# Extract coordinates of the nodes of a subboundary

**URL:** <https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429>\
**Category:** mesh\
**Created:** [June 4, 2020, 1:03pm UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429 "2020-06-04T13:03:41Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![freya](https://avatars.discourse-cdn.com/v4/letter/f/a9a28c/32.png) [@freya](https://fenicsproject.discourse.group/u/freya)\
**Post date:** [June 4, 2020, 1:03pm UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429/1 "2020-06-04T13:03:42Z")

</div>

The boundary of my mesh is divided into several parts with different physical meaning. I implemented this via gmsh and

```
facets = df.MeshFunction('size_t',mesh,'my-mesh_facet_region.xml')

```

I can extract the coordinates of the whole boundary via

```
boundary_coordinates = facets.mesh().coordinates()

```

But I need the coordinates of a part of the boundary only, subdomain 1, say, and it is difficult in this case to sort these out afterwards. So, how can I get the coordinates of just the subboundary directly?

By the way, I also would like to evaluate a function u exactly at these nodes. So, how can I relate the entries of u.array()[:] with those boundary nodes?

Thank you!

---

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**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:** [June 4, 2020, 7:30pm UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429/2 "2020-06-04T19:30:04Z")

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Consider this minimal example:

```auto
from dolfin import *
import numpy as np

class boundary(SubDomain):
    def inside(self, x, on_boundary):
        return x[0] < 0.4 and on_boundary

mesh = UnitSquareMesh(20,20)
V = FunctionSpace(mesh, "CG", 1)
v = project(Expression("x[0]+x[1]", degree=2),V)
mf = MeshFunction("size_t", mesh, mesh.topology().dim()-1, 0)
boundary().mark(mf, 1)
v2d = vertex_to_dof_map(V)
dofs = []
for facet in facets(mesh):
    if mf[facet.index()] == 1:
        vertices = facet.entities(0)
        for vertex in vertices:
            dofs.append(v2d[vertex])

unique_dofs = np.array(list(set(dofs)), dtype=np.int32)
boundary_coords = V.tabulate_dof_coordinates()[unique_dofs]
for i, dof in enumerate(unique_dofs):
    print(boundary_coords[i], v.vector()[dof])

```

---

<div class="post-metadata">

**Author:** ![freya](https://avatars.discourse-cdn.com/v4/letter/f/a9a28c/32.png) [@freya](https://fenicsproject.discourse.group/u/freya)\
**Post date:** [June 8, 2020, 11:52am UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429/3 "2020-06-08T11:52:50Z")

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Thank you, dokken! This essentially solves my problem, indeed.

However, my function v is from

```
V2 = FunctionSpace(mesh, "CG", 2)

```

so

```
v.vector()[dof]

```

will not give a correct result in this case. Unfortunately,

```
vertex_to_dof_map(V2)

```

yields an error: Can only tabulate dofs on vertices.

---

<div class="post-metadata">

**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:** [June 8, 2020, 12:34pm UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429/4 "2020-06-08T12:34:03Z")

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That is not an error, that is simply from the fact that a CG-2 space has degrees of freedom on facets as well as vertices. Therefore you cannot use vertex\_to\_dof\_map for this operation. You need a more complex operation for this:

```auto
from dolfin import *
import numpy as np

class boundary(SubDomain):
    def inside(self, x, on_boundary):
        return x[0] <= 0.5 and on_boundary

mesh = UnitSquareMesh(5,5)
V = FunctionSpace(mesh, "CG", 2)
v = project(Expression("x[0]+x[1]", degree=2),V)
mf = MeshFunction("size_t", mesh, mesh.topology().dim()-1, 0)
boundary().mark(mf, 1)

mesh.init(2,1)
dofs = []
cell_to_facets = mesh.topology()(2,1)
for cell in cells(mesh):
    facets = cell_to_facets(cell.index())
    for facet in facets:
        if mf[facet] == 1:
            dofs_ = V.dofmap().entity_closure_dofs(mesh, 1, [facet])
            for dof in dofs_:
                dofs.append(dof)

```

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<div class="post-metadata">

**Author:** ![freya](https://avatars.discourse-cdn.com/v4/letter/f/a9a28c/32.png) [@freya](https://fenicsproject.discourse.group/u/freya)\
**Post date:** [June 9, 2020, 12:26pm UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429/5 "2020-06-09T12:26:46Z")

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Excellent! Thank you.

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<div class="post-metadata">

**Author:** ![Alexsta123](https://avatars.discourse-cdn.com/v4/letter/a/e9a140/32.png) [@Alexsta123](https://fenicsproject.discourse.group/u/Alexsta123)\
**Post date:** [July 6, 2022, 2:46pm UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429/6 "2022-07-06T14:46:25Z")

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The MeshTopology() class is not adequately documented, and Its not clear what the commands mesh.init(2,1) and mesh.topology()(2,1) do. How we can get more information to use in different applicaions?

---

<div class="post-metadata">

**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:** [July 6, 2022, 8:55pm UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429/7 "2022-07-06T20:55:55Z")

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> [@Alexsta123](#):
>
> mesh.init(2,1)

This function creates the connectivity between entities of topological dimension 2 (triangles) to entities of topological dimension 1 (lines) using indices local to a process. Each triangle will have three line segments connected, i.e.

> [@Alexsta123](#):
>
> mesh.topology()(2,1)

gives you a map from each cell (local to process) to the three line segments (index local to process).

---

<div class="post-metadata">

**Author:** ![Alexsta123](https://avatars.discourse-cdn.com/v4/letter/a/e9a140/32.png) [@Alexsta123](https://fenicsproject.discourse.group/u/Alexsta123)\
**Post date:** [July 7, 2022, 10:41am UTC](https://fenicsproject.discourse.group/t/extract-coordinates-of-the-nodes-of-a-subboundary/3429/8 "2022-07-07T10:41:17Z")

</div>

Thanks a lot for your fast answer!