As far as I know the gradient is an opperation on scalar fields
giving a vector, while the jacobian is on vector fields giving a
tensor. There's no assumption on the dimension of the vector (which
you have with the divergence). I then guess page 42 of ffc
documentation must be corrected, since there is stated that grad()
applied to vectors gives the jacobian matrix.
Alessio
________________________________________ Da: Garth N. Wells
[gnw20@xxxxxxxxx] Inviato: venerdì 28 novembre 2008 10.25 A: Alessio
Quaglino Cc: ffc-dev@xxxxxxxxxx Oggetto: Re: [FFC-dev] R: bug with
triangles?
Alessio Quaglino wrote:
Thank you for the reply. So you mean that such limitation in
present only for triangles, while for tets you can take gradients
of n-vectors?
It's not a limitation and it applies to all spatial dimensions. The
gradient is an operator that is only defined for tensors of
dimension n in a space of dimension n. The gradient of a function
with three components in two dimensions is not defined.
Then I don't understand, also because the workaround I
used in the code I posted treats grad(phi) and grad(b) as 3x2
matrices and converts them to vectors, and I don't get any "index
out of range" error.
We should add a test that would give an error for your second piece
of code because the gradient isn't defined for the type of function
that it's being given.
You can still take derivatives of your function with three
components, but you'll have to to it using .dx(0), etc or by defining
you own grad-like operator.
Garth
Alessio
________________________________________ Da: Garth N. Wells
[gnw20@xxxxxxxxx] Inviato: venerdì 28 novembre 2008 9.41 A: Alessio
Quaglino Cc: ffc-dev@xxxxxxxxxx Oggetto: Re: [FFC-dev] bug with
triangles?
Alessio Quaglino wrote:
I have the following code:
q = 2 EL1 = VectorElement("Lagrange", "triangle", q, 3) EL2 =
VectorElement("Lagrange", "triangle", q - 1, 3) Mh = EL1 + EL2
(psi, phi) = TestFunctions(Mh) (b, w) = TrialFunctions(Mh) k =
dot( grad(phi),grad(b) )
which gives me the error:
k = dot( grad(phi),grad(b) ) File
"/Library/Python/2.5/site-packages/ffc/compiler/language/operators.py",
line 102, in dot form = form + v[i][j]*w[i][j] IndexError: list
index out of range
I don't think I hven't understood what I supposed to give to ffc,
since if I define the following I get the desired behavior:
def vect(a): return [ a[i][j] for j in range(2) for i in range(3)
] gphi = vect( grad(phi) ) gb = vect( grad(b) ) k = dot( gphi,gb
)
Is there a problem in handling (n x d) matrices with 2D meshes?
The problem is that FFC doesn't know how to take the gradient of a
vector function of length 3 on a 2D element (triangle). The below
works
q = 2 EL1 = VectorElement("Lagrange", "triangle", q, 2) EL2 =
VectorElement("Lagrange", "triangle", q - 1, 2) Mh = EL1 + EL2
(psi, phi) = TestFunctions(Mh) (b, w) = TrialFunctions(Mh) k = dot(
grad(phi),grad(b) )
The '2' at the end of the element definition is redundant in this
case since FFC will default to 2 for 2D elements.
Garth
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