[petsc-users] shell preconditioner for Schur complement
Matthew Knepley
knepley at gmail.com
Wed Feb 10 15:23:05 CST 2021
On Wed, Feb 10, 2021 at 4:05 PM Elena Travaglia <
elena.travaglia at edu.unito.it> wrote:
> Thanks for the link.
>
> We have set a Schur factorization of type FULL, and we passed it when we
> run the code with
> -pc_fieldsplit_schur_fact_type full
>
> Here there is the output of -ksp_view
>
> KSP Object: 1 MPI processes
> type: fgmres
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=1, initial guess is zero
> tolerances: relative=1e-08, absolute=1e-50, divergence=10000.
> right preconditioning
> using UNPRECONDITIONED 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 A11
> 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
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> 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
> 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=44, cols=44
> package used to perform factorization: petsc
> total: nonzeros=482, allocated nonzeros=482
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 13 nodes, limit used is 5
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_0_) 1 MPI processes
> type: seqaij
> rows=44, cols=44
> total: nonzeros=482, allocated nonzeros=482
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 13 nodes, limit used is 5
> KSP solver for S = A11 - A10 inv(A00) A01
> KSP Object: (fieldsplit_1_) 1 MPI processes
> type: gmres
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=1, initial guess is zero
> tolerances: relative=1e-09, absolute=1e-50, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: (fieldsplit_1_) 1 MPI processes
> type: shell
> no name
> linear system matrix followed by preconditioner matrix:
> Mat Object: (fieldsplit_1_) 1 MPI processes
> type: schurcomplement
> rows=20, cols=20
> Schur complement A11 - A10 inv(A00) A01
> A11
> Mat Object: (fieldsplit_1_) 1 MPI processes
> type: seqaij
> rows=20, cols=20
> total: nonzeros=112, allocated nonzeros=112
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 10 nodes, limit used is 5
> A10
> Mat Object: 1 MPI processes
> type: seqaij
> rows=20, cols=44
> total: nonzeros=160, allocated nonzeros=160
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 10 nodes, limit used is 5
> KSP of A00
> KSP Object: (fieldsplit_0_) 1 MPI processes
> type: gmres
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> 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
> 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=44, cols=44
> package used to perform factorization: petsc
> total: nonzeros=482, allocated nonzeros=482
> total number of mallocs used during MatSetValues
> calls=0
> using I-node routines: found 13 nodes, limit
> used is 5
> linear system matrix = precond matrix:
> Mat Object: (fieldsplit_0_) 1 MPI processes
> type: seqaij
> rows=44, cols=44
> total: nonzeros=482, allocated nonzeros=482
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 13 nodes, limit used is 5
> A01
> Mat Object: 1 MPI processes
> type: seqaij
> rows=44, cols=20
> total: nonzeros=156, allocated nonzeros=156
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 12 nodes, limit used is 5
> Mat Object: (fieldsplit_1_) 1 MPI processes
> type: seqaij
> rows=20, cols=20
> total: nonzeros=112, allocated nonzeros=112
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 10 nodes, limit used is 5
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=64, cols=64
> total: nonzeros=910, allocated nonzeros=2432
> total number of mallocs used during MatSetValues calls=128
> using I-node routines: found 23 nodes, limit used is 5
>
>
> We would like to understand why the first r.h.s, passed to our function
> for the Schur preconditioner, is not
> b_1-A_10*inv(A_00)*b_0,
> even if we used the full factorization ( without dropping any terms ).
>
Here is the code:
https://gitlab.com/petsc/petsc/-/blob/master/src/ksp/pc/impls/fieldsplit/fieldsplit.c#L1182
I think you are saying that ilinkD->x is not what you expect on line 1196.
It should be easy to print out the value
at any of the intermediate stages.
Thanks,
Matt
> Thank you,
> Elena
>
>
>
>
> Il giorno mer 10 feb 2021 alle ore 18:05 Matthew Knepley <
> knepley at gmail.com> ha scritto:
>
>> On Wed, Feb 10, 2021 at 11:51 AM Matteo Semplice <
>> matteo.semplice at uninsubria.it> wrote:
>>
>>> Dear PETSc users,
>>> we are trying to program a preconditioner for the Schur complement
>>> of a Stokes system, but it seems that the r.h.s. for the Schur
>>> complement system differs from what we expect by a scale factor, which
>>> we don't understand.
>>>
>>> Our setup has a system matrix A divided in 2x2 blocks for velocity and
>>> pressure variables. We have programmed our preconditioner in a routine
>>> PrecondSchur and in the main program we do
>>>
>>> PC pc;
>>> KSPGetPC(kspA,&pc);
>>> PCSetFromOptions(pc);
>>> KSPSetOperators(kspA, A, A);
>>> KSPSetInitialGuessNonzero(kspA,PETSC_FALSE);
>>> KSPSetFromOptions(kspA);
>>> KSP *subksp;
>>> PetscInt nfield;
>>> PCSetUp(pc);
>>> PCFieldSplitGetSubKSP(pc, &nfield, &subksp);
>>> PC pcSchur;
>>> KSPGetPC(subksp[1],&pcSchur);
>>> PCSetType(pcSchur,PCSHELL);
>>> PCShellSetApply(pcSchur,PrecondSchur);
>>> KSPSetFromOptions(subksp[1]);
>>>
>>> and eventually
>>>
>>> KSPSolve(A,b,solution);
>>>
>>> We run the code with options
>>>
>>> -ksp_type fgmres \
>>> -pc_type fieldsplit -pc_fieldsplit_type schur \
>>> -pc_fieldsplit_schur_fact_type full \
>>>
>>> and, from reading section 2.3.5 of the PETSc manual, we'd expect that
>>> the first r.h.s. passed to PrecondSchur be exactly
>>> b_1-A_10*inv(A_00)*b_0
>>>
>>> Instead (from a monitor function attached to the subksp[1] solver), the
>>> first r.h.s. appears to be scalar multiple of the above vector; we are
>>> guessing that we should take into account this multiplicative factor in
>>> our preconditioner routine, but we cannot understand where it comes from
>>> and how its value is determined.
>>>
>>> Could you explain us what is going on in the PC_SCHUR exactly, or point
>>> us to some working code example?
>>>
>>
>> 1) It is hard to understand solver questions without the output of
>> -ksp_view
>>
>> 2) The RHS will depend on the kind of factorization you are using for the
>> system
>>
>>
>> https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetSchurFactType.html#PCFieldSplitSetSchurFactType
>>
>> I can see which one in the view output
>>
>> Thanks,
>>
>> Matt
>>
>>
>>> Thanks in advance!
>>>
>>> Matteo
>>>
>>>
>>
>> --
>> 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
>>
>> https://www.cse.buffalo.edu/~knepley/
>> <http://www.cse.buffalo.edu/~knepley/>
>>
>
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--
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
https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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