[petsc-dev] DMPLEX cannot support two different edges for the same two vertices, hence DMPLEX cannot?

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

> On Wed, Dec 1, 2021 at 5:17 PM Abhyankar, Shrirang G <
> shrirang.abhyankar at pnnl.gov> wrote:
>
>> “You can certainly have many fields on a given edge, but I don't know
>> what it would mean to have two edges since no topological query could tell
>> the difference.”
>>
>>
>>
>> The two edges in a power grid represent two parallel power lines that are
>> connected between two locations (vertices). There are line ids (stored in
>> the component data) to distinguish the two lines.
>>
>
> Yes, so you can tell the difference in the function space (since difference
> current passes down each one), but _topologically_ you cannot. If you put
> duplicate cells in, then
> some topological queries will give unexpected results, like the join of the
> two vertices.

This could be modeled with some ghost vertices. So instead of

  a ------ b
   \_____/

you would set up

  a ---o---- b
   \___o___/

Those ghost vertices don't have to "do" anything, but they make the edges topologically distinct.

Shri, what problems might this cause?