dolfin team mailing list archive

[Kristian Ølgaard <k.b.oelgaard@xxxxxxxxx>]

On 4 September 2010 15:32, Dominique
<question123984@xxxxxxxxxxxxxxxxxxxxx> wrote:
> Question #123984 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/123984
>
>    Status: Answered => Open
>
> Dominique is still having a problem:
> Johan,
>
> Thanks for the pointer. I had looked at the hyperelasticity demo. I
> should have called my post "Second derivatives of a weak form". In the
> hyperelasticity demo, the weak form is L(v,u)=0 and that is only
> differentiated once. What I'd like to do is differentiate the result
> once more. If I try
>
> d2u = TrialFunction(V)

Test- and TrialFunction are just helper functions for pretty syntax.
They will both return an instance of the class ufl.Argument, the
TestFunction with count = -2, TrialFunction with count = -1, when you
take the derivative w.r.t. yet another TrialFunction in your form I
suspect you end up with something TrialFunction*TrialFunction which is
not a linear in each basis function argument. So I think you need to
use Argument(element, 0), or something to get your rank 3 tensor.

Kristian

> da = derivative(a, u, d2u)
> print assemble(da, mesh=mesh)
>
> in the hyperelasticity demo, I get the same error as in my initial
> message.
>
> In my test example above, a(v,u)=0 is a weak form. Differentiating it
> once is OK, but what is the trick to compute second derivatives?
>
> If I'm missing your point, I'm sorry but could you please explain what
> is wrong in my example? I'm expecting to obtain a tensor of order 3, or
> a collection of matrices. I may not be going about it in the right way.
>
> Thanks!
> Dominique
>
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