I would email the author. He's been helpful in the past and that newer paper may have been extensions that didn't make it into the upstream example.
Alexander Lindsay <alexlindsay...@gmail.com> writes: > Maybe that example was a jumping point for some of those studies, but it > looks to me like that example has been around since ~2012 and initially > only touched on SIMPLE, as opposed to addition of SIMPLE into an > augmented lagrange scheme. > > But it does seem that at some point Carola Kruse added Golub-Kahan > bidiagonalization tests to ex70. I don't know very much about that although > it seems to be related to AL methods ... but requires that the matrix be > symmetric? > > On Fri, Jul 28, 2023 at 7:04 PM Jed Brown <j...@jedbrown.org> wrote: > >> See src/snes/tutorials/ex70.c for the code that I think was used for that >> paper. >> >> Alexander Lindsay <alexlindsay...@gmail.com> writes: >> >> > Sorry for the spam. Looks like these authors have published multiple >> papers on the subject >> > >> > cover.jpg >> > Combining the Augmented Lagrangian Preconditioner with the Simple Schur >> Complement Approximation | SIAM Journal on >> > Scientific Computingdoi.org >> > cover.jpg >> > >> > On Jul 28, 2023, at 12:59 PM, Alexander Lindsay < >> alexlindsay...@gmail.com> wrote: >> > >> > Do you know of anyone who has applied the augmented Lagrange >> methodology to a finite volume discretization? >> > >> > On Jul 6, 2023, at 6:25 PM, Matthew Knepley <knep...@gmail.com> wrote: >> > >> > On Thu, Jul 6, 2023 at 8:30 PM Alexander Lindsay < >> alexlindsay...@gmail.com> wrote: >> > >> > 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 >> > >> > That is for incompressible NS. The results are not better than >> https://arxiv.org/abs/1810.03315, and that PC is considerably >> > simpler and already implemented in PETSc. There is an update in to this >> > >> > >> > >> https://epubs.siam.org/doi/abs/10.1137/21M1430698?casa_token=Fp_XhuZStZ0AAAAA:YDhnkW9XvAom_b8KocWz-hBEI7FAt46aw3ICa0FvCrOVCtYr9bwvtqJ4aBOTkDSvANKh6YTQEw >> > >> > >> > which removes the need for complicated elements. >> > >> > You might need stuff like ILU for compressible flow, but I think >> incompressible is solved. >> > >> > Thanks, >> > >> > Matt >> > >> > On Wed, Jun 28, 2023 at 11:37 AM Alexander Lindsay < >> alexlindsay...@gmail.com> 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 < >> alexlindsay...@gmail.com> 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 < >> alexlindsay...@gmail.com> 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 < >> alexlindsay...@gmail.com> 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 <pierre.joli...@lip6.fr> >> wrote: >> > >> > On 23 Jun 2023, at 10:06 PM, Pierre Jolivet <pierre.joli...@lip6.fr> >> wrote: >> > >> > On 23 Jun 2023, at 9:39 PM, Alexander Lindsay <alexlindsay...@gmail.com> >> 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 < >> alexlindsay...@gmail.com> >> > 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 < >> alexlindsay...@gmail.com> >> > 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 <j...@jedbrown.org> wrote: >> > >> > Alexander Lindsay <alexlindsay...@gmail.com> 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. >> > >> > -- >> > 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/ >>
