Re: [Libmesh-users] Fwd: Periodic BC with adaptive mesh

[Roy S. <roy...@ic...>]

Sorry about the delay; you emailed while I was out of town and right
before I got sick and this almost got buried in my inbox.

On Sat, 30 Oct 2010, cod...@gm... wrote:

> I was looking at this thread since Derek has asked me to look into
> this problem

The problem fixed in this thread was a silly typo in the point locator
construction.  For the "AMR on periodic boundaries" problem in general
there's two aspects: making sure the constraints are correct and
making sure the refinement pattern is correct, and the two seem to be
conflated a bit in your email.  But the first aspect should be
completely solved (since failing to solve it correctly can make your
solution grossly wrong), and the second aspect we haven't even
attempted to solve (since failing to solve it correctly just makes
your convergence rate slightly poorer).

And that second aspect is really a host of other little problems -
making sure the refinement pattern is correct would require making
changes to multiple different error estimator algorithms as well as to
the MeshRefinement code itself.  Right now we should be applying
correct constraints to non-level-one-conforming hanging nodes on
periodic sides, but we're ignoring any users' request to be level-one
conforming on those sides.  Likewise for interior unrefined islands on
periodic sides, for constructing optimal patches when doing
PatchRecovery on elements at periodic boundaries, for calculating
JumpErrorEstimator terms... I don't have time to work on any of these
myself but I'd be happy to look over any patches you can cook up.

> We just need to make the elements on the periodic boundaries "see"
> their respective mirrored elements as neighbors for the purpose of
> this algorithm. This could be done by adding in the appropriate
> logic right inside of the respective "_maintain_level_one" loops.
> Does this seem reasonable?

I think the right place to add the logic may be in elem.h - right now
Elem::neighbor() gives you your geometric neighbor - if we had an
Elem::topological_neighbor(PeriodicBoundaries&) alternative, which
would give the same result as neighbor() in most cases but would do
the right thing in the periodic BC case too, I think we could avoid
adding more if/else/andanother special cases to a lot of these
MeshRefinement/ErrorEstimator methods.

> I'd be happy to take a crack at this unless you have any other
> ideas.

Thanks!
---
Roy