[petsc-users] Solving Stokes problem in high aspect ratio domains

[Mark Adams]

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.kothari at 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.kothari at corintis.com* <hardik.kothari at corintis.com>
>
> Corintis SA
> EPFL Innovation Park Building C
> 1015 Lausanne
>
>
>
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