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. > > https://doi.org/10.1016/j.jcp.2007.09.026 > 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/>
