Trying to resolve an error with expressions of different shapes

1

Hi,
I’m pretty new to Fenics and have run into this error for the first time.

Exception has occurred: UFLException
Can’t add expressions with different shapes.
File “/home/ucarsten/Desktop/PG_0_1_5_G.py”, line 126, in
rhoJ= ((2*rho_2 )/ epsi)- dot(E,grad(grad(rho_2)))

As this seems to be an error that should be quiet common I seem to have been lucky till now.

As this is for an university assignment I wont post the full code (besides it being quiet long at the moment). But what I have been trying to do is calculate some related Differential equations over a 2D mesh. The formula I got problems with is the Jacobian of this
aC = (dot((rho_2**2) / epsi, u) - dot(dot(E, grad(rho_2)), u))*dx
which I’m trying to feed into a non-linear solver

epsi=Constant(1)

V = VectorFunctionSpace(mesh, ‘P’, 1)
Q = FunctionSpace(mesh, ‘Lagrange’, 1)

E = Function(V)
E.assign(project(grad(phi), V))
phi being the result of a previous Differential equation over the same mesh

rho_2=TrialFunction(Q)
u=TestFunction(Q)
rho_2=Function(Q)

aC = (dot((rho_2**2) / epsi, u) - dot(dot(E, grad(rho_2)), u))*dx

rhoJ=((2*rho_2 )/ epsi)- dot(E,grad(grad(rho_2)))

rhoproblem = NonlinearVariationalProblem(aC, rho_2, bcd,rhoJ)

rhosolver = NonlinearVariationalSolver(rhoproblem)

So since the normal solve function can work with aC just not calculate it the problem itself seems to be a dimension mismatch in the jacobian rhoJ and the error underlines the / or the epsi depending if there is a space or between them or not. If this were Matlab I would take a look of the dimensions of the variables and have a play around with that but in Fenics if I print them I get these

(2*rho_2 )/epsi =
2 * f_62 / f_0
dot(E,grad(grad(rho_2))) =
(f_43) . (grad(grad(f_62)))
and to be honest that doesn’t tell me much

I think the problem is either that it isn’t sure how to divide the Trialfunction rho_2 through a Constant or it cant subtract a function x function from a function
but after searching the documentation and googling a lot I don’t think I have gotten any closer to the solution…

any ideas?

2

It’s difficult to decipher how you derived the Jacobian but rhoJ doesn’t look dimensionally correct. Consider this post.

With the following code:

from fenics import *
mesh  = UnitSquareMesh(20, 20)
epsi = Constant(20)

V = VectorFunctionSpace(mesh, 'P', 1)
Q = FunctionSpace(mesh, 'Lagrange', 1)

E = Function(V)

rho_2 = TrialFunction(Q)
u = TestFunction(Q)
rho_2 = Function(Q)

b = ((2*rho_2 )/ epsi)*dx
b_compiled = fem.form.Form(b)
print(b_compiled.rank())

a = dot(E,grad(grad(rho_2)))*dx
a_compiled = fem.form.Form(a)
print(a_compiled.rank())

The first integrand returns a rank of 0 while the second:

Can only integrate scalar expressions. The integrand is a tensor expression with value shape (2,) and free indices with labels ().

The grad(grad(rho_2)) generates a tensor of rank 2 which can’t be summed with your other term of rank 0.

1 Like
3

Ok so I need to find a way adjust the rank of the first part to fit with the second.
Thanks for pointing out where the actual error is.

As for how I got to that Jacobian I simply derived aC for rho_2 by hand since that is the only variable in that formula.