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Moment based reffes #1048

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Moment based reffes #1048

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JordiManyer
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@JordiManyer JordiManyer commented Nov 8, 2024

So we've been having a look at the current implementation of Raviart-Thomas and Nedelec. It has become clear that the current implementation

  • has issues with high-order, that have to do with how we choose our basis/prebasis when computing the moments.
  • has issues related to scaling in mixed formulations.
  • is outright wrong when using high-order approximations for the geometry.
  • is very hard to read, modify and extend.

Moreover, there has been interest lately in implementing more types of moment-based discretisations like Crouzeix-Raviart.

We believe the best way to solve all these issues at once is to create some extendable machinery to easily create moment-based FEs.

TODOs:

  • Create the moment-based machinery
  • Create the pullback machinery Pullbacks #1067
  • Replicate RT and ND in 2D/3D with oriented meshes
  • Replicate RT and ND in 2D/3D with non-oriented meshes
  • Benchmark against current implementations
  • Change of basis needs to be transposed and inverted on pushforward.

New RefFEs:

  • Crouzeix-Raviart
  • Hellan-Herrmann-Jhonson
  • Mardal-Tai-Winther
  • Arnold-Winther

Other: Polynomial bases

The solution to the first issue requires extending Jacobi-type polynomial bases. Although it could be done blindly, I think we could try to merge a lot of code together. In the future we might want to have even more basis of polynomials, which would require a lot of copied code.

@JordiManyer JordiManyer self-assigned this Nov 8, 2024
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codecov bot commented Nov 8, 2024

Codecov Report

Attention: Patch coverage is 61.51603% with 924 lines in your changes missing coverage. Please review.

Project coverage is 85.62%. Comparing base (3b87738) to head (4ed24bf).
Report is 25 commits behind head on master.

Files with missing lines Patch % Lines
src/ReferenceFEs/deprecated/RaviartThomasRefFEs.jl 0.00% 266 Missing ⚠️
src/ReferenceFEs/deprecated/NedelecRefFEs.jl 0.00% 197 Missing ⚠️
src/FESpaces/deprecated/DivConformingFESpaces.jl 0.00% 94 Missing ⚠️
src/ReferenceFEs/deprecated/BDMRefFEs.jl 0.00% 87 Missing ⚠️
src/ReferenceFEs/MomentBasedReferenceFEs.jl 76.85% 56 Missing ⚠️
src/ReferenceFEs/AWRefFEs.jl 0.00% 38 Missing ⚠️
src/ReferenceFEs/MTWRefFEs.jl 0.00% 30 Missing ⚠️
src/ReferenceFEs/HHJRefFEs.jl 0.00% 29 Missing ⚠️
src/ReferenceFEs/Pullbacks.jl 62.66% 28 Missing ⚠️
src/ReferenceFEs/CRRefFEs.jl 4.00% 24 Missing ⚠️
... and 15 more
Additional details and impacted files
@@            Coverage Diff             @@
##           master    #1048      +/-   ##
==========================================
- Coverage   89.04%   85.62%   -3.42%     
==========================================
  Files         197      211      +14     
  Lines       23887    24336     +449     
==========================================
- Hits        21270    20838     -432     
- Misses       2617     3498     +881     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

JordiManyer and others added 29 commits January 3, 2025 10:30
- homogenized names and updated exported names
- updated news.md
- handled deprecated APIs
- added some docstrings
- updated tests with new APIs
in place De Casteljau
combine De Casteljau's for _derivatives_1d
add test
Moment based reffes: refactoring and extension of Gridap.Polynomials
@@ -197,6 +196,7 @@ export bdm
export nedelec
export bezier
export modalC0
export cr
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shouldn't we name Crouziex-Raviart reffename: crouziex_raviart = CrouziexRaviart() for clarity and consistency with raviart_thomas = RaviartThomas() ?

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@Jai-Tushar Jai-Tushar Jan 14, 2025

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In the literature, people just refer to it as "cr" just like "bdm". I would suggest that we should name "raviart_thomas" as "RT" instead, which is how people refer to it in the literature and probably modify "cr" to "CR" and "bdm" to "BDM".

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@JordiManyer JordiManyer Jan 14, 2025

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I prefer longer names. CR, RT, ... could mean anything. If you start abbreviating you end up with fortran77 codes...
If a user doesn't know that CR means Crouziex-Raviart, maybe they should not be using it.

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Also: If you don't know what Raviart-Thomas is, you can google it. Going the other direction is not as easy.

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3 participants