[BUG]: wrong output of interpolation_points() method for higher order N1curl elements (tetrahedra)?
Closed this issue · 1 comments
Summarize the issue
Related to a recent question (https://fenicsproject.discourse.group/t/tabulate-dof-coordinates-of-n1curl-space/16090/2), I noticed an unexpected behavior testing the described mechanics to calculate the locations of the dofs for higher order (tested p2 and p3) N1curl elements: The lengths of the output arrays of the method
element.interpolation_points() are 24 (p2) and 47(p3)
does not match the expected numbers 20(p2) or 45 (p3). For p2, first 12 entries appear correct to me, but the remaing 12 appear wrong, and there should be only 8 further entries for the dofs associated with the four faces according to the common definition I know, e.g. (https://defelement.com/elements/examples/tetrahedron-nedelec1-lagrange-2.html)
I have not looked into detail for the p3 elements tested higher order or other element types. Just tested for P-elements and the output looks absolutely fine.
How to reproduce the bug
run minimum example provided
Minimal Example (Python)
import dolfinx as dfx
from basix.ufl import element, mixed_element
from mpi4py import MPI
mesh = dfx.mesh.create_unit_cube(MPI.COMM_WORLD, 1, 1, 1)
for elemtype in ["P", "N1curl"]:
for p in [1, 2, 3]:
ele = element(elemtype, mesh.basix_cell(), p)
V = dfx.fem.functionspace(mesh, ele)
print("Type: " + elemtype, 'polynomial order: ' + str(p))
print('expected len: ', V.element.space_dimension)
print('len of interpolation points: ', len(V.element.interpolation_points()))
print(V.element.interpolation_points())
print('"'*80)Output (Python)
Type: P polynomial order: 1
expected len: 4
len of interpolation points: 4
[[0. 0. 0.]
[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
Type: P polynomial order: 2
expected len: 10
len of interpolation points: 10
[[0. 0. 0. ]
[1. 0. 0. ]
[0. 1. 0. ]
[0. 0. 1. ]
[0. 0.5 0.5]
[0.5 0. 0.5]
[0.5 0.5 0. ]
[0. 0. 0.5]
[0. 0.5 0. ]
[0.5 0. 0. ]]
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
Type: P polynomial order: 3
expected len: 20
len of interpolation points: 20
[[0. 0. 0. ]
[1. 0. 0. ]
[0. 1. 0. ]
[0. 0. 1. ]
[0. 0.7236068 0.2763932 ]
[0. 0.2763932 0.7236068 ]
[0.7236068 0. 0.2763932 ]
[0.2763932 0. 0.7236068 ]
[0.7236068 0.2763932 0. ]
[0.2763932 0.7236068 0. ]
[0. 0. 0.2763932 ]
[0. 0. 0.7236068 ]
[0. 0.2763932 0. ]
[0. 0.7236068 0. ]
[0.2763932 0. 0. ]
[0.7236068 0. 0. ]
[0.33333333 0.33333333 0.33333333]
[0. 0.33333333 0.33333333]
[0.33333333 0. 0.33333333]
[0.33333333 0.33333333 0. ]]
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
Type: N1curl polynomial order: 1
expected len: 6
len of interpolation points: 6
[[0. 0.5 0.5]
[0.5 0. 0.5]
[0.5 0.5 0. ]
[0. 0. 0.5]
[0. 0.5 0. ]
[0.5 0. 0. ]]
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
Type: N1curl polynomial order: 2
expected len: 20
len of interpolation points: 24
[[0. 0.78867513 0.21132487]
[0. 0.21132487 0.78867513]
[0.78867513 0. 0.21132487]
[0.21132487 0. 0.78867513]
[0.78867513 0.21132487 0. ]
[0.21132487 0.78867513 0. ]
[0. 0. 0.21132487]
[0. 0. 0.78867513]
[0. 0.21132487 0. ]
[0. 0.78867513 0. ]
[0.21132487 0. 0. ]
[0.78867513 0. 0. ]
[0.66666667 0.16666667 0.16666667]
[0.16666667 0.16666667 0.66666667]
[0.16666667 0.66666667 0.16666667]
[0. 0.16666667 0.16666667]
[0. 0.16666667 0.66666667]
[0. 0.66666667 0.16666667]
[0.16666667 0. 0.16666667]
[0.16666667 0. 0.66666667]
[0.66666667 0. 0.16666667]
[0.16666667 0.16666667 0. ]
[0.16666667 0.66666667 0. ]
[0.66666667 0.16666667 0. ]]
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
Type: N1curl polynomial order: 3
expected len: 45
len of interpolation points: 47
[[0. 0.88729833 0.11270167]
[0. 0.5 0.5 ]
[0. 0.11270167 0.88729833]
[0.88729833 0. 0.11270167]
[0.5 0. 0.5 ]
[0.11270167 0. 0.88729833]
[0.88729833 0.11270167 0. ]
[0.5 0.5 0. ]
[0.11270167 0.88729833 0. ]
[0. 0. 0.11270167]
[0. 0. 0.5 ]
[0. 0. 0.88729833]
[0. 0.11270167 0. ]
[0. 0.5 0. ]
[0. 0.88729833 0. ]
[0.11270167 0. 0. ]
[0.5 0. 0. ]
[0.88729833 0. 0. ]
[0.09157621 0.81684757 0.09157621]
[0.09157621 0.09157621 0.81684757]
[0.81684757 0.09157621 0.09157621]
[0.44594849 0.10810302 0.44594849]
[0.44594849 0.44594849 0.10810302]
[0.10810302 0.44594849 0.44594849]
[0. 0.81684757 0.09157621]
[0. 0.09157621 0.81684757]
[0. 0.09157621 0.09157621]
[0. 0.10810302 0.44594849]
[0. 0.44594849 0.10810302]
[0. 0.44594849 0.44594849]
[0.81684757 0. 0.09157621]
[0.09157621 0. 0.81684757]
[0.09157621 0. 0.09157621]
[0.10810302 0. 0.44594849]
[0.44594849 0. 0.10810302]
[0.44594849 0. 0.44594849]
[0.81684757 0.09157621 0. ]
[0.09157621 0.81684757 0. ]
[0.09157621 0.09157621 0. ]
[0.10810302 0.44594849 0. ]
[0.44594849 0.10810302 0. ]
[0.44594849 0.44594849 0. ]
[0.25 0.25 0.25 ]
[0.5 0.16666667 0.16666667]
[0.16666667 0.5 0.16666667]
[0.16666667 0.16666667 0.5 ]
[0.16666667 0.16666667 0.16666667]]
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""Version
main branch
DOLFINx git commit
No response
Installation
used dolfin version 0.8.0 via conda installation
Additional information
No response
Invalid bug. The whole point is that one doesn’t use a single node for interpolation for higher order nedelec dofs. To properly represent the dual basis, which is an integral, one require several points per edge.
See for instance chapter 7.3 and figure 10 of:
https://orbilu.uni.lu/bitstream/10993/59327/1/dolfinx-paper-zenodo.10447666.pdf