NC mesh with hanging element?

[dongzhangim]

hello, all
i'm new to mfem. I wanna use MFEM for the simulation of elastic deformation of a nonconforming mesh with hanging element. Hanging element means when a quad or hex element is refined, some subdivided elements are deleted leaving the remaining ones(one) hanging. That's my understanding.

First, I tested two elements with one refined (see Figure A). The results (generated by ex21) are shown in Figure B.

The mesh files are as follows.

MFEM NC mesh v1.0

dimension
2

elements
6
0 1 3 0 0 1 4 3
0 2 3 3 2 3 4 5
0 2 3 0 1 8 10 7
0 2 3 0 8 2 9 10
0 2 3 0 7 10 6 4
0 2 3 0 10 9 5 6

boundary
9
3 1 0 1
3 1 1 8
3 1 2 8
3 1 3 4
3 1 4 6
3 1 5 6
1 1 0 3
2 1 2 8
2 1 5 9

vertex_parents
5
6 4 5
7 1 4
8 1 2
9 2 5
10 6 8

coordinates
6
2
0 0
1 0
2 0
0 1
1 1
2 1

mfem_mesh_end

Second, I try to delete the element with id 5 by removing its id from the element of id 1 as depicted in Figure C, however, it does not work with errors:

Verification failed: (geom == Geometry::SEGMENT || geom == Geometry::TRIANGLE || geom == Geometry::SQUARE || geom == Geometry::CUBE || geom == Geometry::PRISM || geom == Geometry::PYRAMID || geom == Geometry::TETRAHEDRON) is false:
--> Element type 0 is not supported by NCMesh.
... in function: void mfem::CheckSupportedGeom(Geometry::Type)
... in file: mesh/ncmesh.cpp:128

The NC mesh files are as follows:

MFEM NC mesh v1.0
dimension
2

elements
5
0 1 3 0 0 1 4 3
0 2 3 3 2 3 4
0 2 3 0 1 8 10 7
0 2 3 0 8 2 9 10
0 2 3 0 7 10 6 4

boundary
9
3 1 0 1
3 1 1 8
3 1 2 8
3 1 3 4
3 1 4 6
3 1 10 6
1 1 0 3
2 1 2 8
2 1 10 9

vertex_parents
5
6 4 5
7 1 4
8 1 2
9 2 5
10 6 8

coordinates
6
2
0 0
1 0
2 0
0 1
1 1
2 1

mfem_mesh_end

So, how can we tackle nc mesh with hanging elements?

[v-dobrev]

One problem that I see is: vertex id 5 is no longer needed, so you can remove it from coordinates and also from vertex_parents. Also, some of the vertices that you previously described in the vertex_parents section have to be added as regular vertices due to the removal of vertex with id 5.

[dongzhangim]

Dear Veselin,
Thanks for your help. After deleting the hanging node with an ID of 5 and making two nodes with coordinates of (1.5, 1) and (2, 0.5) regular, it works as shown below, although the refinement hierarchy cannot be stored.

MFEM NC mesh v1.0
dimension
2

elements
4
0 1 3 0 0 1 4 3
0 2 3 0 1 8 9 7
0 2 3 0 8 2 6 9
0 2 3 0 7 9 5 4

boundary
9
3 1 0 1
3 1 1 8
3 1 2 8
3 1 3 4
3 1 4 5
3 1 5 9
3 1 6 9
1 1 0 3
2 1 2 6

vertex_parents
3
7 1 4
8 1 2
9 5 8

coordinates
7
2
0 0
1 0
2 0
0 1
1 1
1.5 1
2 0.5

mfem_mesh_end

Also, we can make the single node with the coordinate of (1 0.5) nonregular, it works as well.

MFEM NC mesh v1.0
dimension
2

elements
4
0 1 3 0 0 1 5 4
0 2 3 0 1 2 7 9
0 2 3 0 2 3 8 7
0 2 3 0 9 7 6 5

boundary
9
3 1 0 1
3 1 1 2
3 1 2 3
3 1 4 5
3 1 5 6
3 1 6 7
3 1 7 8
1 1 0 4
2 1 3 8

vertex_parents
1
9 1 5

coordinates
9
2
0 0
1 0
1.5 0
2 0
0 1
1 1
1.5 1
1.5 0.5
2 0.5

mfem_mesh_end