# Integral over the domain of a tensorial quantity **URL:** \ **Category:** dolfinx\ **Created:** [June 15, 2022, 3:01pm UTC](https://fenicsproject.discourse.group/t/integral-over-the-domain-of-a-tensorial-quantity/8548 "2022-06-15T15:01:19Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![cas91](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/cas91/32/174_2.png) [@cas91](https://fenicsproject.discourse.group/u/cas91)\ **Post date:** [June 15, 2022, 3:01pm UTC](https://fenicsproject.discourse.group/t/integral-over-the-domain-of-a-tensorial-quantity/8548/1 "2022-06-15T15:01:19Z")
Hi to all of you :)! I have a problem regarding the integration of a second order tensor over the volume (3D mesh) in post-processing. Let T(uh), be a second order tensor function acting on the discrete displacement field uh at each dof. The integral of the second order tensor (size=(3,3)) over the domain (Omega) is giving an error. First problem was that ufl perform integration only on scalar quantities, the error was: ufl.log.UFLException: Can only integrate scalar expressions. The integrand is a tensor expression with value shape (3, 3) and free indices with labels (). Then checking the solution proposed in [Integration of a gradient of function - #11 by Alberto\_Lolli](https://fenicsproject.discourse.group/t/integration-of-a-gradient-of-function/7428/11), Then, I modified my formulation in the same fashion to compute the integral of each component of the tensor. A new problem arise when trying to do so, my code is below. > define Ten(u): > eps = ufl.sym(ufl.grad(u)) > return ufl.as\_tensor(L[p,q,r,s]\*eps[r,s],(p,q)) > > Ten2 = Ten(uh) > Q = dolfinx.fem.TensorFunctionSpace(mesh,(“DG”,0)) > Ten2Int = dolfinx.fem.Function(Q) > Ten2Int.interpolate(Ten2) > Ten2Int2 = numpy.zeros((3,3)) > for i in range(3): > for j in range(3): > Ten2Int2 = dolfinx.assemble\_scalar(Ten2Int[i,j]\*ufl.dx) the error is the following: File “/home/camilo/.local/lib/python3.8/site-packages/dolfinx/fem/assemble.py”, line 128, in assemble\_scalar constants = constants or \_pack\_constants(M) TypeError: pack\_constants(): incompatible function arguments. The following argument types are supported: 1. (arg0: dolfinx::fem::Form) → numpy.ndarray[numpy.float64] 2. (arg0: dolfinx::fem::Expression) → numpy.ndarray[numpy.float64] 3. (arg0: dolfinx::fem::Form) → numpy.ndarray[numpy.float32] 4. (arg0: dolfinx::fem::Expression) → numpy.ndarray[numpy.float32] 5. (arg0: dolfinx::fem::Form\) → numpy.ndarray[numpy.complex128] 6. (arg0: dolfinx::fem::Expression\) → numpy.ndarray[numpy.complex128] Invoked with: Form([Integral(Sum(Indexed(Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement(‘Lagrange’, tetrahedron, 1, variant=‘equispaced’), dim=3, variant=‘equispaced’), 0), TensorElement(FiniteElement(‘Discontinuous Lagrange’, tetrahedron, 0), shape=(3, 3), symmetry={})), 2), MultiIndex((FixedIndex(0), FixedIndex(0)))), Indexed(Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement(‘Lagrange’, tetrahedron, 1, variant=‘equispaced’), dim=3, variant=‘equispaced’), 0), TensorElement(FiniteElement(‘Discontinuous Lagrange’, tetrahedron, 0), shape=(3, 3), symmetry={})), 3), MultiIndex((FixedIndex(0), FixedIndex(0))))), ‘cell’, Mesh(VectorElement(FiniteElement(‘Lagrange’, tetrahedron, 1, variant=‘equispaced’), dim=3, variant=‘equispaced’), 0), ‘everywhere’, {}, None)]) Did you forget to `#include `? Or \, \, \, etc. Some automatic conversions are optional and require extra headers to be included when compiling your pybind11 module. Thanks a lot in adavance !!! ---
**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 15, 2022, 3:54pm UTC](https://fenicsproject.discourse.group/t/integral-over-the-domain-of-a-tensorial-quantity/8548/2 "2022-06-15T15:54:46Z")
Im not quite sure which version of DOLFINx you are using, but I guess you should call `dolfinx.fem.form(Ten2Int[i,j]*ufl.dx)` prior to calling `dolfinx.fem.assemble_scalar`. ---
**Author:** ![cas91](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/cas91/32/174_2.png) [@cas91](https://fenicsproject.discourse.group/u/cas91)\ **Post date:** [June 15, 2022, 4:07pm UTC](https://fenicsproject.discourse.group/t/integral-over-the-domain-of-a-tensorial-quantity/8548/3 "2022-06-15T16:07:48Z")
Thanks a lot Mr. Dokken, I think now is working that part ^^, then a third problem arise XD, the problem is that I’m in complex mode of my 0.4.0 dolfinx version (complex petsc) and the dolfinx.fem.assemble scalar gives me the following type error: TypeError: can’t convert complex to float should I compute the integral of the real and imaginary part of each component ? or there is a way to force it to work on complex numbers ? Thanks a lot in advance ^^!!! ---
**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 15, 2022, 4:57pm UTC](https://fenicsproject.discourse.group/t/integral-over-the-domain-of-a-tensorial-quantity/8548/4 "2022-06-15T16:57:22Z")
Without a minimal working example it is quite hard to give any guidance, but i can guess it is related to:[Interpolate expression with complex litteral - #4 by dokken](https://fenicsproject.discourse.group/t/interpolate-expression-with-complex-litteral/8251/4) ---
**Author:** ![cas91](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/cas91/32/174_2.png) [@cas91](https://fenicsproject.discourse.group/u/cas91)\ **Post date:** [June 17, 2022, 5:20pm UTC](https://fenicsproject.discourse.group/t/integral-over-the-domain-of-a-tensorial-quantity/8548/5 "2022-06-17T17:20:20Z")
Hi Mr Dokken 🙂 Thanks a lot again for your help, quite a good intuition ^^. All is working smooth now. Kind regards Camilo