[petsc-users] Recursive fieldsplit PCs

[Lawrence Mitchell]

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?

Cheers,

Lawrence