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

[Hardik Kothari]

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<mailto:hardik.kothari at corintis.com>

Corintis SA
EPFL Innovation Park Building C
1015 Lausanne



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