Index notation on trial function?

1

Hi there,

I know how to use ufl index notation, but I can’t make it work on trial/test functions.

Any idea on how to make the following mwe run?

from dolfin import *

class Right(SubDomain):
    def inside(self,x, on_boundary):
        return x[0] > 1-DOLFIN_EPS and on_boundary

class Left(SubDomain):
    def inside(self,x, on_boundary):
        return x[0] < DOLFIN_EPS and on_boundary

mesh = UnitSquareMesh(10,10)
V1   = FunctionSpace(mesh, 'CG', 2)
V2   = TensorFunctionSpace(mesh, 'CG', 2, (2,2))

u  = TrialFunction(V1)
v  = TestFunction(V1)

J  = Expression((('x[0]', '0'), ('0', 'x[1]')), degree = 2)
J  = interpolate(J, V2)

g1 = Constant(0)
g2 = Constant(1)
g3 = Constant(2)

a = inner(grad(J)*grad(u), grad(v))*dx
L = g1*v*dx

left = Left()
right = Right()

bc1 = DirichletBC(V1, g1, left)
bc2 = DirichletBC(V1, g2, right)
bc = [bc1, bc2]

u = Function(V1)

solve(a == L, u, bc)
2

Please state what you are trying to achieve. To me this does not really make sense, as you are trying to multiply the gradient of a tensor (3rd order tensor) with a vector. What shape should this become?

4

I want to mutiply a rank 3 tensor with a vector indeed.
But I just noticed that the mwe that I postet doesn’t make sense.
I can make a correct mwe, but what I basically have is a variational formulation, where my trial function - which is a vector - is mutiplied with a rank 3 tensor like this:

grad_J[i,j,k] * u[j]

The problem is that using ufl index notation doesn’t seem to be applicable to trialfunctions.

5

Please adjust your example to reflect what would actually like to do, and add the error message obtain with your indices approach.

6

As you have not adjust your example, this is my suggestion for you:

from ufl import indices
i, j, k = indices(3)
gradj = grad(J)[i,j,k]
gradu = grad(u)[j]
gJu = gradj*gradu

However, I can’t help you any further as your example does not make sense to me.

7

It seems that dot(grad(J), u) does the job, even for a rank 3 mutiplication with a vector.
But thank you anyways.

8

Based on what you have written above, I don’t think that dot(grad(J), grad(u)) will be gradJ[i,j,k]*gradu[j] but rather gradJ[i,j,k]*gradu[k]