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

[Matthew Knepley]

On Wed, Oct 16, 2019 at 1:05 AM Jed Brown <jed at jedbrown.org> wrote:

> I think this thread got dropped when I was on travel (two months ago and
> I'm just now getting back to it, eek!).  Matt, could you please comment
> on this model?
>

The real answer is that you could do it (like most things in programming)
but I think it would

  a) definitely break things, and I don't want to fix them

  b) I believe that fixing these things would result in more complex code

The model is that the topology is defined by one structure. Some of the
queries might be incomplete
are boundaries (star), but not fundamentally changed. You would have to
remember everywhere that
you need to check the SF. I don't think it would simplify our lives.

   Matt


> Jed Brown via petsc-dev <petsc-dev at mcs.anl.gov> writes:
>
> > 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?
>


-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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