Grad, Nabla_grad and other operators

On Mon, Feb 27, 2012 at 09:30:58PM -0000, Marcos Samudio wrote:
> New question #189030 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/189030
>
> Hello everyone,
>
> I am trying to formulate some variational forms, and I have doubts concerning the operators grad(), nabla_grad() and their use.
> What is the exact difference among them? I am working with both scalars and vectors.

No difference for scalars.

For vectors:

  (grad v)_ij = dv_i / dx_j
  (nabla_grad v)_ij = dv_j / dx_i

For matrices:

  (div v)_i = dv_ij / dx_j
  (nabla_div v)_j = dv_ij / dx_i

> Another concern is about the inner product of them, is it
> commutative?

The inner product is always symmetric, yes.

> Because I have seen, for instance, inner(grad(u), v) and inner(v,
> grad(u)) being used in similar circumstances.

Both are the same.

But notice that for the convective term of Navier-Stokes, you must
write it either

  dot(u, nabla_grad(u))

or

  dot(grad(u), u)

> I have checked the Python API and found nothing concerning these functions. Is there some resource I can access to somewhere else?

It's documented in the FEniCS book:

  http://www.fenicsproject.org/book/

--
Anders

> I have checked the Python API and found nothing concerning these functions.
> Is there some resource I can access to somewhere else?

May I suggest looking at the docstrings of the functions in question? Anders also gave some useful links.

In [1]: import ufl

In [2]: ufl.grad?
Type: function
Base Class: <type 'function'>
String Form: <function grad at 0x21ca6e0>
Namespace: Interactive
File: /home/martinal/opt/fenics/dorsal-stable/lib/python2.7/site-packages/ufl/operators.py
Definition: ufl.grad(f)
Docstring:
    UFL operator: Take the gradient of f.

    This operator follows the grad convention where

      grad(s)[i] = s.dx(j)

      grad(v)[i,j] = v[i].dx(j)

      grad(T)[:,i] = T[:].dx(i)

    for scalar expressions s, vector expressions v,
    and arbitrary rank tensor expressions T.

In [3]: ufl.nabla_grad?
Type: function
Base Class: <type 'function'>
String Form: <function nabla_grad at 0x21ca7d0>
Namespace: Interactive
File: /home/martinal/opt/fenics/dorsal-stable/lib/python2.7/site-packages/ufl/operators.py
Definition: ufl.nabla_grad(f)
Docstring:
    UFL operator: Take the gradient of f.

    This operator follows the grad convention where

      nabla_grad(s)[i] = s.dx(j)

      nabla_grad(v)[i,j] = v[j].dx(i)

      nabla_grad(T)[i,:] = T[:].dx(i)

    for scalar expressions s, vector expressions v,
    and arbitrary rank tensor expressions T.

Thank you both Anders and Martin, that is just what I was looking for.

Marcos

I've imported the ufl module but the command Martin suggested is not working. Typing ufl.grad? yields a syntax error in my python console. I can still access the docstring by __doc__, but this is much less extensive.

Is there something I'm missing??

Thanks again,

Marcos

Thanks Jack Hale, that solved my question.

Which version of ufl do you have?

Martin
Den 28. feb. 2012 16.00 skrev "Marcos Samudio" <
<email address hidden>> følgende:

> Question #189030 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/189030
>
> Status: Solved => Open
>
> Marcos Samudio is still having a problem:
> I've imported the ufl module but the command Martin suggested is not
> working. Typing ufl.grad? yields a syntax error in my python console. I
> can still access the docstring by __doc__, but this is much less
> extensive.
>
> Is there something I'm missing??
>
> Thanks again,
>
> Marcos
>
> --
> You received this question notification because you are a member of
> DOLFIN Team, which is an answer contact for DOLFIN.
>

My ufl version is 1.0.0.