[petsc-dev] Periodic meshes with <3 elements per edge?

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

>>> >> The local points could be distinct for
>>> >> both fields and coordinates, with the global SF de-duplicating the
>>> >> periodic points for fields, versus leaving them distinct for
>>> >> coordinates.
>>> >
>>> >
>>> > Oh, no I would never do that.
>>>
>>> Can you help me understand why that model is bad?
>>>
>>
>> I'm also interested in the answer to this question, because I am
>> considering something similar for DMStag; if DM has a periodic BC, the
>> corresponding coordinate DM has a "none"  BC, so the boundary points are
>> duplicated - this would hopefully make it much easier to locate particles
>> in elements.
>>
>
> If you start asking topological questions of the mesh, it looked
> complicated to get them all right. For example, if you start expanding
> the overlap over the periodic boundary. 

How is this different from what we have now?  You have to go through
global points anyway to connect between processors, so why would it
matter if the point and its periodic alias may appear separately in a
local space?

> Fundamentally, periodicity is a topological notion. It is not defined
> by the coordinate chart.

The global SF would be the same as you have now.  The local SF would
distinguish the alias only so those points would be valid in the
coordinate chart.  So the periodic mesh

  A -- B -- C -- D -- a

on two processes would be represented via the cones

  {AB, BC}  {CD, Da}

with l2g

  {0,1,2} {2,3,0} for fields
  {0,1,2} {2,3,4} for coordinates


Why doesn't this work, or where is the greater complexity of this model
versus the present scheme of localizing coordinates?