[petsc-users] Starting point for Stokes fieldsplit

[Max Rudolph]

Hi Dave,
	Thanks for your help. 

Max

> Hey Max,
> 
> Without knowing anything about the specific application related to
> your Stokes problem, or information about the mesh you are using, I
> have a couple of questions and suggestions which might help.

The test case that I am working with is isoviscous convection, benchmark case 1a from Blankenbach 1989.

> 1) If  A, is your stokes operator A = ( K,B ; B^T, 0 ), what is your
> precondition operator?
> Specifically, what is in the (2,2) slot in the precondioner? - i.e.
> what matrix are you you applying -stokes_fieldsplit_1_pc_type jacobi
> -stokes_fieldsplit_1_ksp_type preonly to?
> Is it the identity as in the SpeedUp notes?

I think that this is the problem. The (2,2) slot in the LHS matrix is all zero (pressure does not appear in the continuity equation), so I think that the preconditioner is meaningless. I am still confused as to why this choice of preconditioner was suggested in the tutorial, and what is a better choice of preconditioner for this block? Should I be using one of the Schur complement methods instead of the additive or multiplicative field split?

> 2) This choice
> -stokes_fieldsplit_0_pc_type ml -stokes_fieldsplit_0_ksp_type preonly
> may simply not be a very effective and degrade the performance of the
> outer solver.
> I'd make the solver for the operator in the (1,1) slot much stronger,
> for example
>  -stokes_fieldsplit_0_ksp_type gmres
>  -stokes_fieldsplit_0_ksp_rtol 1.0e-4
>  -stokes_fieldsplit_0_mg_levels_ksp_type gmres
>  -stokes_fieldsplit_0_mg_levels_pc_type bjacobi
>  -stokes_fieldsplit_0_mg_levels_ksp_max_it 4
> 
> Add a monitor on this solver (-stokes_fieldsplit_0_ksp_XXX) to see how
> ML is doing.
> 
> 3) Using -stokes_pc_fieldsplit_type MULTIPLICATIVE should reduce the
> number of outer iterations by a factor of two, but it will use more
> memory.
> 4) You should use a flexible Krylov method on the outer most solve
> (-stokes_ksp_XXX) as the preconditioner is varying between each outer
> iteration. Use -stokes_ksp_type fgmres or -stokes_ksp_type gcr

Thanks for pointing this out. I made that change.

> 5) Depending on how the physical problem is scaled
> (non-dimensionalised), the size of the residuals associated with the
> momentum and continuity equation make be quite different. You are
> currently use the entire residual from (u,p) to determine when to stop
> iterating. You might want to consider writing a monitor which examines
> the these residuals independently.

I think that I have scaled the problem correctly. I (slowly) obtain a sufficiently accurate solution using as options only:
-stokes_ksp_atol 1e-5 -stokes_ksp_rtol 1e-5 -stokes_ksp_monitor_true_residual -stokes_ksp_norm_type UNPRECONDITIONED

> 
> 
> Cheers,
>  Dave

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