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. A few more comments below: On Mon, Feb 4, 2013 at 10:20 AM, John Peterson <[email protected]> wrote: > On Thu, Dec 27, 2012 at 4:31 AM, Francesco Ballarin > <[email protected]> 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 [email protected] 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 > [email protected] > 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 ------------------------------------------------------------------------------ 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 [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
