[petsc-users] Nullspaces for schur complement PCs

[Matthew Knepley]

On Fri, Nov 7, 2014 at 11:04 AM, Lawrence Mitchell <
lawrence.mitchell at imperial.ac.uk> wrote:

> Hi petsc-dev,
>
> I'm solving a pure Neumann mixed Poisson-like problem, preconditioning
> with a schur complement.  The pressure space has a nullspace of the
> constant functions and so I attach the appropriate nullspace to the krylov
> solver, and compose the constant nullspace with the IS defining the
> pressure space.  My RHS is consistent.
>

That is supposed to work, and I think it does in my tests. The code is here


https://bitbucket.org/petsc/petsc/src/1f0d623c8336219eb98f7ded6f95c151ca603fe7/src/ksp/pc/impls/fieldsplit/fieldsplit.c?at=master#cl-562

so maybe we can track this down in the debugger.

  Thanks,

    Matt


> When I precondition with:
>
> -pc_type fieldsplit -pc_fieldsplit_type schur
> -pc_fieldsplit_schur_fact_type full \
> -pc_fieldsplit_schur_precondition selfp
>
> I notice that the nullspace is not transferred over to the preconditioning
> matrix for S.  Is this a deliberate choice?
>
> ksp_view output below, note that the schurcomplement mat has an attached
> nullspace, but the generated pmat does not.
>
> Cheers,
>
> Lawrence
>
> KSP Object: 1 MPI processes
>   type: gmres
>     GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
>     GMRES: happy breakdown tolerance 1e-30
>   maximum iterations=30, initial guess is zero
>   tolerances:  relative=1e-07, absolute=1e-50, divergence=10000
>   left preconditioning
>   has attached null space
>   using PRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
>   type: fieldsplit
>     FieldSplit with Schur preconditioner, factorization FULL
>     Preconditioner for the Schur complement formed from Sp, an assembled
> approximation to S, which uses (the lumped) A00's diagonal's inverse
>     Split info:
>     Split number 0 Defined by IS
>     Split number 1 Defined by IS
>     KSP solver for A00 block
>       KSP Object:      (fieldsplit_0_)       1 MPI processes
>         type: gmres
>           GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
>           GMRES: happy breakdown tolerance 1e-30
>         maximum iterations=10000, initial guess is zero
>         tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
>         left preconditioning
>         using PRECONDITIONED norm type for convergence test
>       PC Object:      (fieldsplit_0_)       1 MPI processes
>         type: ilu
>           ILU: out-of-place factorization
>           0 levels of fill
>           tolerance for zero pivot 2.22045e-14
>           matrix ordering: natural
>           factor fill ratio given 1, needed 1
>             Factored matrix follows:
>               Mat Object:               1 MPI processes
>                 type: seqaij
>                 rows=72, cols=72
>                 package used to perform factorization: petsc
>                 total: nonzeros=1080, allocated nonzeros=1080
>                 total number of mallocs used during MatSetValues calls =0
>                   using I-node routines: found 23 nodes, limit used is 5
>         linear system matrix = precond matrix:
>         Mat Object:        (fieldsplit_0_)         1 MPI processes
>           type: seqaij
>           rows=72, cols=72
>           total: nonzeros=1080, allocated nonzeros=0
>           total number of mallocs used during MatSetValues calls =0
>             using I-node routines: found 23 nodes, limit used is 5
>     KSP solver for S = A11 - A10 inv(A00) A01
>       KSP Object:      (fieldsplit_1_)       1 MPI processes
>         type: gmres
>           GMRES: restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
>           GMRES: happy breakdown tolerance 1e-30
>         maximum iterations=10000, initial guess is zero
>         tolerances:  relative=1e-05, absolute=1e-50, divergence=10000
>         left preconditioning
>         using PRECONDITIONED norm type for convergence test
>       PC Object:      (fieldsplit_1_)       1 MPI processes
>         type: ilu
>           ILU: out-of-place factorization
>           0 levels of fill
>           tolerance for zero pivot 2.22045e-14
>           matrix ordering: natural
>           factor fill ratio given 1, needed 1
>             Factored matrix follows:
>               Mat Object:               1 MPI processes
>                 type: seqaij
>                 rows=24, cols=24
>                 package used to perform factorization: petsc
>                 total: nonzeros=216, allocated nonzeros=216
>                 total number of mallocs used during MatSetValues calls =0
>                   using I-node routines: found 8 nodes, limit used is 5
>         linear system matrix followed by preconditioner matrix:
>         Mat Object:        (fieldsplit_1_)         1 MPI processes
>           type: schurcomplement
>           rows=24, cols=24
>             has attached null space
>             Schur complement A11 - A10 inv(A00) A01
>             A11
>               Mat Object:              (fieldsplit_1_)               1 MPI
> processes
>                 type: seqaij
>                 rows=24, cols=24
>                 total: nonzeros=72, allocated nonzeros=0
>                 total number of mallocs used during MatSetValues calls =0
>                   has attached null space
>                   using I-node routines: found 8 nodes, limit used is 5
>             A10
>               Mat Object:               1 MPI processes
>                 type: seqaij
>                 rows=24, cols=72
>                 total: nonzeros=288, allocated nonzeros=0
>                 total number of mallocs used during MatSetValues calls =0
>                   using I-node routines: found 8 nodes, limit used is 5
>             KSP of A00
>               KSP Object:              (fieldsplit_0_)               1 MPI
> processes
>                 type: gmres
>                   GMRES: restart=30, using Classical (unmodified)
> Gram-Schmidt Orthogonalization with no iterative refinement
>                   GMRES: happy breakdown tolerance 1e-30
>                 maximum iterations=10000, initial guess is zero
>                 tolerances:  relative=1e-05, absolute=1e-50,
> divergence=10000
>                 left preconditioning
>                 using PRECONDITIONED norm type for convergence test
>               PC Object:              (fieldsplit_0_)               1 MPI
> processes
>                 type: ilu
>                   ILU: out-of-place factorization
>                   0 levels of fill
>                   tolerance for zero pivot 2.22045e-14
>                   matrix ordering: natural
>                   factor fill ratio given 1, needed 1
>                     Factored matrix follows:
>                       Mat Object:                       1 MPI processes
>                         type: seqaij
>                         rows=72, cols=72
>                         package used to perform factorization: petsc
>                         total: nonzeros=1080, allocated nonzeros=1080
>                         total number of mallocs used during MatSetValues
> calls =0
>                           using I-node routines: found 23 nodes, limit
> used is 5
>                 linear system matrix = precond matrix:
>                 Mat Object:                (fieldsplit_0_)
>  1 MPI processes
>                   type: seqaij
>                   rows=72, cols=72
>                   total: nonzeros=1080, allocated nonzeros=0
>                   total number of mallocs used during MatSetValues calls =0
>                     using I-node routines: found 23 nodes, limit used is 5
>             A01
>               Mat Object:               1 MPI processes
>                 type: seqaij
>                 rows=72, cols=24
>                 total: nonzeros=288, allocated nonzeros=0
>                 total number of mallocs used during MatSetValues calls =0
>                   using I-node routines: found 23 nodes, limit used is 5
>         Mat Object:         1 MPI processes
>           type: seqaij
>           rows=24, cols=24
>           total: nonzeros=216, allocated nonzeros=216
>           total number of mallocs used during MatSetValues calls =0
>             using I-node routines: found 8 nodes, limit used is 5
>   linear system matrix = precond matrix:
>   Mat Object:   1 MPI processes
>     type: nest
>     rows=96, cols=96
>       has attached null space
>       Matrix object:
>         type=nest, rows=2, cols=2
>         MatNest structure:
>         (0,0) : prefix="fieldsplit_0_", type=seqaij, rows=72, cols=72
>         (0,1) : type=seqaij, rows=72, cols=24
>         (1,0) : type=seqaij, rows=24, cols=72
>         (1,1) : prefix="fieldsplit_1_", type=seqaij, rows=24, cols=24
>
>


-- 
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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