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 > > > > > > ------------------------------------------------------------------------------ > > Everyone hates slow websites. So do we. > > Make your web apps faster with AppDynamics > > Download AppDynamics Lite for free today: > > http://p.sf.net/sfu/appdyn_d2d_jan > > _______________________________________________ > > Libmesh-users mailing list > > Libmesh-users at lists.sourceforge.net > > https://lists.sourceforge.net/lists/listinfo/libmesh-users > > > > > > -- > 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
