# Different material properties in subdomains, tensor instead of scalar

**URL:** <https://fenicsproject.discourse.group/t/different-material-properties-in-subdomains-tensor-instead-of-scalar/9887>\
**Category:** General\
**Created:** [December 3, 2022, 1:12pm UTC](https://fenicsproject.discourse.group/t/different-material-properties-in-subdomains-tensor-instead-of-scalar/9887 "2022-12-03T13:12:51Z")\
**Posts on this page:** 1\
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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:** [December 5, 2022, 8:18am UTC](https://fenicsproject.discourse.group/t/different-material-properties-in-subdomains-tensor-instead-of-scalar/9887/2 "2022-12-05T08:18:10Z")

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How do you expect a tensor to be assigned to a scalar function space?  
The space `("CG", 1)` contains one degree of freedom at any point. It does not make sense to try to add a scalar to it.  
If you want to do so, you need to use a `TensorElement` or a `TensorFunctionSpace` as shown for a dummy rho below:

```python
import dolfinx
from mpi4py import MPI
import ufl
import numpy as np
mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)

el = ufl.TensorElement("Lagrange", mesh.ufl_cell(), 1, shape=(2, 2))

V = dolfinx.fem.FunctionSpace(mesh, el)
u = dolfinx.fem.Function(V)

def rho_B(x):
    tensor = np.array([[1, 2], [3, 4.]])

    values = np.repeat(tensor, x.shape[1])
    return values.reshape(tensor.shape[0]*tensor.shape[1], x.shape[1])

u.interpolate(rho_B)

for i in range(2):
    for j in range(2):
        print(i, j, dolfinx.fem.assemble_scalar(
            dolfinx.fem.form(u[i, j]*ufl.dx)))

```

if you want the `rho` to be different in different subdomains, you should use the `cells` kwarg of interpolate, as it will then only do interpolation on dofs associated to those entities. In your case that would be  
`u.interpolate(rho_B, cells=ct.find(11))`

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