Error: Transposed is only defined for rank 2 tensors

variational formulation
1

I am getting the following error at the line where a is defined:
ufl.log.UFLException: Transposed is only defined for rank 2 tensors.

My code is below, please assist if you can, thank you!

""" Boundary Conditions (Part 1) """
class PeriodicBoundary_x(SubDomain):
	def inside(self, x, on_boundary):
		return x[0] == 0 and on_boundary
	def map ( self, x, y ):
		y[0] = x[0] - Le
		y[1] = x[1]
pbc_x = PeriodicBoundary_x()

""" Define Mesh and Function Spaces """
domain = Rectangle(Point(0.0, 0.0), Point(Le, He))
mesh = generate_mesh(domain, 16.0) 
V = FiniteElement("CG", mesh.ufl_cell(), 2)
Q = FiniteElement("CG", mesh.ufl_cell(), 1)
W_elem = MixedElement([V, Q])
W = FunctionSpace(mesh, W_elem, constrained_domain = pbc_x)

""" Boundary Conditions (Part 2) """
def LowerBoundary(x, on_boundary):
	return x[1] < DOLFIN_EPS and on_boundary
SlipRate = Expression("(3.0 + 1.7*sin(2.0*pi*x[0]/L))", degree = 1, L = 31557686.4)
bcD = DirichletBC(W.sub(0), SlipRate, LowerBoundary)

""" Define Variational Problem """
(v_i, q_i) = TestFunctions(W)
(u_i, p_i) = TrialFunctions(W)
a = (0.5*mu*inner(grad(v_i) + grad(v_i).T, grad(u_i) + grad(u_i).T) - div(v_i)*pi + q_i*div(u_i))*dx
L = inner(v_i, G)*dx
2

As V is a scalar element, grad(u) is a vector, and is does not make sense to transpose the vector, as you cannot add a (2,) vector with a (,2) vector

1 Like
3

How would I go about fixing this issue as I am still confused, would I change the rank to be 1 instead of 2?

4

You Need to write out your variational form for me to be of any further help.

5

variational_form
variational_form1194×153 12 KB

This is the variational form, let me know if you may need anything else for further assistance.

1 Like
6

So here \mathbf{u} is a vector, therefore

has to be replaced by

V = VectorElement("CG", mesh.ufl_cell(), 2)
1 Like
7

Thank you, this has fixed my issue, but now I am getting another error with the solve portion of the code as seen below.

U = Function(W)
solve(a==L, U, bcD)
(u, p) = U.split()

Traceback (most recent call last):
File “main.py”, line 46, in
solve(a==L, U, bcD)
File “/usr/lib/petsc/lib/python3/dist-packages/dolfin/fem/solving.py”, line 233, in solve
_solve_varproblem(*args, **kwargs)
File “/usr/lib/petsc/lib/python3/dist-packages/dolfin/fem/solving.py”, line 268, in _solve_varproblem
problem = LinearVariationalProblem(eq.lhs, eq.rhs, u, bcs,
File “/usr/lib/petsc/lib/python3/dist-packages/dolfin/fem/problem.py”, line 59, in init
a = Form(a, form_compiler_parameters=form_compiler_parameters)
File “/usr/lib/petsc/lib/python3/dist-packages/dolfin/fem/form.py”, line 43, in init
ufc_form = ffc_jit(form, form_compiler_parameters=form_compiler_parameters,
File “/usr/lib/petsc/lib/python3/dist-packages/dolfin/jit/jit.py”, line 50, in mpi_jit
return local_jit(*args, **kwargs)
File “/usr/lib/petsc/lib/python3/dist-packages/dolfin/jit/jit.py”, line 100, in ffc_jit
return ffc.jit(ufl_form, parameters=p)
File “/usr/lib/python3/dist-packages/ffc/jitcompiler.py”, line 217, in jit
module = jit_build(ufl_object, module_name, parameters)
File “/usr/lib/python3/dist-packages/ffc/jitcompiler.py”, line 130, in jit_build
module, signature = dijitso.jit(jitable=ufl_object,
File “/usr/lib/python3/dist-packages/dijitso/jit.py”, line 165, in jit
header, source, dependencies = generate(jitable, name, signature, params[“generator”])
File “/usr/lib/python3/dist-packages/ffc/jitcompiler.py”, line 65, in jit_generate
code_h, code_c, dependent_ufl_objects = compile_object(ufl_object,
File “/usr/lib/python3/dist-packages/ffc/compiler.py”, line 142, in compile_form
return compile_ufl_objects(forms, “form”, object_names,
File “/usr/lib/python3/dist-packages/ffc/compiler.py”, line 185, in compile_ufl_objects
analysis = analyze_ufl_objects(ufl_objects, kind, parameters)
File “/usr/lib/python3/dist-packages/ffc/analysis.py”, line 89, in analyze_ufl_objects
form_datas = tuple(_analyze_form(form, parameters)
File “/usr/lib/python3/dist-packages/ffc/analysis.py”, line 89, in
form_datas = tuple(_analyze_form(form, parameters)
File “/usr/lib/python3/dist-packages/ffc/analysis.py”, line 169, in _analyze_form
form_data = compute_form_data(form,
File “/usr/lib/python3/dist-packages/ufl/algorithms/compute_form_data.py”, line 407, in compute_form_data
check_form_arity(preprocessed_form, self.original_form.arguments(), complex_mode) # Currently testing how fast this is
File “/usr/lib/python3/dist-packages/ufl/algorithms/check_arities.py”, line 177, in check_form_arity
check_integrand_arity(itg.integrand(), arguments, complex_mode)
File “/usr/lib/python3/dist-packages/ufl/algorithms/check_arities.py”, line 159, in check_integrand_arity
arg_tuples = map_expr_dag(rules, expr, compress=False)
File “/usr/lib/python3/dist-packages/ufl/corealg/map_dag.py”, line 26, in map_expr_dag
result, = map_expr_dags(function, [expression], compress=compress)
File “/usr/lib/python3/dist-packages/ufl/corealg/map_dag.py”, line 75, in map_expr_dags
r = handlers[v.ufl_typecode](v, *[vcache[u] for u in v.ufl_operands])
File “/usr/lib/python3/dist-packages/ufl/algorithms/check_arities.py”, line 48, in sum
raise ArityMismatch(“Adding expressions with non-matching form arguments {0} vs {1}.”.format(_afmt(a), _afmt(b)))
ufl.algorithms.check_arities.ArityMismatch: Adding expressions with non-matching form arguments (‘v_0’,) vs (‘v_0’, ‘v_1’).

8

Please note that the code you have supplied is not complete, and can not reproduce your error message. For further questions, I would recommend you to follow the examples posted at: Read before posting: How do I get my question answered? - #4 by nate
and make sure your code reproduces your error message.

For this particular problem, the culprit is most likely

as I think you meant to use p_i and not pi