[petsc-users] Fw: left and right preconditioning with a constant null space

Tue Mar 28 08:58:25 CDT 2017

On Tue, Mar 28, 2017 at 8:54 AM, Klaij, Christiaan <C.Klaij at marin.nl> wrote:

> Matt,
>
> Yes, null space vector attached to the large matrix and
> consistent rhs. This seems to be what Barry wants (or I
> misunderstood his previous email)
>
> a) that was Lawrence's suggestion as well, using
> petscObjectCompose, but that doesn't seem to work in fortran as I
> reported earlier.
>
This is just because there is a string there and we are lazy. I will do it
as soon as I can.

> b) Good to know, but so far I don't have a DM.
>
> c) same problem as a)
>
> I understand your last point about pulling apart the global null
> vector. Then again how would a user know the null space of any
> submatrices that arise somewhere within PCFieldSplit?
>
Because the user is specifying the split. I agree that if FS were deciding
how to split on its own,
this is not possible, but that is why it can't. It has to be told.

  Thanks,

     Matt

> Chris
>
>
> dr. ir. Christiaan Klaij | Senior Researcher | Research & Development
> MARIN | T +31 317 49 33 44 <+31%20317%20493%20344> | C.Klaij at marin.nl |
> www.marin.nl
>
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> ------------------------------
> *From:* Matthew Knepley <knepley at gmail.com>
> *Sent:* Tuesday, March 28, 2017 3:27 PM
> *To:* Klaij, Christiaan
> *Cc:* Lawrence Mitchell; petsc-users at mcs.anl.gov
> *Subject:* Re: Fw: [petsc-users] left and right preconditioning with a
> constant null space
>
> On Tue, Mar 28, 2017 at 8:19 AM, Klaij, Christiaan <C.Klaij at marin.nl>
> wrote:
>
>> Barry,
>>
>> That seems by far the best way to proceed! As a user I'm
>> responsible for the velocity-pressure matrix and its null space,
>> all the rest is up to PCFieldSplit. But unfortunately it doesn't
>> work:
>>
>> I've constructed the null space [u,p]=[0,1], attached it to the
>> velocity-pressure matrix and verified it by MatNullSpaceTest. I'm
>> making sure the rhs is consistent with "MatNullSpaceRemove".
>>
>> However, the null space doesn't seem to propagate to the Schur
>> complement, which therefore doesn't converge, see
>> attachment "out1".
>>
>> When I attach the constant null space directly to A11, it does
>> reach the Schur complement and I do get convergence, see
>> attachment "out2".
>>
>
> So you attach a null space vector to the large matrix, and have a
> consistent rhs?
> This is not quite what we want. If you
>
>   a) Had a consistent rhs and attached the constant nullspace vector to
> the pressure IS, then things will work
>
>   b) Had a consistent rhs and attached the constant nullspace vector to
> the "field" object from a DM, it should work
>
>   c) Attached the global nullspace vector to A^T and the constant
> nullspace to the pressure IS, it should work
>
> We can't really pull apart the global null vector because there is no
> guarantee that its the nullspace of the submatrix.
>
>   Thanks,
>
>      Matt
>
>
>> Chris
>>
>> ________________________________________
>> From: Barry Smith <bsmith at mcs.anl.gov>
>> Sent: Monday, March 27, 2017 6:35 PM
>> To: Klaij, Christiaan
>> Cc: Lawrence Mitchell; Matthew Knepley; petsc-users at mcs.anl.gov
>> Subject: Re: [petsc-users] left and right preconditioning with a constant
>> null space
>>
>> > On Mar 27, 2017, at 2:23 AM, Klaij, Christiaan <C.Klaij at marin.nl>
>> wrote:
>> >
>> > Barry,
>> >
>> > I removed the null space from the rhs in the debug program that I
>> > wrote to just solve Sp x = b once. In this debug program I've
>> > constructed Sp myself after reading in the four blocks from the
>> > real program. So this is independent of PCFieldSplit. Indeed I
>> > also see bad convergence when using pc_type svd for this debug
>> > program unless I remove the null space from the rhs.
>> >
>> > So far I haven't managed to translate any of this to the real
>> > program.
>> >
>> > - Setting the null space for Sp in the real program seems to work
>> >  by happy accident, but Lawrence gave me the hint to
>> >  use "PetscObjectCompose" to set the nullspace using is1.
>> >
>> > - I still have to understand Lawrence's hint and Matt's comment
>> >  about MatSetTransposeNullSpace.
>> >
>> > - I'm not sure how to remove the null space from the rhs vector
>> >  in the real pogram, since I have one rhs vector with both
>> >  velocity and pressure and the null space only refers to the
>> >  pressure part. Any hints?
>> >
>> > - Or should I set the null space for the velocity-pressure matrix
>> >  itself, instead of the Schur complement?
>>
>>    I would first check if the entire full velocity-pressure right hand
>> side is consistent. If it is not you can make it consistent by removing the
>> transpose null space. You can use MatCreateNullSpace() to create the null
>> space by passing in a vector that is constant on all the pressure variables
>> and 0 on the velocity variables.
>>
>>    Barry
>>
>> >
>> > - Besides this, I'm also wondering why the rhs would be
>> >  inconsistent in the first place, it's hard to understand from
>> >  the discretization.
>> >
>> > Thanks for your reply,
>> > Chris
>> >
>> >
>> >
>> > dr. ir. Christiaan Klaij  | Senior Researcher | Research & Development
>> > MARIN | T +31 317 49 33 44 | mailto:C.Klaij at marin.nl |
>> http://www.marin.nl
>> >
>> > MARIN news: http://www.marin.nl/web/News/N
>> ews-items/Comfort-and-Safety-at-Sea-March-29-Rotterdam.htm
>> >
>> > ________________________________________
>> > From: Barry Smith <bsmith at mcs.anl.gov>
>> > Sent: Saturday, March 25, 2017 1:29 AM
>> > To: Klaij, Christiaan
>> > Cc: Lawrence Mitchell; Matthew Knepley; petsc-users at mcs.anl.gov
>> > Subject: Re: [petsc-users] left and right preconditioning with a
>> constant null space
>> >
>> >> On Mar 24, 2017, at 10:11 AM, Klaij, Christiaan <C.Klaij at marin.nl>
>> wrote:
>> >>
>> >> I've written a small PETSc program that loads the four blocks,
>> >> constructs Sp, attaches the null space and solves with a random
>> >> rhs vector.
>> >>
>> >> This small program replicates the same behaviour as the real
>> >> code: convergence in the preconditioned norm, stagnation in the
>> >> unpreconditioned norm.
>> >>
>> >> But when I add a call to remove the null space from the rhs
>> >> vector ("MatNullSpaceRemove"),
>> >
>> >   Are you removing the null space from the original full right hand
>> side or inside the solver for the Schur complement problem?
>> >
>> >   Note that if instead of using PCFIELDSPLIT you use some other simpler
>> PC you should also see bad convergence, do you? Even if you use -pc_type
>> svd you should see bad convergence?
>> >
>> >
>> >
>> >> I do get convergence in both
>> >> norms! Clearly, the real code must somehow produce an
>> >> inconsistent rhs vector. So the problem is indeed somewhere else
>> >> and not in PCFieldSplit.
>> >>
>> >> Chris
>> >>
>> >>
>> >>
>> >> dr. ir. Christiaan Klaij  | Senior Researcher | Research & Development
>> >> MARIN | T +31 317 49 33 44 | mailto:C.Klaij at marin.nl |
>> http://www.marin.nl
>> >>
>> >> MARIN news: http://www.marin.nl/web/News/N
>> ews-items/Meet-us-again-at-the-OTC-2017.htm
>> >>
>> >> ________________________________________
>> >> From: Klaij, Christiaan
>> >> Sent: Friday, March 24, 2017 1:34 PM
>> >> To: Lawrence Mitchell; Matthew Knepley
>> >> Cc: petsc-users at mcs.anl.gov
>> >> Subject: Re: [petsc-users] left and right preconditioning with a
>> constant null space
>> >>
>> >> I've also loaded the four blocks into matlab, computed
>> >>
>> >> Sp = A11 - A10 inv(diag(A00)) A01
>> >>
>> >> and confirmed that Sp has indeed a constant null space.
>> >>
>> >> Chris
>> >> ________________________________________
>> >> From: Klaij, Christiaan
>> >> Sent: Friday, March 24, 2017 9:05 AM
>> >> To: Lawrence Mitchell; Matthew Knepley
>> >> Cc: petsc-users at mcs.anl.gov
>> >> Subject: Re: [petsc-users] left and right preconditioning with a
>> constant null space
>> >>
>> >> Lawrence,
>> >>
>> >> I think you mean "-fieldsplit_1_mat_null_space_test"? This
>> >> doesn't return any info, should it? Anyway, I've added a "call
>> >> MatNullSpaceTest" to the code which returns "true" for the null
>> >> space of A11.
>> >>
>> >> I also tried to run with "-fieldsplit_1_ksp_constant_null_space"
>> >> so that the null space is only attached to S (and not to
>> >> A11). Unfortunately, the behaviour is still the same: convergence
>> >> in the preconditioned norm only.
>> >>
>> >> Chris
>> >> ________________________________________
>> >> From: Lawrence Mitchell <lawrence.mitchell at imperial.ac.uk>
>> >> Sent: Thursday, March 23, 2017 4:52 PM
>> >> To: Klaij, Christiaan; Matthew Knepley
>> >> Cc: petsc-users at mcs.anl.gov
>> >> Subject: Re: [petsc-users] left and right preconditioning with a
>> constant null space
>> >>
>> >> On 23/03/17 15:37, Klaij, Christiaan wrote:
>> >>> Yes, that's clearer, thanks! I do have is0 and is1 so I can try
>> >>> PetscObjectCompose and let you know.
>> >>>
>> >>> Note though that the viewer reports that both S and A11 have a
>> >>> null space attached... My matrix is a matnest and I've attached a
>> >>> null space to A11, so the latter works as expected. But is the viewer
>> >>> wrong for S?
>> >>
>> >> No, I think this is a consequence of using a matnest and attaching a
>> >> nullspace to A11.  In that case you sort of "can" set a nullspace on
>> >> the submatrix returned in MatCreateSubMatrix(Amat, is1, is1), because
>> >> you just get a reference.  But if you switched to AIJ then you would
>> >> no longer get this.
>> >>
>> >> So it happens that the nullspace you set on A11 /is/ transferred over
>> >> to S, but this is luck, rather than design.
>> >>
>> >> So maybe there is something else wrong.  Perhaps you can run with
>> >> -fieldsplit_1_ksp_test_null_space to check the nullspace matches
>> >> correctly?
>> >>
>> >> Lawrence
>> >>
>> >
>>
>>
>
>
> --
> 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
>
>

-- 
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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