[petsc-users] Multigrid Preconditioned CG on cell-centered Poisson with DMStag

[Barry Smith]

   Use -mg_coarse_pc_type svd

   Verify that when you apply the restriction to a constant vector (all ones) it returns a constant vector, maybe scaled

   Verify that when you apply the interpolation to a constant vector it returns a constant vector



> On Oct 2, 2024, at 12:29 PM, Gautam Luhana <gkluhana at cs.ubc.ca> wrote:
> 
> GMRES is similar i.e. converges but iteration counts go +1-2 with every doubling of the mesh.
> 
> I am attaching the output from a cg and gmres run for a single stokes iteration with a velocity and pressure subdomain solves, subsequent iterations are similar. The pressure subdomain ksp is titled pre_mgcg.
> 
> Adding more information in case it is relevant to isolating the issue:
> 
> -> The coarse grid operators are formed by setting PCMGSetGalerkin to PC_MG_GALERKIN_BOTH.
> 
> -> The interpolation / restriction operators are formed using the DMCreateInterpolation and DMCreateRestriction functions on coarsened DMs (DMStag implementation) and sent to PCMGSetInterpolation/PCMGSetRestriction.
> 
> Thanks for the help!
> 
> -Gautam
> 
> 
> On 2024-10-02 7:42 a.m., Barry Smith wrote:
>> [CAUTION: Non-UBC Email]
>> 
>> Using
>> 
>> PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dmPressure), PETSC_TRUE, 0, nullptr, &matNullSpace));
>> 
>> should be fine (the other approach is equivalent).
>> 
>> Any change if you use -ksp_type gmres?
>> 
>> Please send all the output from a sample run with -ksp_monitor_true_residual -ksp_view
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>>> On Oct 1, 2024, at 6:42 PM, Gautam Luhana <gkluhana at cs.ubc.ca> wrote:
>>> 
>>> I did think that I accounted for that but now I see that I am getting the same number of iterations in the pressure space with and without the call to MatSetNullspace so maybe I am not doing that correctly and that's where the problem is.
>>> 
>>> I tried it in the following way first:
>>> 
>>> PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dmPressure), PETSC_TRUE, 0, nullptr, &matNullSpace));
>>> 
>>>       PetscCall(MatSetNullSpace(*A, matNullSpace));
>>> 
>>> and then also as:
>>> 
>>>       PetscCall(DMGetGlobalVector(dmPressure, &constantPressure));
>>>       PetscCall(VecSet(constantPressure, 1.0));
>>>       PetscCall(VecNorm(constantPressure, NORM_2, &nrm));
>>>       PetscCall(VecScale(constantPressure, 1.0 / nrm));
>>>       PetscCall(DMCreateGlobalVector(dmPressure, &basis));
>>>       PetscCall(VecCopy(constantPressure, basis));
>>> PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dmPressure), PETSC_FALSE, 1, &basis, &matNullSpace));
>>>       PetscCall(MatSetNullSpace(*A, matNullSpace));
>>> 
>>> Is this the right way? are there other options that need to be set?
>>> 
>>> -Gautam
>>> 
>>> On 2024-10-01 12:47 p.m., Barry Smith wrote:
>>>> [CAUTION: Non-UBC Email]
>>>> 
>>>>    Are you handling the null space? Like with MatSetNullSpace()?
>>>> 
>>>>    Can you try src/ksp/ksp/tutorials/ex32.c it solves the same problem but with a simpler DMDA. I don't see any reason why using DMStag with the cell-centered values should be different.
>>>> 
>>>>    Barry
>>>> 
>>>> 
>>>>> On Oct 1, 2024, at 3:37 PM, Gautam Luhana <gkluhana at cs.ubc.ca> wrote:
>>>>> 
>>>>> Hello,
>>>>> 
>>>>> I am solving the stokes equations on the MAC grid using DMStag with an approximate Schur complement based preconditioner. The preconditioner needs a subdomain solve of the Poisson equation on both the velocity as well as the pressure space. I am using multigrid preconditioned CG for both the subdomain solves. While the subdomain solve on the velocity space converges in 4-5 iterations and is independent of mesh-size, the pressure solve is not mesh-size independent. Relevant information:
>>>>> 
>>>>> Pressure space operator has Neumann boundary conditions.
>>>>> 
>>>>> Coarse-grid operators are being generated using the Galerkin approach (A = P*Af*Pt) for both of the subdomains.
>>>>> 
>>>>> For the pressure space, the jacobi and sor smoothers were tried with several omega and damping parameter choices.
>>>>> 
>>>>> Symmetric smoothing (same number of pre- and post-smoothing iterations)
>>>>> 
>>>>> Has anyone tried solving the poisson operator on the cell-centered pressure space with DMStag? Or know what might be going wrong with the mg-cg convergence?
>>>>> 
>>>>> Thanks!
>>>>> 
>>>>> -Gautam
>>>>> 
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