Re: [petsc-users] Scalable Solver for Incompressible Flow
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 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 wrote: > >> See src/snes/tutorials/ex70.c for the code that I think was used for that >> paper. >> >> Alexander Lindsay 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 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_XhuZStZ0A: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 >> wrote: >> > >> > On 23 Jun 2023, at 10:06 PM, Pierre Jolivet >> wrote: >> > >> > On 23 Jun 2023, at 9:39 PM, Alexander Lindsay >> 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 >>
Re: [petsc-users] Scalable Solver for Incompressible Flow
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 wrote: > See src/snes/tutorials/ex70.c for the code that I think was used for that > paper. > > Alexander Lindsay 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 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_XhuZStZ0A: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 > wrote: > > > > On 23 Jun 2023, at 10:06 PM, Pierre Jolivet > wrote: > > > > On 23 Jun 2023, at 9:39 PM, Alexander Lindsay > 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 < >
