Interface for LGL mass lumping?

[inducer]

See #344 for context. Diagonal mass matrices on LGL points are a common approximation. I'm thinking they should not be the default behavior, since they're not exact, and exact evaluation is totally doable (if more expensive). (Do we agree on that?) Hence we need permission from the user to use lumping. How should that permission be given?

• Once for the whole DiscretizationCollection? (i.e. as a flag living on that)
• Once per (volume) element group? (and likely inherited by corresponding surface groups?)
• Per-operation?
• A combination of the above?

cc @MTCam @a-alveyblanc @alexfikl @lukeolson @majosm @anderson2981

[MTCam]

I probably don't have a full appreciation of the nuance here. I think per volume per group might be the best option. This mapping from vol/group -> lumping would be set up at dcoll creation, right? Still fire-and-forget, but versatile enough to support varied options per vol and group.

[alexfikl]

Once for the whole DiscretizationCollection? (i.e. as a flag living on that)
Once per (volume) element group? (and likely inherited by corresponding surface groups?)

I'm not quite sure how much flexibility is required here. Is using some groups with lumping and some without something that could be useful in practice? Maybe in some multi-volume case?

Shouldn't be too hard to teach tensor product element groups and factories about lumping though, so maybe that's a good place to put it.

Per-operation?

Generally not a big fan, since anything wrapping the operation will also need to pass the flag around.

[a-alveyblanc]

I'm thinking they should not be the default behavior, since they're not exact

100% agree here.

Once per (volume) element group? (and likely inherited by corresponding surface groups?)

I think this makes the most sense given the context.