Built-in Lagrange Local Node Ordering

[NamjaeChoi]

Hello,

Where can I find the local node ordering of each element type used by the built-in Lagrange basis? We want to check if it's consistent with the one currently used in MOOSE.

Thank you.

[jeremylt]

For a 2D cubic element, the ordering is

01 02 03 04
05 06 07 08
09 10 11 12
13 14 15 16

[jeremylt]

Though, my point above I think is still important. AtPoints is significantly slower than standard basis evaluations, so I'd only use it when you cannot do otherwise

[lindsayad]

Sorry @knepley that face vs. volume was unclear. Yes I am talking about the face integrals. And thanks to @jedbrown it's clear how we might "optimally" handle the non-conforming case with AtPoints. However

For conforming faces, you can use a regular quadrature.

It is still unclear to me how to implement this more basic/common case. I believe there have been two suggestions? One was @jrwrigh:

To handle the boundary flux CeedOperator, I think it'd need 2 inputs, one for the "left" element, one for the "right" element. The CeedBasis would be an interpolation from those element DoFs to the face quadrature points. Tricky part there becomes orientation of DoFs. One way to address that is to have a CeedBasis per orientation and thus a CeedOperator per relative orientation of the "left" and "right" element faces.

And then the other suggestion is two different element restrictions?

[knepley]

Oh, I think you handle this the same way we do FV for RDyCore. Namely, you have a separate restriction for the left and right cells, and that restriction has the orientation embedded in it. This does not resolve the "flip" for some elements, so it would be nice if the CEED interface would do that.

[jedbrown]

Yeah, restrict from the left cell and use a Basis to evaluate to quadrature points, and the same from the right. These will be two inputs to the qfunction. In RDycore (FV), the qfunction sets two outputs (for contribution to each cell) that differ by a sign (and cell volumes in that case).

[lindsayad]

Awesome, thanks guys. It's pretty clear now