming. However, is this a state you would expect? From my understanding BFBT was supposed to be a better approximation to the real Schur complement than the inverse mass matrix and therefore should reduce the number of outer GMRES iterations. Did you find a theoretical reason why it is worse?

Yes, we are aware. I asked him to open PRs to add tests so we can document the current status and can correctly track progress.

In short: we do not implement the corrections mentioned in the original paper for coarse meshes and I suspect our inner solver is not done correctly either.