ABLASTR: Coarsen Functions

[ax3l]

Move coarsen functions to ABLASTR.

Needed for BLAST-ImpactX/impactx#261

Follow-up to:

• Interpolation with coarsening for general staggering #853
• Generalize coarsening for MR #945

Edit by @EZoni:
Here's a few slides describing the interpolation operations refactored in this PR (interpolation between grids with arbitrary index type and mesh refinement ratio, for I/O and MR): Slides-Interpolation-IO-MR.pdf. The slides date back to 2020, when the PRs listed above were opened and merged.

[ax3l]

I moved this out as a tiny optimization. The compiler probably did this already.

[EZoni]

@ax3l I added some comments above, which hopefully clarify the scope of the various interpolation functions that you are refactoring here, to the best of my knowledge. As a general remark, note that the two sets of interpolation routines had been named originally with the tags IO and MR, because the type of interpolation we chose to do for I/O and MR is different (simple nearest-neighbors interpolation for I/O, and more complicated weights to guarantee certain conservation properties for MR - more details in the slides linked in the PR description), regardless of whether there could be constraints on the index type of the input/output data in certain cases.

[ax3l]

Thanks @EZoni - I think all that is left then is finding a good name, especially for the I/O stuff, which I find not very descriptive. Do you think we could describe the properties of the two classes (e.g., conservation properties and time/space average) in the name(s)?

[EZoni]

@ax3l We discussed with @jlvay and @WeiqunZhang and had the following ideas:

• The old CoarsenIO operation could be renamed sample;
• The old CoarsenMR operation could be renamed average (as in the AMReX AverageDown) or interpolate.

Let's discuss here more if you have any comments or concerns on these suggestions.

P.S. Again, if we want the I/O one to be specialized for cell-centered output, there is the option of simplifying the formulas, by setting the corresponding output index type to zero in the code, and then calling it sample_to_cell_centers or something along these lines.

[ax3l]

Thanks a lot - I updated the PR accordingly and it's now ready for review with the new names :)

[EZoni]

Copying here what I commented on Slack.

Would it be possible and would it make sense to consider removing one intermediate layer? Like doing something like this:

• rename namespace ablastr::coarsen::sample as namespace ablastr:sample_with_coarsening
• rename namespace ablastr::coarsen::average as namespace ablastr::average_with_coarsening

(or similar names), which keeps the information about "coarsening" in the name but removes one layer in terms of structure?

Then one would have things like
ablastr::sample_with_coarsening::Coarsen or ablastr::sample_with_coarsening::Interp
instead of things like (current code)
ablastr::coarsen::sample::Coarsen or ablastr::coarsen::sample::Interp.

What do you think?

[ax3l]

Thanks a ton! Discussed between Edoardo, Remi & Axel: we'll keep the current naming for now since it mirrors the directory structure.
I'll rebase. - Done.

[EZoni]

Thank you, @ax3l! This looks great. I just left two minor comments, see below.

[EZoni]

Great, ready to merge! I think I'll open an issue to keep track of the fact that it would be good to add some documentation of these interpolation methods (sampling, averaging), including a link to the slides attached in the PR description, as you suggested some time ago.

[ax3l]

Good idea! You could copy the slide content in a new theory sub-section of the manual.