[petsc-dev] Composing PetscSections for FieldSplit

[Matthew Knepley]

On Wed, Apr 2, 2014 at 8:14 AM, Michael Lange
<michael.lange at imperial.ac.uk>wrote:

> Hi Matt,
>
> We are  trying to implement fieldsplit for mixed function spaces in
> Firedrake. For this we want to compose a set of sections with one field
> each into one section with several fields. The is to add a
> PetscSectionSetField() function and then use this to build a container
> section with something like:
>
> sec_offset = 0
> msec = PETSc.Section().create()
> for i, s in enumerate(spaces):
>     sec = shift_offsets(s.clone(), sec_offset)
>     msec.setField(i, sec)
>     sec_offset += s.getStorageSize()
>
> We have tried setting this as the DefaultSection in our DM and then
> passing this to SNES via SNESSetDM(), but the problem we encountered is
> that we get an empty global section, because PetscSectionCreateGlobalSection()
> can currently not handle multiple fields.
>

Global section handles multiple fields, for instance SNES ex62. I am
guessing the problem here is that you
increment the offsets in the section, but fail to increment the aggregate
sizes for each point when you add a
field.

I personally would not do it this way, although there is nothing wrong with
it. I would make descriptions of each discrezation and build
the unified Section once. This is what currently happens in ex12 and ex62:

   - Build PetscFE for each field and call DMAddBoundary()

  - PetscFE makes numDof[] and DMBoundary gives a set of (field, IS) pairs

  - Call DMPlexCreateSection()

This cannot constrain individual field components, like y-velocity, but we
could
write a more specific version of DMPlexCreateSection() and upgrade
DMAddBoundary()
to take field component as well. I will do this myself when PyLith switches
over if it
does not happen before that.

   Matt


> Do you agree with this approach? And if so, can we make
> PetscSectionCreateGlobalSection() aware of fields?
>
> Thanks,
>
> Michael
>



-- 
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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