[petsc-users] [Libmesh-users] Preconditioning of a Stokes problem

Mon Feb 4 12:45:53 CST 2013

On Mon, Feb 04, 2013 at 12:30:39PM -0600, Dmitry Karpeev wrote:
> Francesco,
> 
> Are you using any pressure stabilization scheme? If not, the 11-block in
> your Jacobian
> A = [A00 A01; A10 A11] would typically be zero, and preconditioning it with
> jacobi wouldn't really work.
> 
> If A11 = 0, you ought to use the fieldsplit of type Schur, for example
> (assuming petsc-3.3; prior versions use slightly different option names):
> -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type full
> The question is then how you want to solve the Schur complement system.
> Since the A11 block for you is zero, the easiest choice is to use S as the
> preconditioning matrix:
> -pc_fieldsplit_schur_precondition self
> 
> Preconditioning options for the Schur solver have prefix -fieldsplit_1_.
> Since for Stokes the Schur complement is spectrally equivalent to the
> pressure mass matrix, you can
> hope that an unpreconditioned GMRES (default when using
> -pc_fieldsplit_schur_precondition self) will solve it.
> 
> 
> A better choice might be to use the Least Squares Commutator preconditioner
> -fieldsplit_1_pc_type lsc
> See
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCLSC.html
> and note the relevant references at the bottom of that manual page.
> You might also find this useful:
> http://www.icfd.rdg.ac.uk/ICFD25/Talks/AWathen.pdf
> 
> PCLSC preconditions S = A10 inv(A00) A01 with  inv(A10A01) A10 A00 A01
> inv(A10A01)
> The "Laplacian" (a true Laplacian in the case of incompressible Stokes) can
> be preconditioned
> using AMG:
> -fieldsplit_1_lsc_pc_type ml
> (assuming you have ML built, e.g., with --download-ml)
> or
> -fieldsplit_1_lsc_pc_type gamg
> with some appropriate choice of gamg options:
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCGAMG.html
> 
> To start with I would use -pc_fieldsplit_type schur
> -pc_fieldsplit_schur_fact_type full -pc_fieldsplit_schur_precondition self
> -fieldsplit_1_pc_type lsc -fieldsplit_1_lsc_pc_type ml
> gamg may also be very good in place of ml, but will require more option
> setting.
> 
> 
> You might find src/ksp/ksp/examples/tutorials/ex42.c and ex43.c useful,
> albeit, possibly, a bit heavyweight for your needs.

Also, if your problem isn't stabilized then your vectors (hopefully)
aren't layed out in strided form.  A good example of how to setup a
fieldsplit preconditioner in this more general setting is
src/snes/examples/tutorials/ex70.c

> 
> A few more comments below:
> 
> On Mon, Feb 4, 2013 at 10:20 AM, John Peterson <jwpeterson at gmail.com> wrote:
> 
> > On Thu, Dec 27, 2012 at 4:31 AM, Francesco Ballarin
> > <francesco.ballarin at mail.polimi.it> wrote:
> > > Dear libMesh users,
> > > I am trying to solve a Stokes problem in a 3D domain, but I am currently
> > > struggling with the choice of the preconditioner.
> > > I have slightly modified systems_of_equations_ex1 to accommodate for the
> > > third velocity component and boundary conditions of the problem at hand
> > > (Dirichlet BCs on the inlet on the walls, enforced using a
> > > DirichletBoundary object, and homogeneous Neumann BC on the outflow)
> > >
> > > I am trying to use PETSc block preconditioners as shown, e.g., in
> > > http://acts.nersc.gov/events/Workshop2012/slides/PETSc.pdf
> > > section 4. I have tried most of the preconditioners discussed during the
> > > talk, but I am not satisfied because I get either PETSc errors or a
> > > performance that I hope can be increased.
> > >
> > > For example, with the following options:
> > > *******
> > >   PetscOptionsSetValue("-ksp_type", "gmres");
> > > PetscOptionsSetValue("-ksp_right_pc", PETSC_NULL);
> > >  PetscOptionsSetValue("-pc_type", "fieldsplit");
> > > PetscOptionsSetValue("-pc_fieldsplit_detect_saddle_point", PETSC_NULL);
> > >  PetscOptionsSetValue("-pc_fieldsplit_type", "multiplicative");
> > > PetscOptionsSetValue("-fieldsplit_0_ksp_type", "preonly");
> > >  PetscOptionsSetValue("-fieldsplit_0_pc_type", "ml");
> > > PetscOptionsSetValue("-fieldsplit_1_ksp_type", "preonly");
> > >  PetscOptionsSetValue("-fieldsplit_1_pc_type", "jacobi");
> >
> 
> You do not need to set options to PETSC_NULL, if you do not intend to use
> them.
> Also, how are you forming the splits?
> -pc_fieldsplit_detect_saddle_point is actually rather useful here.
> 
> Further, there are programmatic ways to set most of these options, for
> example:
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetType.html
> 
> Even so, we typically recommend setting these on the command line whenever
> possible:
> this way you do not hardwire your solver choices and can quickly experiment
> with different
> solvers from the command-line without recompiling your code.
> 
> 
> >  > *******
> > > I obtain a reasonable solution but after thousands of gmres iterations.
> > Is
> > > there any way to improve that?
> > >
> > > Or, if I try to embed the previous block preconditioner in mg:
> > > *******
> > > PetscOptionsSetValue("-pc_type", "mg");
> > >  PetscOptionsSetValue("-pc_mg_levels", "5");
> > > PetscOptionsSetValue("-pc_mg_galerkin", PETSC_NULL);
> > >  PetscOptionsSetValue("-ksp_type", "gmres");
> > > PetscOptionsSetValue("-mg_levels_pc_type", "fieldsplit");
> > >  PetscOptionsSetValue("-mg_levels_pc_fieldsplit_detect_saddle_point",
> > > PETSC_NULL);
> > > PetscOptionsSetValue("-mg_levels_pc_fieldsplit_type", "multiplicative");
> > >  PetscOptionsSetValue("-mg_levels_fieldsplit_0_ksp_type", "preonly");
> > > PetscOptionsSetValue("-mg_levels_fieldsplit_0_pc_type", "gamg");
> > >  PetscOptionsSetValue("-mg_levels_fieldsplit_1_ksp_type", "preonly");
> > > PetscOptionsSetValue("-mg_levels_fieldsplit_1_pc_type", "jacobi");
> > > *******
> > > I get the following error:
> >
> Always send the full stack trace, when reporting errors.
> 
> Finally, in the future you might want to post these questions to
> petsc-users at mcs.anl.gov
> 
> Dmitry.
> 
> > > *******
> > > PETSC ERROR: Null argument, when expecting valid pointer!
> > > PETSC ERROR: Null Object: Parameter # 2!
> > > PETSC ERROR: MatPtAP() line 8237 in
> > petsc-3.3-p4/src/mat/interface/matrix.c
> > > *******
> > >
> > > Do you have any suggestion? What are you currently using as
> > preconditioner
> > > for saddle point problems?
> >
> > Apologies, it appears that this email fell through the cracks
> > somewhere back around the holidays.
> >
> > Did you ever find a satisfactory answer to your question?
> >
> > Petsc developers may occasionally read this list, but for questions
> > that are this advanced you would probably have better luck mailing the
> > petsc developers list directly.
> >
> > And of course if you do find a good block preconditioning strategy for
> > systems_of_equations_ex1, please feel free to report it here!
> >
> > --
> > John
> >
> >
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> 
> 
> 
> -- 
> Dmitry Karpeev, Ph.D.
> Assistant Computational Mathematician
> Mathematics and Computer Science
> Argonne National Laboratory
> Argonne, Illinois, USA
> and
> Fellow
> Computation Institute
> University of Chicago
> 5735 S. Ellis Avenue
> Chicago, IL 60637
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