[petsc-users] [Libmesh-users] Preconditioning of a Stokes problem
Matthew Knepley
knepley at gmail.com
Mon Feb 4 13:01:48 CST 2013
On Mon, Feb 4, 2013 at 1:45 PM, Tobin Isaac <tisaac at ices.utexas.edu> wrote:
> 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
Note that this is also done for unstructured mesh Stokes in SNES ex62, and
you can see all the tests here:
https://bitbucket.org/petsc/petsc-dev/src/e273ef2c2517b1e5787fa19bd0738bf91d2229e2/config/builder.py?at=default#cl-301
Thanks,
Matt
> >
> > 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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> > > _______________________________________________
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> > > Libmesh-users at lists.sourceforge.net
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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
> > -----------------------
> > Phone: 630-252-1229
> > Fax: 630-252-5986
>
--
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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