[petsc-users] Recursive fieldsplit PCs

[Matthew Knepley]

On Mon, Dec 2, 2013 at 9:47 AM, Lawrence Mitchell <
lawrence.mitchell at imperial.ac.uk> wrote:

>
> On 2 Dec 2013, at 15:20, Matthew Knepley <knepley at gmail.com> wrote:
>
> > 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.
>
> OK, I think I see.  I wonder if, until I have a DM in place, I can hack
> this together by building my MatNest recursively?  That is build
>
> A = [A' B'
>      C' D']
>
> and then build
>
> F = [A B
>      C D]
>
> would that work, or am I barking up the wrong tree?
>

MatNest is only an optimization. It makes no-copy extraction of submatrices
feasible. It is not an interface, and thus does not
tell FieldSplit anything. Everything you can do with MatNest you can do
without it.

   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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