# Split a 3D vector function into a scalar and a 2D vector

**URL:** <https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944>\
**Category:** Uncategorized\
**Created:** [June 3, 2021, 6:52am UTC](https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944 "2021-06-03T06:52:56Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![a516095046](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@a516095046](https://fenicsproject.discourse.group/u/a516095046)\
**Post date:** [June 3, 2021, 6:52am UTC](https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944/1 "2021-06-03T06:52:56Z")

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Hello, I want to split a 3D vector function into a scalar and a 2D vector, but the typical `split()` function splits it into 3 scalars instead, anyone know how to do that split?

```auto
from dolfin import *
mesh = RectangleMesh(dl.Point(0., 0.), dl.Point(5., 5.),10,10)
V = VectorFunctionSpace(mesh, 'Lagrange', 2, 3)
X = Function(V)

```

I want to split the first dimension of `X` into `T` for temperature, and the second and third dimensions of `X` into `u` as 2D vector displacement.

Thank you in advance!

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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 3, 2021, 7:58am UTC](https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944/2 "2021-06-03T07:58:17Z")

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I would suggest you use a `MixedElement`, i.e.

```python
from dolfin import * 
mesh = RectangleMesh(Point(0., 0.), Point(5., 5.), 10, 10)
v_el = VectorElement("CG", mesh.ufl_cell(), 1, dim=2)
t_el = FiniteElement("CG", mesh.ufl_cell(), 1) 
V = FunctionSpace(mesh, MixedElement([v_el, t_el]))
uT = Function(V)
u = uT.sub(0)
T = uT.sub(1)

```

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<div class="post-metadata">

**Author:** ![a516095046](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@a516095046](https://fenicsproject.discourse.group/u/a516095046)\
**Post date:** [June 3, 2021, 6:11pm UTC](https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944/3 "2021-06-03T18:11:14Z")

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Good idea! A following up question is that I ran into this error saying that there is no `sub`

> T = u.sub(1)  
> AttributeError: ‘Argument’ object has no attribute ‘sub’

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<div class="post-metadata">

**Author:** ![a516095046](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@a516095046](https://fenicsproject.discourse.group/u/a516095046)\
**Post date:** [June 3, 2021, 6:23pm UTC](https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944/4 "2021-06-03T18:23:02Z")

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Looks like the following codes worked instead of `sub()`, what do you think?

```auto
u,T = split(uT)

```

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<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 3, 2021, 8:11pm UTC](https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944/5 "2021-06-03T20:11:14Z")

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So I guess you are using `u=TrialFunction(V)`. Then you need to use split.

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<div class="post-metadata">

**Author:** ![a516095046](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@a516095046](https://fenicsproject.discourse.group/u/a516095046)\
**Post date:** [June 3, 2021, 10:56pm UTC](https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944/6 "2021-06-03T22:56:35Z")

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Yes, thanks! Following on the same setup, how should I correctly define surface integrant `ds()` for only one of the functions?

for example, I want to define `ds(1)` for the top edge for `T` and `ds(2)` for the right edge for `u`, I usually use the following code:

```auto
class TopSurf(SubDomain):
        def inside(self, x, on_boundary):
            return on_boundary and near(x[1],1.)
class RightSurf(SubDomain):
        def inside(self, x, on_boundary):
            return on_boundary and near(x[0],1.)
boundary_parts = MeshFunction("size_t", mesh, mesh.topology().dim()-1, 0)
boundary_parts.set_all(0) #marks whole cube as domain 0

top = TopSurf()
top.mark(boundary_parts, 1)
right = RightSurf()
right.mark(boundary_parts, 2)

ds=Measure('ds',subdomain_data=boundary_parts)

```

But looks like using the above code, `ds(1)` ended up to be the top boundary of both `T` and `u`, and same situation for `ds(2)`. I tried to use something like `ds(1).sub(1)` but didn’t work.

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<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 4, 2021, 5:42am UTC](https://fenicsproject.discourse.group/t/split-a-3d-vector-function-into-a-scalar-and-a-2d-vector/5944/7 "2021-06-04T05:42:30Z")

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Integration measures are not directly linked to the function space. Simply integrate only the subfunction over that boundary, and not both functions.