On Tue, May 2, 2023 at 2:29 PM Jed Brown <[email protected]> wrote:
Sebastian Blauth <[email protected]> writes:
I agree with your comment for the Stokes equations - for these, I have already tried and used the pressure mass matrix as part of a (additive) block preconditioner and it gave mesh independent results.
However, for the Navier Stokes equations, is the Schur complement really spectrally equivalent to the pressure mass matrix?
No, it's not. You'd want something like PCD (better, but not algebraic) or LSC.
I think you can do a better job than that using something like https://arxiv.org/abs/1810.03315 Basically, you use an augmented Lagrangian thing to make the Schur complement well-conditioned, and then use a special smoother to handle that perturbation.
And even if it is, the convergence is only good for small Reynolds numbers, for moderately high ones the convergence really deteriorates. This is why I am trying to make fieldsplit_schur_precondition selfp work better (this is, if I understand it correctly, a SIMPLE type preconditioner).
SIMPLE is for short time steps (not too far from resolving CFL) and bad for steady. This taxonomy is useful, though the problems are super academic and they don't use high aspect ratio.
Thanks, Matt -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>