[petsc-users] Starting point for Stokes fieldsplit

[Max Rudolph]

Matt, 
Thank you for your help.
> On Mon, Feb 20, 2012 at 2:05 PM, Max Rudolph <rudolph at berkeley.edu> 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 (see
> http://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



-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120220/221d8f3f/attachment.htm>