[petsc-users] Solving Poisson equation with multigrid

[Matthew Knepley]

On Fri, May 24, 2013 at 2:55 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> Michele Rosso <mrosso at uci.edu> writes:
>
> > Hi Jed,
> >
> > I followed your suggestion by using:
> >
> > -pc_type gamg  -pc_mg_cycle_type v  -pc_gamg_agg_nsmooths 1
> >
> > This works perfectly if I have a non-singular matrix. When instead I use
> > periodic conditions for my system ( I set  the nullspace removal
> > correctly ),
> > I receive an error saying a zero pivot is detected in the LU
> > factorization. So, after some research, I found in the mailinglist a fix
> :
> >
> > -pc_type gamg -pc_mg_cycle_type v -pc_gamg_agg_nsmooths 1
> > -mg_coarse_pc_factor_shift_nonzero
>
> It'll need to be -mg_coarse_sub_pc_factor_shift_nonzero
>
> With petsc-3.4 (which you should upgrade to), use
> -mg_coarse_sub_pc_factor_shift_type NONZERO
>
> The reason you need this "sub" prefix is that the code always restricts
> using block Jacobi (usually localized so that all the entries are in one
> block), before applying the direct coarse solver.


I think this is less elegant than

  -mg_coarse_pc_type svd

    Matt


> > Still I am receiving the following error
> >
> >
> > [0]PETSC ERROR: --------------------- Error Message
> > ------------------------------------
> > [0]PETSC ERROR: Detected zero pivot in LU factorization:
> > see http://www.mcs.anl.gov/petsc/documentation/faq.html#ZeroPivot!
> > [0]PETSC ERROR: Zero pivot row 280 value 6.5908e-17 tolerance
> 2.22045e-14!
> > [0]PETSC ERROR:
> > ------------------------------------------------------------------------
> > [0]PETSC ERROR: Petsc Release Version 3.3.0, Patch 3, Wed Aug 29
> > 11:26:24 CDT 2012
> > [0]PETSC ERROR: See docs/changes/index.html for recent updates.
> > [0]PETSC ERROR: See docs/faq.html for hints about trouble shooting.
> > [0]PETSC ERROR: See docs/index.html for manual pages.
> > [0]PETSC ERROR:
> > ------------------------------------------------------------------------
> > [0]PETSC ERROR: ./hit on a  named nid09458 by Unknown Fri May 24
> > 14:40:48 2013
> > [0]PETSC ERROR: Libraries linked from
> > [0]PETSC ERROR: Configure run at
> > [0]PETSC ERROR: Configure options
> > [0]PETSC ERROR:
> > ------------------------------------------------------------------------
> > [0]PETSC ERROR: MatPivotCheck_none() line 583 in
> >
> src/mat/impls/aij/seq//ptmp/skelly/petsc/3.3.03/cray_interlagos_build/real/src/include/petsc-private/matimpl.h
> > [0]PETSC ERROR: MatPivotCheck() line 602 in
> >
> src/mat/impls/aij/seq//ptmp/skelly/petsc/3.3.03/cray_interlagos_build/real/src/include/petsc-private/matimpl.h
> > [0]PETSC ERROR: MatLUFactorNumeric_SeqAIJ() line 585 in
> > src/mat/impls/aij/seq/aijfact.c
> > [0]PETSC ERROR: MatLUFactorNumeric() line 2803 in
> src/mat/interface/matrix.c
> > [0]PETSC ERROR: PCSetUp_LU() line 160 in src/ksp/pc/impls/factor/lu/lu.c
> > [0]PETSC ERROR: PCSetUp() line 832 in src/ksp/pc/interface/precon.c
> > [0]PETSC ERROR: KSPSetUp() line 278 in src/ksp/ksp/interface/itfunc.c
> > [0]PETSC ERROR: PCSetUpOnBlocks_BJacobi_Singleblock() line 715 in
> > src/ksp/pc/impls/bjacobi/bjacobi.c
> > [0]PETSC ERROR: PCSetUpOnBlocks() line 865 in
> src/ksp/pc/interface/precon.c
> > [0]PETSC ERROR: KSPSetUpOnBlocks() line 154 in
> > src/ksp/ksp/interface/itfunc.c
> > [0]PETSC ERROR: KSPSolve() line 403 in src/ksp/ksp/interface/itfunc.c
> > [0]PETSC ERROR: PCMGMCycle_Private() line 20 in src/ksp/pc/impls/mg/mg.c
> > [0]PETSC ERROR: PCMGMCycle_Private() line 49 in src/ksp/pc/impls/mg/mg.c
> > [0]PETSC ERROR: PCMGMCycle_Private() line 49 in src/ksp/pc/impls/mg/mg.c
> > [0]PETSC ERROR: PCMGMCycle_Private() line 49 in src/ksp/pc/impls/mg/mg.c
> > [0]PETSC ERROR: PCApply_MG() line 326 in src/ksp/pc/impls/mg/mg.c
> > [0]PETSC ERROR: PCApply() line 384 in src/ksp/pc/interface/precon.c
> > [0]PETSC ERROR: KSPSolve_CG() line 139 in src/ksp/ksp/impls/cg/cg.c
> > [0]PETSC ERROR: KSPSolve() line 446 in src/ksp/ksp/interface/itfunc.c
> >
> > What could the reason be?
> > Thank you,
> >
> > Michele
> >
> >
> >
> > On 05/17/2013 07:35 PM, Michele Rosso wrote:
> >> Thank you very much. I will try and let you know.
> >>
> >> Michele
> >>
> >> On 05/17/2013 07:01 PM, Jed Brown wrote:
> >>> Michele Rosso<mrosso at uci.edu>  writes:
> >>>
> >>>> I noticed that the problem appears even if I use CG with the default
> >>>> preconditioner: commenting KSPSetDM() solves the problem.
> >>> Okay, this issue can't show up if you use SNES, but it's a consequence
> >>> of making geometric multigrid work with a pure KSP interface.  You can
> >>> either use KSPSetComputeOperators() to put your assembly in a function
> >>> (which will also be called on coarse levels if you use -pc_type mg
> >>> without Galerkin coarse operators) or you can can provide the Jacobian
> >>> using KSPSetOperators() as usual, but also call KSPSetDMActive() so
> that
> >>> the DM is not used for computing/updating the Jacobian.
> >>>
> >>> The logic is cleaner in petsc-3.4 and I think it just does the right
> >>> thing in your case.
> >>>
> >>>> So basically without a proper grid (it seems no grid with an even
> >>>> numbers of nodes qualifies) and with my own system matrix, I cannot
> use
> >>>> any type of multigrid
> >>>> pre-conditioner?
> >>> You can use all the AMG methods without setting a DM.
> >>>
> >>
>



-- 
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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