[petsc-users] Starting point for Stokes fieldsplit

[Matthew Knepley]

On Mon, Feb 20, 2012 at 4:36 PM, Max Rudolph <rudolph at berkeley.edu> wrote:

> Matt,
>
> Thank you for your help.
>
> On Mon, Feb 20, 2012 at 2:05 PM, Max Rudolph <rudolph at berkeley.edu <https://lists.mcs.anl.gov/mailman/listinfo/petsc-users>> wrote:
>
> >* 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?*>**
> Its not suggested, it is demonstrated. Its the first logical choice, since
> Jacobi gives the identity for a 0 block (seehttp://www.jstor.org/pss/2158202). Its
> not meaningless. All the better preconditioners involve either a Schur
> complement (also shown in the tutorial), or an auxiliary operator which is
> more
> difficult to setup and thus not shown.
>
>
> Thank you for clarifying this.
>
>
> >* 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*>**
> How do you know the problem is scaled correctly? Have you looked at norms
> of the residuals for the two systems
>
>   Thanks,
>
>      Matt
>
>
> >* Cheers,*>*  Dave*
>
>
> Yes, here are the norms computed for the P, X, and Y components, following
> the last residual that ksp_monitor_true_residual returned:
>
> 383 KSP unpreconditioned resid norm 1.121628211019e-03 true resid norm
> 1.121628224178e-03 ||r(i)||/||b|| 9.626787321554e-10
> P, X, Y residual norms 5.340336e-02, 4.463404e-02, 2.509621e-02
>

I am more interested in the initial residuals.

  Thanks

    Matt


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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