Refactor shapes

[inducer]

This pushes inducer#16 towards relying even more heavily on the shapes stuff.

• Test unmodified meshmode against this: Test modepy's alexfikl:tensor-face-mass-matrix branch inducer/meshmode#95
• Looks like CI isn't running here. PR for CI (same branch!): Refactor shapes (DUPE FOR CI) inducer/modepy#19

[alexfikl]

This is definitely more of a refactor that I would have been comfortable doing! It looks really nice!

[inducer]

It occurred to me that it still equates "shape + order = polynomial space", which is not totally true. I'm thinking of introducing a separate object for the polynomial space. Is that crazy? (Not a big change, just Pk and Qk for now.)

[alexfikl]

It occurred to me that it still equates "shape + order = polynomial space", which is not totally true. I'm thinking of introducing a separate object for the polynomial space. Is that crazy? (Not a big change, just Pk and Qk for now.)

Isn't that mostly what the discretization ElementGroups in meshmode are?

[inducer]

Isn't that mostly what the discretization ElementGroups in meshmode are?

In a way, sure... but they're about multiple elements, not just the reference element.

What worries me more is that we're currently answering the question "give me a basis for tetrahedra", which is nonsense. "Give me a basis for P^k" makes incrementally more sense. The motivating examples where things break down that I think about are pyramids and inhomogeneous tensor products.

[alexfikl]

What worries me more is that we're currently answering the question "give me a basis for tetrahedra", which is nonsense.

Yes, I agree it's a bit clunky. Especially as inducer#15 would already introduce a non-tensor product set for squares. It makes sense to add something like a polynomial space to express these things.

[alexfikl]

@inducer Should I merge this back into inducer#16 now?

[inducer]

Not yet. There's another big chunk coming.

[alexfikl]

Added a few more comments. I can fix these after we merge back into inducer#16.

[inducer]

The "big chunk of stuff" is now in, mostly consisting of introducing a notion of polynomial spaces. Take a look. Good to merge back once the checks on inducer/meshmode#95 pass.

[alexfikl]

It looks good to me! inducer/meshmode#95 also seems to have passed too!

I'll merge this back into inducer#16 and we can nitpick it more there!