How to calculate a tensor at each quadrature point?

Question

Dear all,

I'm trying to calculate a tensor that depends on the values of another system's solution e.g.,

C = C ( d (x))

where d(x) is the solution from another system. I want to use this C tensor later in a generic inner product for a bilinear form.
I'm doing something like:

def C(d):
M11 = (1.0-d)(math.pow(2.0d+1.0,0.5))
M12 = 0.5(1.0-d)(2.0*d+1.0)
D = np.zeros((2,2,2,2))
D[0][0][0][0] = M11
D[1][1][1][1] = M11
D[0][1][0][1] = M12
D[0][1][1][0] = M12
D[1][0][0][1] = M12
D[1][0][1][0] = M12
return as_tensor(D)

I was wondering if anyone has an idea on how to do this?

Best,
Navid

hernan_mella · Answer 1 · Sep 29, 2015

In the .ufl code you can to do something like this:

FE = FiniteElement('CG', cell, 1,)
TE = TensorElement('CG', cell, 1, shape=(2,2,2,2))    

d = Coefficient(FE)
D = Coefficient(TE)

def C(d):
  M11 = (1.0 - d)*(pow(2.0*d + 1.0, 0.5))
  M12 = 0.5*(1.0 - d)*(2.0*d + 1.0)
  D[0, 0, 0, 0] = M11 
  D[1, 1, 1, 1] = M11
  D[0, 1, 0, 1] = M12
  D[0, 1, 1, 0] = M12
  D[1, 0, 0, 1] = M12
  D[1, 0, 1, 0] = M12
   return D

regards.

answered Sep 29, 2015 by hernan_mella FEniCS Expert (19,460 points)

I just realized of the date of your question :P

commented Sep 29, 2015 by hernan_mella FEniCS Expert (19,460 points)

Many thanks, learning new things is always good no matter when it happens.

commented Sep 29, 2015 by Navid Mozaffari FEniCS Novice (510 points)

How to calculate a tensor at each quadrature point?

1 Answer