AMR for non-cell centered fields

[lroberts36]

PR Summary

This PR does the last few things required to make full AMR work with non-cell centered fields:

• Separates the prolongation and restriction caches from the boundary caches by creating a new ProResInfo type that is similar to BndInfo.
• Unifies the boundary index calculation routine further.
• Switch to restriction in one during RedistributeAndRefineMeshBlocks
• Switch to prolongation in one during RedistributeAndRefineMeshBlocks
• Updates TryRecvFineToCoarse to deal with non-cell centered fields
• Updates TryRecvCoarseToFine to deal with non-cell centered fields
• Test that things actually work
• Come up with some good test problems for Parthenon (any ideas are appreciated)

B^2/2 w/ AMR

divB w/ AMR

PR Checklist

• Code passes cpplint
• New features are documented.
• Adds tests for new features.
• Code is formatted
• Changes are summarized in CHANGELOG.md
• CI has been triggered on Darwin for performance regression tests.
• Docs build
• (@lanl.gov employees) Update copyright on changed files

[lroberts36]

A possible test problem is to evolve

$$\partial_t \vec{F} + \nabla \times \vec{G} = 0$$ $$\partial_t \vec{G} + \nabla \times \vec{F} = 0$$

which should obey the wave equation but also have $\nabla \cdot \vec{F} = 0$ and $\nabla \cdot \vec{G} = 0$.

[Yurlungur]

I'm sorry it took me so long to review this... looks like I had started reviewing it and then I must have gotten interrupted and forgotten because I never finished. Overall this looks good.

One thing: we should probably document the ownership model somewhere in the docs.

[Yurlungur]

P.S. I am so excited by this

[Yurlungur]

A possible test problem is to evolve

which should obey the wave equation but also have ∇⋅F→=0 and ∇⋅G→=0.

👍 Vector wave equation seems like a good test problem and a nice demonstration of the technology. Maybe as a new example?

[lroberts36]

Yeah, we should add it as an example. I think maybe we save that for a documentation/test PR. As you say, it would be good to have documentation about how the ownership model works, etc. It would be especially good to get done before it is forgotten...

[Yurlungur]

Yeah I think the ownership model makes sense, and your code is clear. But it's sufficiently different from how Athena++ does it, and there are a sufficiently large number of choices to make, we should clarify which choices we made in a single place.

[Yurlungur]

I'm fine with putting docs and an example off into a final PR though.

[pdmullen]

Not too much to contribute here... LGTM. The test problems you have presented from various downstream applications give me confidence in the implementation.

[bprather]

Finally using this in earnest and it works great. Can't yet provide a working downstream due to my own bugs, but the machinery's all there and the interface has been easy to use.
Though it shouldn't delay this PR longer, we should remember to add the InternalRefinementOp template arg to Metadata when we get a chance, I started implementing the B field internal refinement outside of Parthenon proper and was briefly stung.