This has been a great discussion to follow. Regarding > when time stepping, you have enough mass matrix that cheaper preconditioners are good enough
I'm curious what some algebraic recommendations might be for high Re in transients. I've found one-level DD to be ineffective when applied monolithically or to the momentum block of a split, as it scales with the mesh size. For high Re boomeramg is ineffective perhaps until https://gitlab.com/petsc/petsc/-/issues/1362 is resolved. I should try fiddling around again with Pierre's work in HPDDM, but curious if there are other PETSc PC recs, or if I need to overcome my inertia/laziness and move beyond command line options. On Mon, May 8, 2023 at 6:46 AM Jed Brown <[email protected]> wrote: > Sebastian Blauth <[email protected]> writes: > > > Hello everyone, > > > > I wanted to briefly follow up on my question (see my last reply). > > Does anyone know / have an idea why the LSC preconditioner in PETSc does > > not seem to scale well with the problem size (the outer fgmres solver I > > am using nearly scale nearly linearly with the problem size in my > example). > > The implementation was tested on heterogeneous Stokes problems from > geodynamics, and perhaps not on NS (or not with the discretization you're > using). > > https://doi.org/10.1016/j.pepi.2008.07.036 > > There is a comment about not having plumbing to provide a mass matrix. A > few lines earlier there is code using PetscObjectQuery, and that same > pattern could be applied for the mass matrix. If you're on a roughly > uniform mesh, including the mass scaling will probably have little effect, > but it could have a big impact in the presence of highly anistropic > elements or a broad range of scales. > > I don't think LSC has gotten a lot of use since everyone I know who tried > it has been sort of disappointed relative to other methods (e.g., inverse > viscosity scaled mass matrix for heterogeneous Stokes, PCD for moderate Re > Navier-Stokes). Of course there are no steady solutions to high Re so you > either have a turbulence model or are time stepping. I'm not aware of work > with LSC with turbulence models, and when time stepping, you have enough > mass matrix that cheaper preconditioners are good enough. That said, it > would be a great contribution to support this scaling. > > > I have also already tried using -ksp_diagonal_scale but the results are > > identical. > > That's expected, and likely to mess up some MG implementations so I > wouldn't recommend it. >
