# Identifying cells and their vertices **URL:** \ **Category:** mesh\ **Created:** [November 3, 2022, 11:28am UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669 "2022-11-03T11:28:01Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![pamgur](https://avatars.discourse-cdn.com/v4/letter/p/e68b1a/32.png) [@pamgur](https://fenicsproject.discourse.group/u/pamgur)\ **Post date:** [November 3, 2022, 11:28am UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669/1 "2022-11-03T11:28:01Z")
Hi all, I have a code in dolfinx that solves a system of PDEs in a rather complex geometry that I mesh using gmsh. The result is a vector field \mathbf m. I would now need to calculate some quantities for each cell of the mesh, for which I need to identify all the vertices that belong to them. Graphically, it would be something like this: ```auto 0 -------- 1 -------- 4 | | | | cell 0 | cell 1 | | | | 2 -------- 3 -------- 5 ``` I would need to know which vertices (in this case, 0, 1, 2, 3) belong to cell 0, calculate some stuff with the value of \mathbf m at them, then do the same for cell 1 (with vertices 1, 4, 5, 3), etc. Can anyone give me a hint on how to achieve this? Thanks in advance! Here’s a MWE on how I create the mesh: ```auto import gmsh model = gmsh.model; geom = gmsh.model.geo from mpi4py import MPI mesh_comm = MPI.COMM_WORLD ms = 0.1 Rbase = 1 gdim = 2 gmsh.initialize() gmsh.option.setNumber("General.Terminal", 0) model.add("model_acorn") p = [ geom.addPoint(Rbase, np.pi, 0, ms), geom.addPoint(Rbase, np.pi/2, 0, ms), geom.addPoint(0, np.pi/2, 0, ms), geom.addPoint(0, np.pi, 0, ms) ] l = [ geom.addLine(p[0], p[1]), geom.addLine(p[1], p[2]), geom.addLine(p[2], p[3]), geom.addLine(p[3], p[0]) ] cl = geom.addCurveLoop([l[j] for j in range(len(l))]) s = geom.addPlaneSurface([cl]) acorn = model.addPhysicalGroup(gdim, [s]) model.setPhysicalName(gdim, acorn, "Flat acorn") base = model.addPhysicalGroup(gdim-1, [l[0]]) model.setPhysicalName(gdim-1, base, "Base") cap = model.addPhysicalGroup(gdim-1, [l[1]]) model.setPhysicalName(gdim-1, cap, "Cap") geom.synchronize() model.mesh.generate(2) domain, cell_markers, facet_markers = gmshio.model_to_mesh(model, mesh_comm, 0, gdim=gdim) ``` ---
**Author:** ![nate](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/nate/32/17_2.png) [@nate](https://fenicsproject.discourse.group/u/nate)\ **Post date:** [November 3, 2022, 1:24pm UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669/2 "2022-11-03T13:24:16Z")
```python import dolfinx from mpi4py import MPI mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 2, 2, cell_type=dolfinx.mesh.CellType.quadrilateral) c2v = mesh.topology.connectivity(mesh.topology.dim, 0) print(c2v) ``` ```auto 0: [0 1 2 3] 1: [1 4 3 5] 2: [2 3 6 7] 3: [3 5 7 8] ``` ![image](https://global.discourse-cdn.com/free1/uploads/fenicsproject1/original/2X/0/0fdb0b4fade61a5c8109417bd7a5caae37e3e9e5.png) ---
**Author:** ![pamgur](https://avatars.discourse-cdn.com/v4/letter/p/e68b1a/32.png) [@pamgur](https://fenicsproject.discourse.group/u/pamgur)\ **Post date:** [November 3, 2022, 1:51pm UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669/3 "2022-11-03T13:51:13Z")
Thanks a lot, @nate ! Could you please give me some more details on how to access these values and how to evaluate a `fem.Function` at them? Let’s say we have the mesh `domain` that I wrote in my previos post, and there I define ```auto element = ufl.VectorElement("CG", domain.ufl_cell(), 1, 3) V = fem.FunctionSpace(domain, element) m = fem.Function(V) ``` I then solve a non-linear problem (I don’t think this is relevant, bust just in case) to find the value for `m` at `domain`. So far so good. But now I want to sum the values of `m` at all the vertices of a given cell i. How can I evaluate something like m[cell\_i[vertex\_j]]? Thanks! ---
**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\ **Post date:** [November 3, 2022, 2:12pm UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669/4 "2022-11-03T14:12:23Z")
See: [Application of point forces, mapping vertex indices to corresponding DOFs - #2 by dokken](https://fenicsproject.discourse.group/t/application-of-point-forces-mapping-vertex-indices-to-corresponding-dofs/9646/2) ---
**Author:** ![pamgur](https://avatars.discourse-cdn.com/v4/letter/p/e68b1a/32.png) [@pamgur](https://fenicsproject.discourse.group/u/pamgur)\ **Post date:** [November 4, 2022, 8:54am UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669/5 "2022-11-04T08:54:31Z")
Hi @dokken, thanks for your reply. I have looked into the post you linked and I think I know now how to access the vertices of a cell and operate with them. However, I don’t really understand the difference between vertices and dofs. I find that `vertices = c_to_v.links(cell)` and `dofs = V0.dofmap.cell_dofs(cell)` give me identical arrays. Is this always the case? ---
**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\ **Post date:** [November 4, 2022, 9:26am UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669/6 "2022-11-04T09:26:00Z")
No, that is not always the case. A vertex is part of the mesh. Every cell has `N` number of vertices. A degree of freedom does not necessarily belong to a vertex (this is only the case for first order Lagrange elements). See for instance: [DefElement](https://defelement.com/elements/examples/triangle-Lagrange-2.html) ---
**Author:** ![pamgur](https://avatars.discourse-cdn.com/v4/letter/p/e68b1a/32.png) [@pamgur](https://fenicsproject.discourse.group/u/pamgur)\ **Post date:** [November 4, 2022, 12:51pm UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669/7 "2022-11-04T12:51:40Z")
Hi again, @nate and @dokken. I realise now that I forgot to say that I actually need to access the nodes of a given cell in order, forming a closed loop (clockwise or anticlockwise is the same as long as I know which one it is). So in my first example, ```auto 0 -------- 1 -------- 4 | | | | cell 0 | cell 1 | | | | 2 -------- 3 -------- 5 ``` I would need to operate with the value of the fem.Function m at nodes 0 2 3 1 0 (in that order) of cell 0, then at nodes 1 3 5 4 1 of cell 1, etc. Is there any way to achieve this? As I see from nate’s response, `mesh.topology.connectivity(mesh.topology.dim, 0)` doesn’t necessarily return the nodes in order. Thank you for your help! ---
**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\ **Post date:** [November 4, 2022, 1:10pm UTC](https://fenicsproject.discourse.group/t/identifying-cells-and-their-vertices/9669/8 "2022-11-04T13:10:18Z")
I don’t understand why the way you are traversing the cell matters. You could always compute the orientation by computing the normal vector based on the geometry. See: > > You should do something similar to this depending on your application.