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[Garth Wells <question123984@xxxxxxxxxxxxxxxxxxxxx>]

Question #123984 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/123984

Garth Wells proposed the following answer:

On 04/09/10 15:20, Kristian Ølgaard wrote:
> 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.
>

And bear in mind that DOLFIN doesn't provide any rank 3 tensors that can 
be assembled into. You would have to provide this yourself.

Garth


> 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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