# Use of symmetric tensor in dolfinx/ufl results in error

**URL:** <https://fenicsproject.discourse.group/t/use-of-symmetric-tensor-in-dolfinx-ufl-results-in-error/12992>\
**Category:** Errors\
**Created:** [December 9, 2023, 6:49am UTC](https://fenicsproject.discourse.group/t/use-of-symmetric-tensor-in-dolfinx-ufl-results-in-error/12992 "2023-12-09T06:49:28Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![19ec94](https://avatars.discourse-cdn.com/v4/letter/1/b2d939/32.png) [@19ec94](https://fenicsproject.discourse.group/u/19ec94)\
**Post date:** [December 9, 2023, 6:49am UTC](https://fenicsproject.discourse.group/t/use-of-symmetric-tensor-in-dolfinx-ufl-results-in-error/12992/1 "2023-12-09T06:49:28Z")

</div>

Hi,  
Currently I am porting an old application code from Fenics (2019.1.0) to new Fenicsx.

The versions of the libraries I used are as follows:  
`dolfinx` : 0.7.2  
`ufl`: 2023.2.0  
`ffcx`: 0.7.0  
I compiled and built these programs from source which I obtained from Fenics git repository.

In my code I would like to use a symmetric trace-free tensor to represent stress tensor. UFL library does allow symmetric tensor flag. When I execute the following MWE code

```auto
import dolfinx as dfx
from mpi4py import MPI
import ufl as ufl

mesh_dfx = dfx.mesh.create_unit_cube(MPI.COMM_WORLD, 8, 8, 8,
        dfx.mesh.CellType.tetrahedron
        ) 

# create 2 finite elements
# Velocity u (vector),
u_elem = ufl.VectorElement("Lagrange", mesh_dfx.ufl_cell(), 1)
# Stress sigma (Tensor)
# Variable sigma should be symmetric and trace-free. 
# UFL library allows me to create symmetric tensor with a flag `symmetric`. 
#NOTE: With symmetry - CODE RETURNS AN ERROR
sigma_elem = ufl.TensorElement("Lagrange", mesh_dfx.ufl_cell(),1, symmetry=True)
# Without symmetry - SEEMS TO RUN WITHOUT ERROR
#sigma_elem = ufl.TensorElement("Lagrange", mesh_dfx.ufl_cell(),1)

# create mixed finite element vector space
mxd_fspace = dfx.fem.FunctionSpace(mesh_dfx,
        ufl.MixedElement([u_elem, sigma_elem])
        )

# setup trial and test functions
(u, sigma) = ufl.TrialFunctions(mxd_fspace)
(v, psi ) = ufl.TestFunctions(mxd_fspace)

# Convert symmetric tensor to symmetric-and-trace-free tensor 
# using the following custom function
def gen3DTFdim3(sigma):
    return ufl.as_tensor([
        [sigma[0, 0], sigma[0, 1], sigma[0, 2]],
        [sigma[1, 0], sigma[1, 1], sigma[1, 2]],
        [sigma[2, 0], sigma[2, 1], -sigma[0, 0] - sigma[1, 1]]]
        )
sigma = gen3DTFdim3(sigma)
psi = gen3DTFdim3(psi)

# For the purpose of demonstration I include only one term 
# from the actual weak formulation of my problem.
a = ufl.dot(ufl.div(sigma), v) * ufl.dx 
print(dfx.fem.assemble_scalar(dfx.fem.form(a)))

```

results in the following error

```auto
Traceback (most recent call last):
  File "/home/sysadmin/py/fenicsxR13/demo_symTensor_unitCube.py", line 43, in <module>
    print(dfx.fem.assemble_scalar(dfx.fem.form(a)))
  File "/home/sysadmin/.local/lib/python3.10/site-packages/dolfinx/fem/forms.py", line 188, in form
    return _create_form(form)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/dolfinx/fem/forms.py", line 183, in _create_form
    return _form(form)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/dolfinx/fem/forms.py", line 141, in _form
    ufcx_form, module, code = jit.ffcx_jit(mesh.comm, form,
  File "/home/sysadmin/.local/lib/python3.10/site-packages/dolfinx/jit.py", line 56, in mpi_jit
    return local_jit(*args, **kwargs)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/dolfinx/jit.py", line 204, in ffcx_jit
    r = ffcx.codegeneration.jit.compile_forms([ufl_object], options=p_ffcx, **p_jit)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/codegeneration/jit.py", line 199, in compile_forms
    raise e
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/codegeneration/jit.py", line 190, in compile_forms
    impl = _compile_objects(decl, forms, form_names, module_name, p, cache_dir,
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/codegeneration/jit.py", line 260, in _compile_objects
    _, code_body = ffcx.compiler.compile_ufl_objects(ufl_objects, prefix=module_name, options=options)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/compiler.py", line 102, in compile_ufl_objects
    ir = compute_ir(analysis, object_names, prefix, options, visualise)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/ir/representation.py", line 197, in compute_ir
    irs = [_compute_integral_ir(fd, i, analysis.element_numbers, integral_names, finite_element_names,
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/ir/representation.py", line 197, in <listcomp>
    irs = [_compute_integral_ir(fd, i, analysis.element_numbers, integral_names, finite_element_names,
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/ir/representation.py", line 492, in _compute_integral_ir
    integral_ir = compute_integral_ir(itg_data.domain.ufl_cell(), itg_data.integral_type,
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/ir/integral.py", line 72, in compute_integral_ir
    S = build_scalar_graph(expression)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/ir/analysis/graph.py", line 80, in build_scalar_graph
    scalar_expressions = rebuild_with_scalar_subexpressions(G)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/ir/analysis/graph.py", line 125, in rebuild_with_scalar_subexpressions
    V_symbols = value_numberer.compute_symbols()
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/ir/analysis/valuenumbering.py", line 68, in compute_symbols
    symbol = f(expr)
  File "/home/sysadmin/.local/lib/python3.10/site-packages/ffcx/ir/analysis/valuenumbering.py", line 184, in _modified_terminal
    raise RuntimeError("Internal error in value numbering.")
RuntimeError: Internal error in value numbering.

```

I have read few posts in this forum regarding the erroneous behaviour of `ufl` when symmetric flag used. However, the error message mentioned in each post seems to be different from one another. Therefore, I’ve posted mine here.

I would like to know how can I fix this problem? Can I use any other version of `dolfinx`/`ufl`/`ffcx` combination to circumvent this error?

Thanks for reading my post!

---

<div class="post-metadata">

**Author:** ![francesco-ballarin](https://avatars.discourse-cdn.com/v4/letter/f/f05b48/32.png) [@francesco-ballarin](https://fenicsproject.discourse.group/u/francesco-ballarin)\
**Post date:** [December 9, 2023, 8:16am UTC](https://fenicsproject.discourse.group/t/use-of-symmetric-tensor-in-dolfinx-ufl-results-in-error/12992/2 "2023-12-09T08:16:01Z")

</div>

Since you are building from source anyways, can you try building `basix`, `ffcx` and `dolfinx` from the current `main` branch?

[Fix \_\_hash\_\_ and \_\_eq\_\_ for basix.ufl elements by conpierce8 · Pull Request #718 · FEniCS/basix · GitHub](https://github.com/FEniCS/basix/pull/718) might have fixed this (see also [[BUG]: Symmetric spaces broken · Issue #2750 · FEniCS/dolfinx · GitHub](https://github.com/FEniCS/dolfinx/issues/2750)). Even if it that does not actually fix this, you can use the updated code to open an issue at [Issues · FEniCS/basix · GitHub](https://github.com/FEniCS/basix/issues) (please do not open an issue with this code at your currently installed version, since you would immediately be asked to try with `main`, because we are aware that this part was changed very recently)

While updating you will need to replace `ufl.VectorElement`/`ufl.TensorElement` creation with `basix` elements, since former `ufl` ones have been removed from `main`. Something like

```auto
basix.ufl.element("Lagrange", mesh.basix_cell(), 1, shape=(mesh.geometry.dim,))
basix.ufl.element("Lagrange", mesh.basix_cell(), 1, shape=(mesh.geometry.dim,mesh.geometry.dim), symmetry=True_or_False)

```

should be the way to do it.

---

<div class="post-metadata">

**Author:** ![19ec94](https://avatars.discourse-cdn.com/v4/letter/1/b2d939/32.png) [@19ec94](https://fenicsproject.discourse.group/u/19ec94)\
**Post date:** [December 9, 2023, 8:09pm UTC](https://fenicsproject.discourse.group/t/use-of-symmetric-tensor-in-dolfinx-ufl-results-in-error/12992/3 "2023-12-09T20:09:53Z")

</div>

Thank you for your prompt reply!  
Following your recommendation, I built the `dolfinx`/`ffcx`/`basix`/`ufl` sources from each of their `main` repository.  
The version numbers are:  
`dolfinx`: 0.8.0.0  
`ffcx`: 0.8.0.dev0  
`basix`: 0.8.0.0  
`ufl`: 2023.3.0.dev0  
Thanks to your suggestion I modified the code. When I run the following code

```auto
import dolfinx as dfx
from mpi4py import MPI
import ufl as ufl
import basix as basix
# create mesh
mesh_dfx = dfx.mesh.create_unit_cube(MPI.COMM_WORLD, 8, 8, 8,
        dfx.mesh.CellType.tetrahedron) 
# define two finite elments: a vector and a symmetric tensor
u_elem = basix.ufl.element("Lagrange", mesh_dfx.basix_cell(), 1,
        shape=(mesh_dfx.geometry.dim,))
sigma_elem = basix.ufl.element("Lagrange", mesh_dfx.basix_cell(),1, 
        shape=(mesh_dfx.geometry.dim, mesh_dfx.geometry.dim), 
        symmetry=True)
# define mixed finite element function space
mxd_fspace = dfx.fem.functionspace(mesh_dfx,
        basix.ufl.mixed_element([u_elem, sigma_elem]))
# define trial and test functions
(u, sigma) = ufl.TrialFunctions(mxd_fspace)
(v, psi ) = ufl.TestFunctions(mxd_fspace)
# define a form expression
a = ufl.dot(ufl.div(sigma), v) * ufl.dx 
# cast it explicitly to form type
compiled_form = dfx.fem.form(a)
# assemble --> NOTE: the following line produces error
print(dfx.fem.assemble_scalar(compiled_form))

```

, it produces the following error:

```auto
[0]PETSC ERROR: ------------------------------------------------------------------------
[0]PETSC ERROR: Caught signal number 11 SEGV: Segmentation Violation, probably memory access out of range
[0]PETSC ERROR: Try option -start_in_debugger or -on_error_attach_debugger
[0]PETSC ERROR: or see https://petsc.org/release/faq/#valgrind and https://petsc.org/release/faq/
[0]PETSC ERROR: --------------------- Stack Frames ------------------------------------
[0]PETSC ERROR: No error traceback is available, the problem could be in the main program. 
--------------------------------------------------------------------------
MPI_ABORT was invoked on rank 0 in communicator MPI_COMM_WORLD
with errorcode 59.

NOTE: invoking MPI_ABORT causes Open MPI to kill all MPI processes.
You may or may not see output from other processes, depending on
exactly when Open MPI kills them.
--------------------------------------------------------------------------

```

It seems to me that because of the new modifications there is something going on under  
the hood which I am not able to understand. Could you please verify if the above code snippet compiles correctly for you?

---

<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:** [December 9, 2023, 8:27pm UTC](https://fenicsproject.discourse.group/t/use-of-symmetric-tensor-in-dolfinx-ufl-results-in-error/12992/4 "2023-12-09T20:27:41Z")

</div>

> [@19ec94](#):
>
> ```auto
> (u, sigma) = ufl.TrialFunctions(mxd_fspace)
> (v, psi ) = ufl.TestFunctions(mxd_fspace)
> # define a form expression
> a = ufl.dot(ufl.div(sigma), v) * ufl.dx 
> # cast it explicitly to form type
> compiled_form = dfx.fem.form(a)
> # assemble --> NOTE: the following line produces error
> print(dfx.fem.assemble_scalar(compiled_form))
> 
> ```

This does not make sense as a command.  
The line that produces an error tries to assemble a matrix into a single scalar value.

Could you try with  
`dolfinx.fem.petsc.assemble_matrix(compiled_form)`?

---

<div class="post-metadata">

**Author:** ![19ec94](https://avatars.discourse-cdn.com/v4/letter/1/b2d939/32.png) [@19ec94](https://fenicsproject.discourse.group/u/19ec94)\
**Post date:** [December 9, 2023, 9:42pm UTC](https://fenicsproject.discourse.group/t/use-of-symmetric-tensor-in-dolfinx-ufl-results-in-error/12992/5 "2023-12-09T21:42:36Z")

</div>

Hi Dokken,  
Thanks for pointing out the error. Indeed, with `dolfinx.fem.petsc.assemble_matrix()` the code does run without error.