Local/global ordering of cell edges and faces (after grid/mesh import)

Question

I am trying to understand how grid edges/faces are numbered internally (in order to set boundary conditions on the correct local external edges/faces with the xml domains/mesh_value_collection property). To test I have created a simple 2d xml test grid with six nodes and four triangles

<dolfin>
  <mesh celltype="triangle" dim="2">
    <vertices size="6">
      <vertex index="0" x="0.0" y="0.0" z="0.0"/>
      <vertex index="1" x="1.0" y="0.0" z="0.0"/>
      <vertex index="2" x="0.0" y="1.0" z="0.0"/>
      <vertex index="3" x="1.0" y="1.0" z="0.0"/>
      <vertex index="4" x="0.5" y="0.0" z="0.0"/>
      <vertex index="5" x="0.5" y="1.0" z="0.0"/>
    </vertices>
    <cells size="4">
      <cell index="0" v0="0" v1="5" v2="2"/>
      <cell index="1" v0="0" v1="4" v2="5"/>
      <cell index="2" v0="4" v1="3" v2="5"/>
      <cell index="3" v0="4" v1="1" v2="3"/>
    </cells>
  </mesh>
</dolfin>

Grid http://imgur.com/a/35pFw

3---6---4
|\  |\  |
|1\2|3\4|
|  \|  \|
1---5---2

And after importing the grid into fenics and inspecting it with

from fenics import *

mesh = Mesh("test.xml")

print "\n cell connectivity:\n"
delements = dict((cell.index(), cell.entities(0)) for cell in cells(mesh))
for element in range(mesh.num_cells()):
  print "   " + repr(element+1) + " : " + str(delements[element]+1)

  print "\n cell edges:\n"
  dfacets = dict((facet.index(), facet.entities(0)) for facet in facets(mesh))
  for facet in range(len(dfacets)):
    print "   " + repr(facet+1) + " : " + str(dfacets[facet]+1)
    print "\n"

    for cell in cells(mesh):
      print "    cell : " + repr(cell.index()+1)
      dfacetsi = dict((faceti.index(), faceti.entities(0)) for faceti in facets(cell))
      for faceti in range(len(dfacetsi)):
        key = dfacetsi.keys()[faceti]
        print "   " + repr(key+1) + " : " + str(dfacetsi[key]+1)

results in

cell connectivity:

1 : [1 3 6]
2 : [1 5 6]
3 : [4 5 6]
4 : [2 4 5]

global edges [vertices]:

1 : [1 3]
2 : [1 5]
3 : [1 6]
4 : [2 4]
5 : [2 5]
6 : [3 6]
7 : [4 5]
8 : [4 6]
9 : [5 6]

this is all fine since I understand that the vertices are ordered with increasing vertex number. However, I cannot find the logic in how the edges are ordered on each cell

local cell and global edges [vertices]:

cell : 1
  local edge 1: global edge 1 : [1 3]
  local edge 2: global edge 3 : [1 6]
  local edge 3: global edge 6 : [3 6]
cell : 2
  local edge 1: global edge 9 : [5 6]
  local edge 2: global edge 2 : [1 5]
  local edge 3: global edge 3 : [1 6]
cell : 3
  local edge 1: global edge 9 : [5 6]
  local edge 2: global edge 7 : [4 5]
  local edge 3: global edge 8 : [4 6]
cell : 4
  local edge 1: global edge 4 : [2 4]
  local edge 2: global edge 5 : [2 5]
  local edge 3: global edge 7 : [4 5]

From reading the Fenics/Dolfin docs and manual I see that local edge 1 should be correlated with local vertices 2 and 3 (edge 2 with vertices 1 and 3 etc.). This does not seem to be the case here since for example cell 1 should have global edge ordering 6-3-1 not 1-3-6. Furthermore, for cells 2 and 3 the edges do neither seem to be ordered with increasing global edge numbering or respect the local edge 1 -> vertices2/3 relation at all.

Is there any clear reference where one can see how the local edges/faces will be ordered (after xml grid import)?

Would these links be helpful?
https://fenicsproject.org/qa/12520/efficient-preserve-boundary-numbering-submeshes-generated
https://fenicsproject.org/qa/13906/implementation-a-modified-dg-jump-condition-with-ode

You can label these as physical/facet regions in GMSH and handle them in aggregate based on their labels and convert them to .xml files with dolfin-convert(). Using the ds(n) measure where n is the boundary label you can assign the appropriate boundary conditions. — treblebrewing, Jun 11, 2017
Thanks for looking into this. I am not using Gmsh though but importing from my own grid format so knowing how fenics orders edges/faces would be useful. — markusj, Jun 12, 2017

RR · Answer 1 · Jun 14, 2017

"Is there any clear reference where one can see how the local edges/faces will be ordered (after xml grid import)?"

--> "UFC Specification and User Manual 1.1" (just google or google scholar the pdf)
--> Chapter 5: Numbering of mesh entities

The ordering of on the fly created meshes (e.g. mesh = UnitCubemesh(3, 3, 3)) or imported meshes (e.g. mesh = Mesh('exported_UCMesh.xml')) is identical (at least for my tests). Local to global ordering always follows the ufl rules, also if you use mpi and distribute your mesh over several processes.

Local/global ordering of cell edges and faces (after grid/mesh import)

1 Answer