Putting a peculiar multilevel scheme into DMMG?

[Jed Brown]

On Sun, 13 Dec 2009 16:59:39 -0600, Barry Smith <bsmith at mcs.anl.gov> wrote:
>     It was never fully developed (i.e. things might not work). It  
> could be we should switch to using that one and slowly remove the  
> regular refine (note that one could still use the refinehierarchy one  
> several times to get the effect of the current refine.

So none of the present DMs implement refinehierarchy.  I think it would
be reasonable for DMMGSetDM to always call DMRefineHierarchy where
DMRefineHierarchy had a default implementation that just repeatedly
called DMRefine.  If you didn't want to deprecate DMRefine, a default
implementation for that could be given in terms of DMRefineHierarchy.
Similarly for coarsening, this would get rid of the extra branching in
DMMGSetDM.

It seems to me that caller of DMMGSetDM knows whether they are setting
the fine or coarse mesh.  In that case, I don't see the point of the
-dmmg_refine option, and would prefer an explicit argument for whether
the DM is on the fine, coarse, or perhaps intermediate level.  Is there
a use case where the caller of DMMGSetDM doesn't know?

DMCoarsenHierarchy is implemented for Mesh, but the array is currently
leaking (DMMGSetDM forgets a PetscFree).  Is it indeed preferred that
the caller does not allocate the array (despite knowing how much is
needed) but is responsible for freeing it (I ask because this is clumsy
for a single level of refinement).  Either way, I'll document the choice
and fix the leak.

Jed