TypeError: Do not know how to compute norm

1

Hello,

I want to compute the L2 norm of a strain tensor, but I received the error that FEniCS doesn’t know how to compute the norm, does anyone know how to resolve this?

from dolfin import *

def eps(u):return sym(grad(u))

mesh = RectangleMesh(Point(0.,0.),Point(1, 0.1),100,10)
P1 = VectorElement("CG", mesh.ufl_cell(), 2)
P2 = FiniteElement("CG", mesh.ufl_cell(), 1)
ME = FunctionSpace(mesh, MixedElement( [P1, P2] ))
Sol   = Function(ME)
u, P  = split(Sol)

quantity = eps(u)/norm(eps(u))

Traceback (most recent call last):
File “x.py”, line 12, in
quantity = norm(eps(u))
File “/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/dolfin/fem/norms.py”, line 151, in norm
raise TypeError(“Do not know how to compute norm of {}”.format(str(v)))
TypeError: Do not know how to compute norm of sym(grad([f_5[0], f_5[1]]))

2

I would use Function.split(deepcopy=True) instead:

u, P = Sol.split(True)
epsu = project(eps(u), TensorFunctionSpace(mesh, "DG", 1))
norm(epsu)
1 Like
3

I implemented your suggestion as follow:

from dolfin import *

def eps(u):return sym(grad(u))

mesh = RectangleMesh(Point(0.,0.),Point(1, 0.1),100,10)
P1 = VectorElement("CG", mesh.ufl_cell(), 2)
P2 = FiniteElement("CG", mesh.ufl_cell(), 1)
ME = FunctionSpace(mesh, MixedElement( [P1, P2] ))
Sol   = Function(ME)
u, P = Sol.split(True)
epsu = project(eps(u), TensorFunctionSpace(mesh, "DG", 1))
quantity = eps(u)/norm(epsu)

I received division by zero error, I don’t understand how the norm could be zero.

Division by zero!
Traceback (most recent call last):
  File "x.py", line 12, in <module>
    quantity = eps(u)/norm(epsu)
  File "/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/ufl/exproperators.py", line 255, in _div
    d = Division(self[ii], o)
  File "/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/ufl/algebra.py", line 236, in __new__
    error("Division by zero!")
  File "/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/ufl/log.py", line 172, in error
    raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: Division by zero!
4

Because the function u is identically zero. I don’t think you have solved for u looking at the snippet you posted. Since u is zero, eps(u) is zero, and therefore it’s norm

1 Like
5

I see, this code is just a minimum example, this quantity goes to my weak form and then solve for u and P, I can’t solve for u and P without this norm.

6

I see. You don’t need the norm then. Norm of a function u would be

\sqrt{\int_\Omega \sum_{i=1}^n u^2_i dx},

what you possibly want is simply the frobenius norm of the tensor \varepsilon_{ij} itself, which could then be

u, P = split(Sol)
epsu = eps(u)
norm_epsu  = sqrt(inner(epsu, epsu))

Is that what you want?

1 Like
7

I have tried this method previously, but when it gets to the weak form, I get the following error with the following code:

from dolfin import *

def eps(u):return sym(grad(u))

mesh = RectangleMesh(Point(0.,0.),Point(1, 0.1),100,10)
P1 = VectorElement("CG", mesh.ufl_cell(), 2)
P2 = FiniteElement("CG", mesh.ufl_cell(), 1)
ME = FunctionSpace(mesh, MixedElement( [P1, P2] ))
Sol   = Function(ME)
u, P = Sol.split(True)
quantity = eps(u)/sqrt(inner(eps(u), eps(u)))

someweakform = quantity * dx

Can only integrate scalar expressions. The integrand is a tensor expression with value shape (2, 2) and free indices with labels ().
Traceback (most recent call last):
  File "y.py", line 14, in <module>
    someweakform = quantity * dx
  File "/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/ufl/measure.py", line 418, in __rmul__
    error("Can only integrate scalar expressions. The integrand is a "
  File "/anaconda3/envs/fenicsproject/lib/python3.8/site-packages/ufl/log.py", line 172, in error
    raise self._exception_type(self._format_raw(*message))
ufl.log.UFLException: Can only integrate scalar expressions. The integrand is a tensor expression with value shape (2, 2) and free indices with labels ().
8

Your definition of someweakform looks incorrect to me. You should have scalar in there. Unless you can provide a more complete minimal example, it is difficult to help you.

1 Like