Moment fitted machinery

[pmartorell]

Dear @fverdugo ,

this PR is adding the moment fitted machinery developed by @ericneiva and used in the publication:
https://doi.org/10.1016/j.camwa.2022.09.027 by @santiagobadia , @ericneiva and @fverdugo .

Comments:

• Coverage in src/AgFEM/AggregateBoundingBoxes.jl and src/MomentFitting/JacobiPolynomialBases.jl
  still need to be improved
• The instances of the input variable cut in src/MomentFitting/CutCellMoments.jl have no type definition due extensibility issues. EmbeddedDiscretization has no abstract types but GridapType<:Any.

[ericneiva]

Hi, @pmartorell , thanks for doing this work :)

Coverage in src/AgFEM/AggregateBoundingBoxes.jl

The BBoxes machinery is definitely covered in the Poisson Modal C0 test, but the tests in the GridapEmbeddedTests folder are not included in the main runtests.jl. They are tested separately here.

Could this be the reason why it appears as "not covered"?

[pmartorell]

They are tested separately here.

Indeed. May be convenient to include some tests into the main runtest.jl ? To keep the high coverage statistics.

[fverdugo]

Hi @ericneiva can you please review the PR?

Once you are happy, I'll merge it.

[ericneiva]

Hi, @fverdugo, I am happy to review it, though it's basically my own code extracted from the InterpolatedAgFEM.jl package and cleaned by @pmartorell.

[codecov-commenter]

Codecov Report

❗ No coverage uploaded for pull request base (master@94dfa39). Click here to learn what that means.
The diff coverage is 71.54%.

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@@            Coverage Diff            @@
##             master      #68   +/-   ##
=========================================
  Coverage          ?   83.43%           
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  Files             ?       17           
  Lines             ?     2258           
  Branches          ?        0           
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  Hits              ?     1884           
  Misses            ?      374           
  Partials          ?        0           

Files Changed	Coverage Δ
src/AgFEM/AggregateBoundingBoxes.jl	0.00% <0.00%> (ø)
src/Interfaces/EmbeddedFacetDiscretizations.jl	75.75% <0.00%> (ø)
src/Interfaces/Interfaces.jl	100.00% <ø> (ø)
src/LevelSetCutters/LevelSetCutters.jl	82.92% <50.00%> (ø)
...MomentFittedQuadratures/MomentFittedQuadratures.jl	85.42% <85.42%> (ø)
src/Interfaces/EmbeddedDiscretizations.jl	80.58% <100.00%> (ø)

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[pmartorell]

Hi @ericneiva,
I have found an important bottleneck in memory consumption related with the usage of CompressedArray in both modal C0 basis and moment fitting measures. It seems that Gridap is not efficient with CompressedArray with a large amount of values, e.g., CompressedArray(vals,1:length(vals)). The usage of flat arrays instead will reduce the memory consumption up to one order of magnitude.

A possible optimization would accommodate the Gridap constructors of CellQuadrature and FESpaces to flat arrays of quadrature and reference FEs, respectively. It is probably better to include this optimization in another PR.

[ericneiva]

Hi, @pmartorell, thanks a lot for identifying this.

Is it possible to get rid of the CompressedArray usage in the Moment Fitted measures without touching Gridap? If so, could you please update this PR with this optimization?

I agree to change the Gridap constructors in another PR.

[pmartorell]

Hi @ericneiva,
the optimization have to be done in Gridap first. Then, eliminating CompressedArray in GridapEmbedded/MomentFittedQuadratures is straighforward.

I do not have much time for the developments right now. I have tested this by editing the FESpace and CellMeasure a posteriori.

[ericneiva]

the optimization have to be done in Gridap first.

Okay, thanks for letting me know.

I do not have much time for the developments right now.

Of course you don't, I know. I was just hoping that changing MomentFittedQuadratures could be quickly done without touching Gridap...

[ericneiva]

Hi, @pmartorell, other than the performance issues, which we won't solve now, is there anything left to add to this branch, before merging it with GE?

[pmartorell]

Hi @ericneiva , I do not have new changes right now. You can merge it. Thanks for asking.

[ericneiva]

Hi, @fverdugo, this is ready to be merged.

If you want, I can merge it myself and release GE 0.8.2 (I think I have the permissions).

Let me know if you are ok with this.

@pmartorell Thanks a lot for your work!

[fverdugo]

@ericneiva feel free to release a new version.