> On 13 May 2025, at 5:40 PM, Jed Brown <j...@jedbrown.org> wrote: > > The preconditioned norm has units of state (like velocity and pressure) while > the residual norm has units of residual. Note that both of these are > dimensionally-inconsistent (they depend on the units/nondimensionalization > you have chosen), and their relative scale also depends on > units/nondimensionalization. So merely being "larger" doesn't mean the > preconditioner isn't working. You'd need to assess whether the spectrum is > better (of which, number of iterations to converge is a convenient surrogate > and the thing you care about anyway). > > I would caution not to infer too much from Stokes if your interest is > turbulence. The time step size is important for turbulence and diffusion is > only of the same scale as advection. For Stokes, one doesn't normally use PCD > because the inverse-viscosity weighted mass matrix is a spectrally equivalent > preconditioner (and simpler than PCD).
That being said, if you have something closer to your target discretization/geometry that you’d be willing to share, some of us (or at the very least, me) would be happy to have a look. I understand you may not want to share either of these publicly if this is part of a closed-source topology optimization framework, in which case you can send stuff at petsc-ma...@mcs.anl.gov <mailto:petsc-ma...@mcs.anl.gov> Thanks, Pierre PS: I’ve tried some of my stuff on your problem (either monolithically or as part of PCFIELDSPLIT), they trivially solve it (even with a slightly refined geometry, notice the number of unknowns), but they have a high setup cost, and I can’t guarantee they’ll work for your final problem, as Jed mentioned. DOFs: 2137103 Residual norms for firedrake_0_ solve. 0 KSP unpreconditioned resid norm 4.898001545440e-03 true resid norm 4.898001545440e-03 ||r(i)||/||b|| 1.000000000000e+00 1 KSP unpreconditioned resid norm 4.897530535125e-03 true resid norm 4.897530535125e-03 ||r(i)||/||b|| 9.999038362258e-01 2 KSP unpreconditioned resid norm 4.895485358665e-03 true resid norm 4.895485358665e-03 ||r(i)||/||b|| 9.994862829765e-01 3 KSP unpreconditioned resid norm 4.892258200545e-03 true resid norm 4.892258200545e-03 ||r(i)||/||b|| 9.988274105589e-01 4 KSP unpreconditioned resid norm 4.832684872769e-03 true resid norm 4.832684872769e-03 ||r(i)||/||b|| 9.866646279988e-01 5 KSP unpreconditioned resid norm 3.484018420031e-03 true resid norm 3.484018420031e-03 ||r(i)||/||b|| 7.113142753650e-01 6 KSP unpreconditioned resid norm 1.317379071184e-03 true resid norm 1.317379071184e-03 ||r(i)||/||b|| 2.689625674803e-01 7 KSP unpreconditioned resid norm 2.393153081654e-04 true resid norm 2.393153081654e-04 ||r(i)||/||b|| 4.885978616895e-02 8 KSP unpreconditioned resid norm 4.276785206897e-05 true resid norm 4.276785206898e-05 ||r(i)||/||b|| 8.731694278210e-03 9 KSP unpreconditioned resid norm 7.000151646440e-06 true resid norm 7.000151646437e-06 ||r(i)||/||b|| 1.429185266990e-03 10 KSP unpreconditioned resid norm 1.407327852370e-06 true resid norm 1.407327852358e-06 ||r(i)||/||b|| 2.873269514723e-04 11 KSP unpreconditioned resid norm 2.223672507944e-07 true resid norm 2.223672507690e-07 ||r(i)||/||b|| 4.539958771063e-05 12 KSP unpreconditioned resid norm 4.643025030927e-08 true resid norm 4.643025033995e-08 ||r(i)||/||b|| 9.479427458160e-06 13 KSP unpreconditioned resid norm 9.835866346159e-09 true resid norm 9.835866346336e-09 ||r(i)||/||b|| 2.008138677599e-06 14 KSP unpreconditioned resid norm 1.658715911665e-09 true resid norm 1.658715908692e-09 ||r(i)||/||b|| 3.386515690745e-07 15 KSP unpreconditioned resid norm 3.674829203051e-10 true resid norm 3.674829226619e-10 ||r(i)||/||b|| 7.502711447776e-08 16 KSP unpreconditioned resid norm 6.299503951584e-11 true resid norm 6.299505159177e-11 ||r(i)||/||b|| 1.286137846372e-08 17 KSP unpreconditioned resid norm 1.078827517736e-11 true resid norm 1.078831394356e-11 ||r(i)||/||b|| 2.202595046872e-09 KSP final norm of residual 1.07883e-11 > Hardik Kothari <hardik.koth...@corintis.com > <mailto:hardik.koth...@corintis.com>> writes: > >> Dear Pierre, Dear PETSc team, >> >> Thank you for your response. >> >> In terms of geometry, we are moving toward more complex domains with more >> refined meshes that include multiple thin channels. We have been >> experimenting with the Stokes problem as a simplified case, but our main >> goal is to solve the high-Reynolds-number Navier–Stokes equations in these >> settings. >> >> We are currently planning to utilize a multi-node CPU architecture. >> >> For the Navier–Stokes system, we have experimented with both >> pressure-convection diffusion (PCD) and LSC preconditioners. In the thin >> channels, the PDC struggles to converge, and the LSC preconditioner is >> computationally slow, but it does converge eventually. Also, for both of >> these preconditioners for the thin channels, the norm of the preconditioned >> residual is much higher than the true residual norm, which likely indicates >> that neither preconditioner provides a sufficiently accurate approximation >> of the Schur complement. >> >> I would appreciate any insights you may have for better preconditioning >> strategies. >> >> Best regards, >> Hardik >> >> >> >> HARDIK KOTHARI >> >> hardik.koth...@corintis.com >> <mailto:hardik.koth...@corintis.com><mailto:hardik.koth...@corintis.com> >> >> Corintis SA >> EPFL Innovation Park Building C >> 1015 Lausanne >> >> >> >> [https://urldefense.us/v3/__https://storcor.s3.eu-central-1.amazonaws.com/logos/Logo-black.png__;!!G_uCfscf7eWS!ZkgL3p_ykjNhChJT714e-SsEGf_se8P03ZonnBbsSYm4XLTWR5khwNuHfc88CuP0c57UyPwjOWYcyMKkTLcXKGkCewbGGmUO$ >> ] >> Here at Corintis we care for your privacy. That is why we have taken >> appropriate measures to ensure that the data you have provided to us is >> always secure >> From: Pierre Jolivet <pie...@joliv.et <mailto:pie...@joliv.et>> >> Date: Sunday, 11 May 2025 at 20:45 >> To: Hardik Kothari <hardik.koth...@corintis.com >> <mailto:hardik.koth...@corintis.com>> >> Cc: petsc-users@mcs.anl.gov <mailto:petsc-users@mcs.anl.gov> >> <petsc-users@mcs.anl.gov <mailto:petsc-users@mcs.anl.gov>> >> Subject: Re: [petsc-users] Solving Stokes problem in high aspect ratio >> domains >> >> You don't often get email from pie...@joliv.et <mailto:pie...@joliv.et>. >> Learn why this is >> important<https://urldefense.us/v3/__https://aka.ms/LearnAboutSenderIdentification__;!!G_uCfscf7eWS!ZkgL3p_ykjNhChJT714e-SsEGf_se8P03ZonnBbsSYm4XLTWR5khwNuHfc88CuP0c57UyPwjOWYcyMKkTLcXKGkCe1E-JiqZ$ >> > >> >> Do you want to refine the geometry or are you fine with the current one? >> What kind of hardware are you planning on using (GPU, single-node…)? >> Do you have a configuration for which LSC fails or does not give you >> good-enough performance? >> >> Thanks, >> Pierre >> >> >> On 9 May 2025, at 9:08 PM, Mark Adams <mfad...@lbl.gov >> <mailto:mfad...@lbl.gov>> wrote: >> >> Hi Hardik, >> >> The domain shape is not critical but the element shapes are. Your 100:1 >> domain aspect ratio is bad if you have N^3 mesh and thus element aspect >> ratios of 100:1. >> If that is the case then you probably want to look at semi-coarsening >> multigrid. >> >> Mark >> >> On Fri, May 9, 2025 at 9:55 AM Hardik Kothari <hardik.koth...@corintis.com >> <mailto:hardik.koth...@corintis.com><mailto:hardik.koth...@corintis.com>> >> wrote: >> Dear PETSc team, >> >> We are solving the Stokes equations using PETSc (via Firedrake) on a highly >> anisotropic 3D domain (L_x=1, L_y=0.01, L_z=0.1). >> >> In this setup, standard Schur complement preconditioners using a mass >> inverse for pressure struggle to converge. We could solve the problem with >> the LSC preconditioner (solver parameters are shown in the script). >> >> We have the following questions: >> >> * Why standard preconditioners struggle in such domains? >> * Why is the preconditioned residual norm for the Schur complement system >> much higher than the true residual norm? >> * Would you recommend alternative or more robust preconditioners for such >> geometries? >> >> Thank you for your help. >> >> Best regards, >> Hardik >> >> >> >> HARDIK KOTHARI >> >> hardik.koth...@corintis.com >> <mailto:hardik.koth...@corintis.com><mailto:hardik.koth...@corintis.com> >> >> Corintis SA >> EPFL Innovation Park Building C >> 1015 Lausanne >> >> >> >> >> [cid:~WRD0000.jpg] >> >> Here at Corintis we care for your privacy. That is why we have taken >> appropriate measures to ensure that the data you have provided to us is >> always secure
