Aiden, Do you have true degrees of freedom on both the edges and the vertices? If only have edge variables and no vertex variables but only use "work" values on vertices than maybe DMNETWORK might behave as you need. But my trivial example defintely shows a problem with only edge vertex variables. The DMPLEX object believes there are more than two vertices when there are only two because it cannot determine that some vertices are actually the same. Barry

On Dec 2, 2021, at 5:31 PM, Zhang, Hong via petsc-dev <[email protected]> wrote:

All, I'm forwarding Aidan's comments on this issue (see below). Aidan has done extensive study on DMPlex and has been working on hyperbolic flow applications.

Satish: Please add Aidan to petsc-dev mailing list.

Hong From: Aidan Hamilton <[email protected] <mailto:[email protected]>> Sent: Thursday, December 2, 2021 2:34 PM To: Zhang, Hong <[email protected] <mailto:[email protected]>> Cc: Sundermann, Rylee Edwin - SDSU Student <[email protected] <mailto:[email protected]>> Subject: Re: [petsc-dev] DMPLEX cannot support two different edges for the same two vertices, hence DMPLEX cannot?

Hong,

I am not on petsc-dev, I guess I should be. Also you can push, you’re always free to push changes.

And it doesn’t matter for anything on my end. Each edge is distinct topological entity, so I have the directed graph

V0 ---- E0 - V1 ----- E1 ---- V0

I don’t need any special identification. And it works in parallel with globaltolocal seemingly working . Now this is not a standard graph, it follows the more general notion of directed graph, see Diestel page 25, that allows for multi-edges.

Now for my case I don’t need to distinguish between the two edges at all beyond each one having their own unique edge id. In all of our use cases for traffic I don’t think we need to care (and honestly I’m not sure if Shri actually needs to care either).

Now we do have the topological distinction of direction for all of our graphs, which we can use to assign direction to traffic flow. And that will always work. And this notion of direction is the only distinction we need to care about, and we have it.

It’s worth noting that a CW-Complex does support this notion of multiedges, no reason for it not to, so DMPlex should be supporting its topological operations with this case in mind. If DMplex can’t support this then dmplex isn’t doing what it claims it does.

As long as you as the user know that you are dealing with a multi-edge graph, I don’t see why there would be any issues. Any topological query of a multi-edge graph should behave as you would expect a multi-edge graph to behave, though it may behave differently than single edge graphs, as long as you are aware of the difference when you code your residuals and other functions on dmnetwork it should be fine.

Best,

Aidan

From: Zhang, Hong <[email protected] <mailto:[email protected]>> Date: Thursday, December 2, 2021 at 1:56 PM To: Aidan Hamilton <[email protected] <mailto:[email protected]>> Cc: Sundermann, Rylee Edwin - SDSU Student <[email protected] <mailto:[email protected]>> Subject: Fw: [petsc-dev] DMPLEX cannot support two different edges for the same two vertices, hence DMPLEX cannot?

Aidan, Are you on petsc-dev email list? How do you distinguish two parallel edges connecting the same junctions in your traffic code? Do you use offset_vto, offset_vfrom in EdgeFE?

I removed white spaces in dgnet.c and dgnet.h. Can I push the changes? Hong From: petsc-dev <[email protected] <mailto:[email protected]>> on behalf of Barry Smith <[email protected] <mailto:[email protected]>> Sent: Wednesday, December 1, 2021 7:41 PM To: Abhyankar, Shrirang G <[email protected] <mailto:[email protected]>> Cc: petsc-dev <[email protected] <mailto:[email protected]>>; Betrie, Getnet <[email protected] <mailto:[email protected]>> Subject: Re: [petsc-dev] DMPLEX cannot support two different edges for the same two vertices, hence DMPLEX cannot?

Shri,

If you provided your graph in parallel I suspect that the GlobalToLocal and LocalToGlobal would not work as you expect and put everything in the appropriate place.

I'll set up a simple code that takes exactly Get's configuration and send it out so everyone can run it and see exactly what happens.

Barry

On Dec 1, 2021, at 8:00 PM, Abhyankar, Shrirang G via petsc-dev <[email protected] <mailto:[email protected]>> wrote:

From: Matthew Knepley <[email protected] <mailto:[email protected]>> Date: Wednesday, December 1, 2021 at 5:57 PM To: "Brown, Jedediah A (VISIT)" <[email protected] <mailto:[email protected]>> Cc: "Abhyankar, Shrirang G" <[email protected] <mailto:[email protected]>>, PETSc Development <[email protected] <mailto:[email protected]>>, Getnet Betrie <[email protected] <mailto:[email protected]>> Subject: Re: [petsc-dev] DMPLEX cannot support two different edges for the same two vertices, hence DMPLEX cannot?

Check twice before you click! This email originated from outside PNNL.

On Wed, Dec 1, 2021 at 6:55 PM Jed Brown <[email protected] <mailto:[email protected]>> wrote: Matthew Knepley <[email protected] <mailto:[email protected]>> writes:

...

On Wed, Dec 1, 2021 at 5:17 PM Abhyankar, Shrirang G < [email protected] <mailto:[email protected]>> 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?

I don’t understand the figure you’ve drawn above. Sorry.

As a user, would I need to add anything to the way I am setting up the network/plex or any additional equations in the residual evaluation?

I do not have any issue right now for the power grid problem since I don’t require DMNetwork or DMPLEX to do the topological distinction between parallel edges. There are unique edge identifiers in my dataset through which I can make this distinction.

Yes, this would work, but it looks like the multiple cells are not causing them problems right now with the questions they are asking the mesh.

Matt

-- 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

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<DiestelGT.pdf>