Have a `GrudgeDOFArray`?

[inducer]

There's a lot of awkwardness in the grudge interface from having to repeatedly specify DOF descriptors (DOFDescs). This is the case because DOFArrays don't know the DOF descriptor with which they're associated. (They can't. DOFArrays are defined in meshmode, and in order to make sense of a DOF descriptor, you need a catalog of discretizations, something like grudge's DiscretizationCollection.)

The idea here is to fix that by introducing a grudge-specific subclass of the DOFArray that does have that information. This would declutter the interface a lot, in many places. There may be some aspects of easier-said-than-done here:

• Would we allow arithmetic like DOFArray + GrudgeDOFArray? (I'm thinking no.)
• What happens if the user passes a GrudgeDOFArray to a meshmode function? (This is still well-defined, since it'd be a subclass. But would meshmode be able to return a GrudgeDOFArray? I'm thinking no. As a result, grudge users probably shouldn't be calling meshmode directly for anything, i.e. we'd possibly need some wrapper code. I don't know how wide-spread this would be.)
• grudge.op was just in the process of asking users to explicitly specify DOFDescs. We would effectively re-un-deprecate the "bare" versions and re-deprecate the explicit versions. We can keep those around for a while, they just need to check that if a GrudgeDOFArray is passed in, its DOFDesc matches the passed parameter. This is mostly mechanical work, I think.

Anyone opposed?

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

[majosm]

Only other potential annoyance that's coming to mind is having to fish out the dd from array containers for each call. Not sure how much clutter that would add?

[inducer]

I think that applies only to very few operations (only divergence comes to mind). In most cases, I think we would just traverse the array container and then apply the operation to each entry separately, without ever figuring whether all entries agree on the same DOFDesc.

For the divergence, I think we will want all $d$ entries of the vector to agree on the DOFDesc, but I think that's a manageable amount of fishing.

[alexfikl]

What happens if the user passes a GrudgeDOFArray to a meshmode function? (This is still well-defined, since it'd be a subclass. But would meshmode be able to return a GrudgeDOFArray? I'm thinking no. As a result, grudge users probably shouldn't be calling meshmode directly for anything, i.e. we'd possibly need some wrapper code. I don't know how wide-spread this would be.)

Hm, that sounds like a lot of wrapping. I imagine most things in meshmode/discretization/ will have to be wrapped in some fashion for grudge. I'm mostly weary of the wrapping because pytential may want to add a DOF descriptor too and it just adds more boilerplate :(

From a quick grep in meshmode, not that many places initialize a DOFArray by calling the constructor, so maybe we can make more use of container traversal functions to construct things based on a "template" (which would be a GrudgeDOFArray in this case)? Hopefully arithmetic won't cause any subtle issues if we disallow DOFArray + GrudgeDOFArray.