[petsc-users] Recursive fieldsplit PCs

[Matthew Knepley]

On Mon, Dec 2, 2013 at 6:31 AM, Lawrence Mitchell <
lawrence.mitchell at imperial.ac.uk> wrote:

>
> On 2 Dec 2013, at 12:23, Matthew Knepley <knepley at gmail.com> wrote:
>
> > On Mon, Dec 2, 2013 at 2:26 AM, Lawrence Mitchell <
> lawrence.mitchell at imperial.ac.uk> wrote:
> > Dear petsc-users,
> >
> > I have a 3x3 block system built as a single MatNest (with 9 Mats in it).
>  I'd like to treat this as a 2x2 system:
> > [ A B
> >   C D ]
> >
> > where A is 2x2 and precondition the A block with a schur complement.
>  Since I have a mat nest, the ISes for the three fields are just
> ISCreateStride(..., mat_i_rows, offset, 1, ...) and these are set on the
> fieldsplit pc.  If I understand the documentation correctly, I think I
> should now be able to do:
> >
> > -pc_type fieldsplit -fieldsplit_0_fields 0,1 -fieldsplit_1_fields 2
> -fieldsplit_0_pc_type field split -fieldsplit_0_pc_fieldsplit_type schur
> >
> > ...
> >
> > However, when doing so, I get an error: "To use Schur complement
> preconditioner you must have exactly 2 fields".  Which suggests to me I
> have failed to inform PETSc that I want the first two fields to be treated
> as 1.
> >
> > Note that I am not using a DM to build any of these objects.  I build a
> SNES, pull the KSP out of the SNES and then the PC out of the KSP.  I never
> explicitly call SetFromOptions on the PC.  Instead, before the SNES solve I
> call SNESSetFromOptions.  Might this be the problem?
> >
> > This is an unfortunately limitation of the implementation right now.
> This option works if you are on a DA with collocation, or if you
> > use a DM, but not if you just specify the ISes. We should probably write
> that code. However, the idea is for people to be moving
> > to using DM. Could you tell us why DM did not work for you here?
>
> At the moment, our mesh infrastructure is not plumbed in to use petsc data
> structures.  We're attempting to migrate to dmplex at the moment but
> currently we're building Mats from third-party connectivity information.
>  It's possible that the move to dmplex will happen soon enough that it
> isn't a big issue, but I don't know the timescales on which we'll be done
> with that.
>

I was feeling bad about not implementing this, but I remembered the problem
with the pure IS solution. The obvious solution
is to just combine several ISes to create the field for PCFIELDSPLIT.
However, once this is done, they lose their identity as
separate fields. Thus, it is not possible to untangle for the second level
of FieldSplit that you want. The DM version maintains
the field identity at the next level so that we can split hierarchically.
So, for the above to work, I think you must use a DM.

  Thanks,

       Matt


> Cheers,
>
> 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
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