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). Hardik Kothari <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> > > 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> > Date: Sunday, 11 May 2025 at 20:45 > To: Hardik Kothari <hardik.koth...@corintis.com> > Cc: petsc-users@mcs.anl.gov <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. 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> 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>> 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> > > 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
