Add get_embedding_dofs() to FE_Nedelec (2-D) #13158

harmonj · 2021-12-30T22:28:25Z

Adds get_embedding_dofs() to the FE_Nedelec element (currently for dim==2).

marcfehling

Code looks great! I have just some minor suggestions, mainly turning variables into const.

tests/fe/nedelec_embed_dofs.cc

source/fe/fe_nedelec.cc

harmonj · 2022-01-18T06:38:58Z

Thank you, @marcfehling!

I added each of your suggestions above and squashed the commits. Please let me know if you'd like to see other changes before merging.

marcfehling · 2022-01-18T10:12:07Z

/rebuild

bangerth

I don't think this function should be in the base class. But that shouldn't mean that it can't be in the Nedelec class itself, of course.

bangerth · 2022-01-18T21:15:48Z

include/deal.II/fe/fe.h

+   * therefore, may not implement it.
+   */
+  virtual std::vector<unsigned int>
+  get_embedding_dofs(const unsigned int sub_degree) const;


I don't think this should be part of the base class. You are assuming that there is a 1:1 relationship between the dofs of a higher and lower degree element, but that is really only the case for very special cases. The more general solution for what you want to do is the get_interpolation_matrix() function, for which your special case leads to a situation where the matrix has specific entry values.

Yes, since the one to one identification is only possible in special cases I agree that it makes more sense to leave this out of the base class.

I'll take a look at implementing get_interpolation_matrix() for a better generalization here.

bangerth · 2022-01-18T21:17:45Z

include/deal.II/fe/fe_nedelec.h

+   * opposed to the Nedelec degree.
+   */
+  virtual std::vector<unsigned int>
+  get_embedding_dofs(const unsigned int sub_degree) const override;


Even for the Nedelec element, isn't this only applicable for, say, element orders 1 and n, 2 and 2n, 3 and 3n (assuming we are using equispaced points), etc?

Perhaps I have misunderstood portions of the Nedelec element implementation in deal.II, but if this were the case I would have expected that this would have been indicated by the test I wrote. I also tested beforehand with the original way I was mapping from p-reduced Nedelec cells to enriched ones using the curl-conforming projection-based interpolation.

I'll have to dive back into the FE_Nedelec implementation and see if there is something I missed that might prevent identification of equivalent dofs between a Nedelec cell of sub_degree and a Nedelec cell of sup_degree in this manner for some cases.

Think about the usual Q_k elements in 2d. If you have a Q_2, it has DoFs at the vertices, edge midpoints, and cell midpoint. If you have a Q_3, it has DoFs at the vertices but also at positions 1/3 and 2/3 along the edge, and 4 in the interior of the cell which are all not located at the cell center. I don't think the Nedelec element has a structure that is different from the general problem outlined above unless it is moment based along edges in which all edge and cell degrees of freedom might be located at edge and cell midpoints.

The case for FE_Nedelec is not quite the same as the standard Q_k element. The support points are the Gauss-Legendre quadrature points (on the faces or the interior of the cell), but the identification of equivalent DoFs from a Nedelec element of sub_degree to an element of sup_degree is based on the hierarchical construction of the mixed order Nedelec polynomials as in PolynomialsNedelec<dim>::create_polynomials(). In other words, the enriched cell includes all the shape functions of the reduced cell, so there is no concern w.r.t. the choice of sub_degree or sup_degree.

bangerth

I don't think this function should be in the base class. But that shouldn't mean that it can't be in the Nedelec class itself, of course.

harmonj · 2022-01-26T01:05:54Z

I removed the function from the base class for the reasons stated above and squashed the commits.

Somewhat unrelated to this specific commit but related to the identification of embedding DoFs, would it be of interest to add illustrations of the shape functions (by component) on the reference cell for FE_Nedelec in the documentation as seen for other finite element classes?

bangerth · 2022-01-26T03:58:10Z

More documentation is always better! It's more difficult for vector-valued elements, of course, but could probably also be scripted. I wished I still knew where the script is (or whether it was preserved at all) with which we generated the existing figures. I know that it used a mesh with a single cell, a solution vector with exactly one one in it, and DataOut::build_patches() with a large number of subdivisions.

But if you wanted to go down that route, let's do it in a separate PR.

harmonj · 2022-01-26T04:36:17Z

More documentation is always better! It's more difficult for vector-valued elements, of course, but could probably also be scripted. I wished I still knew where the script is (or whether it was preserved at all) with which we generated the existing figures. I know that it used a mesh with a single cell, a solution vector with exactly one one in it, and DataOut::build_patches() with a large number of subdivisions.

Sounds good. I'll have to play around with the visualization for the script I wrote last week to plot these shape functions and keep things consistent with the other elements. I'll do that for a separate PR.

jppelteret · 2022-01-26T07:34:13Z

Somewhat unrelated to this specific commit but related to the identification of embedding DoFs, would it be of interest to add illustrations of the shape functions (by component) on the reference cell for FE_Nedelec in the documentation as seen for other finite element classes?

If it helps, I placed a small program in #8634 (comment) that outputs all shape functions in the VTU format. It works for the Nedelec elements too.

harmonj · 2022-01-28T05:10:27Z

If it helps, I placed a small program in #8634 (comment) that outputs all shape functions in the VTU format. It works for the Nedelec elements too.

Thank you. The script that I wrote is similar, though I was plotting the components individually as scalar quantities. I will experiment with the visualization and submit a separate pull request soon.

Otherwise, this PR should be good to go, unless there are other changes anyone would like me to make.

marcfehling · 2022-01-31T17:22:51Z

include/deal.II/fe/fe_nedelec.h

@@ -324,6 +324,18 @@ class FE_Nedelec : public FE_PolyTensor<dim>
  virtual std::unique_ptr<FiniteElement<dim, dim>>
  clone() const override;

+  /**
+   * For a finite element of degree @p sub_degree < @p degree, we return a


Suggested change

* For a finite element of degree @p sub_degree < @p degree, we return a

* For a finite element of degree larger than @p sub_degree, we return a

I think this is easier to read.

I agree that this is easier to understand. I pushed this change.

Would you like me to make the same modification to the description for the equivalent function in FE_Q_Hierarchical?

Would you like me to make the same modification to the description for the equivalent function in FE_Q_Hierarchical?

I think that this would be a nice improvement, so go for it! I suggest opening a separate PR for this change.

Sounds good. Will do.

peterrum · 2022-04-24T13:13:08Z

Is this PR ready to be merged?

harmonj · 2022-04-24T15:30:42Z

Is this PR ready to be merged?

Yes, I believe so.

kronbichler

I think we somehow forgot to merge this one. @tamiko do we want to still merge it for the upcoming release, as the milestone suggests? I would be in favor, but we need a second opinion at this stage.

tamiko · 2022-06-14T01:45:53Z

We need in particular @bangerth to OK the pull request :-)

The change request (refactoring into the Nedelec class itself has been addressed).

bangerth · 2022-06-16T08:26:28Z

My apologies for dropping the ball in the first place (and then being on vacation until Monday and in the air Tuesday+Wednesday). Thanks everyone for handling the patch, and to @harmonj for writing it in the first place!

Add get_embedding_dofs() to FE_Nedelec (2-D)

marcfehling added the Finite Element label Jan 15, 2022

marcfehling requested changes Jan 17, 2022

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harmonj force-pushed the FE_NEDELEC_EMBEDDING_DOFS branch from 06a401d to 052acb4 Compare January 18, 2022 06:29

marcfehling approved these changes Jan 18, 2022

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marcfehling added the ready to test label Jan 18, 2022

bangerth reviewed Jan 18, 2022

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harmonj force-pushed the FE_NEDELEC_EMBEDDING_DOFS branch from 052acb4 to 5d5339f Compare January 26, 2022 00:49

marcfehling approved these changes Jan 31, 2022

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Add get_embedding_dofs() to FE_Nedelec (2-D)

fb1286c

harmonj force-pushed the FE_NEDELEC_EMBEDDING_DOFS branch from 5d5339f to fb1286c Compare February 6, 2022 05:06

harmonj requested a review from bangerth February 21, 2022 02:10

harmonj mentioned this pull request Feb 21, 2022

Add shape function illustrations for FE_Nedelec #13427

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peterrum added this to the Release 9.4 milestone Apr 24, 2022

kronbichler approved these changes Jun 13, 2022

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tamiko approved these changes Jun 14, 2022

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tamiko merged commit a7521be into dealii:master Jun 14, 2022

mkghadban pushed a commit to OpenFCST/dealii that referenced this pull request Sep 8, 2022

Merge pull request dealii#13158 from harmonj/FE_NEDELEC_EMBEDDING_DOFS

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Add get_embedding_dofs() to FE_Nedelec (2-D) #13158

Add get_embedding_dofs() to FE_Nedelec (2-D) #13158

harmonj commented Dec 30, 2021 •

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bangerth commented Jun 16, 2022

	* For a finite element of degree @p sub_degree < @p degree, we return a
	* For a finite element of degree larger than @p sub_degree, we return a

Add get_embedding_dofs() to FE_Nedelec (2-D) #13158

Add get_embedding_dofs() to FE_Nedelec (2-D) #13158

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edited