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

[Pierre Jolivet]

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