This is an interesting article that compares a multi-level ILU algorithm to approximate commutator and augmented Lagrange methods: https://doi.org/10.1002/fld.5039
On Wed, Jun 28, 2023 at 11:37 AM Alexander Lindsay <[email protected]> wrote: > I do believe that based off the results in > https://doi.org/10.1137/040608817 we should be able to make LSC, with > proper scaling, compare very favorably with PCD > > On Tue, Jun 27, 2023 at 10:41 AM Alexander Lindsay < > [email protected]> wrote: > >> I've opened https://gitlab.com/petsc/petsc/-/merge_requests/6642 which >> adds a couple more scaling applications of the inverse of the diagonal of A >> >> On Mon, Jun 26, 2023 at 6:06 PM Alexander Lindsay < >> [email protected]> wrote: >> >>> I guess that similar to the discussions about selfp, the approximation >>> of the velocity mass matrix by the diagonal of the velocity sub-matrix will >>> improve when running a transient as opposed to a steady calculation, >>> especially if the time derivative is lumped.... Just thinking while typing >>> >>> On Mon, Jun 26, 2023 at 6:03 PM Alexander Lindsay < >>> [email protected]> wrote: >>> >>>> Returning to Sebastian's question about the correctness of the current >>>> LSC implementation: in the taxonomy paper that Jed linked to (which talks >>>> about SIMPLE, PCD, and LSC), equation 21 shows four applications of the >>>> inverse of the velocity mass matrix. In the PETSc implementation there are >>>> at most two applications of the reciprocal of the diagonal of A (an >>>> approximation to the velocity mass matrix without more plumbing, as already >>>> pointed out). It seems like for code implementations in which there are >>>> possible scaling differences between the velocity and pressure equations, >>>> that this difference in the number of inverse applications could be >>>> significant? I know Jed said that these scalings wouldn't really matter if >>>> you have a uniform grid, but I'm not 100% convinced yet. >>>> >>>> I might try fiddling around with adding two more reciprocal >>>> applications. >>>> >>>> On Fri, Jun 23, 2023 at 1:09 PM Pierre Jolivet <[email protected]> >>>> wrote: >>>> >>>>> >>>>> On 23 Jun 2023, at 10:06 PM, Pierre Jolivet <[email protected]> >>>>> wrote: >>>>> >>>>> >>>>> On 23 Jun 2023, at 9:39 PM, Alexander Lindsay < >>>>> [email protected]> wrote: >>>>> >>>>> Ah, I see that if I use Pierre's new 'full' option for >>>>> -mat_schur_complement_ainv_type >>>>> >>>>> >>>>> That was not initially done by me >>>>> >>>>> >>>>> Oops, sorry for the noise, looks like it was done by me indeed >>>>> in 9399e4fd88c6621aad8fe9558ce84df37bd6fada… >>>>> >>>>> Thanks, >>>>> Pierre >>>>> >>>>> (though I recently tweaked MatSchurComplementComputeExplicitOperator() >>>>> a bit to use KSPMatSolve(), so that if you have a small Schur complement — >>>>> which is not really the case for NS — this could be a viable option, it >>>>> was >>>>> previously painfully slow). >>>>> >>>>> Thanks, >>>>> Pierre >>>>> >>>>> that I get a single iteration for the Schur complement solve with LU. >>>>> That's a nice testing option >>>>> >>>>> On Fri, Jun 23, 2023 at 12:02 PM Alexander Lindsay < >>>>> [email protected]> wrote: >>>>> >>>>>> I guess it is because the inverse of the diagonal form of A00 becomes >>>>>> a poor representation of the inverse of A00? I guess naively I would have >>>>>> thought that the blockdiag form of A00 is A00 >>>>>> >>>>>> On Fri, Jun 23, 2023 at 10:18 AM Alexander Lindsay < >>>>>> [email protected]> wrote: >>>>>> >>>>>>> Hi Jed, I will come back with answers to all of your questions at >>>>>>> some point. I mostly just deal with MOOSE users who come to me and tell >>>>>>> me >>>>>>> their solve is converging slowly, asking me how to fix it. So I >>>>>>> generally >>>>>>> assume they have built an appropriate mesh and problem size for the >>>>>>> problem >>>>>>> they want to solve and added appropriate turbulence modeling (although >>>>>>> my >>>>>>> general assumption is often violated). >>>>>>> >>>>>>> > And to confirm, are you doing a nonlinearly implicit >>>>>>> velocity-pressure solve? >>>>>>> >>>>>>> Yes, this is our default. >>>>>>> >>>>>>> A general question: it seems that it is well known that the quality >>>>>>> of selfp degrades with increasing advection. Why is that? >>>>>>> >>>>>>> On Wed, Jun 7, 2023 at 8:01 PM Jed Brown <[email protected]> wrote: >>>>>>> >>>>>>>> Alexander Lindsay <[email protected]> writes: >>>>>>>> >>>>>>>> > 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. >>>>>>>> >>>>>>>> What mesh aspect ratio and streamline CFL number? Assuming your >>>>>>>> model is turbulent, can you say anything about momentum thickness >>>>>>>> Reynolds >>>>>>>> number Re_θ? What is your wall normal spacing in plus units? (Wall >>>>>>>> resolved >>>>>>>> or wall modeled?) >>>>>>>> >>>>>>>> And to confirm, are you doing a nonlinearly implicit >>>>>>>> velocity-pressure solve? >>>>>>>> >>>>>>>> > 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. >>>>>>>> >>>>>>>> I wouldn't put too much weight on "scaling with mesh size" per se. >>>>>>>> You want an efficient solver for the coarsest mesh that delivers >>>>>>>> sufficient >>>>>>>> accuracy in your flow regime. Constants matter. >>>>>>>> >>>>>>>> Refining the mesh while holding time steps constant changes the >>>>>>>> advective CFL number as well as cell Peclet/cell Reynolds numbers. A >>>>>>>> meaningful scaling study is to increase Reynolds number (e.g., by >>>>>>>> growing >>>>>>>> the domain) while keeping mesh size matched in terms of plus units in >>>>>>>> the >>>>>>>> viscous sublayer and Kolmogorov length in the outer boundary layer. >>>>>>>> That >>>>>>>> turns out to not be a very automatic study to do, but it's what >>>>>>>> matters and >>>>>>>> you can spend a lot of time chasing ghosts with naive scaling studies. >>>>>>>> >>>>>>> >>>>> >>>>>
