Dear prof. Bangerth,
Thanks. I have decided to implement my problem using the alternate
approach. However, I am now facing another issue, somewhat different from
the above but related to the Differentiation::SD class.
I am trying to compute the fourth-order elasticity tensor in the spatial
description using the formula Jc = 4*b*d2W_db_db*b (as in step-44). I am
using symbolic differentiation to compute all of the quantities in the
formula. Finally, I would like to have Jc of the type SymmetricTensor<4,
dim, NumberType>. This is where I run into a problem, which I explain below.
Since all the quantities in the rhs are SymmetricTensors, the operator*()
recognises the multiplication as a double contraction. However, we want it
to be a single contraction. So I must first convert 'b' to the type Tensor
and then apply the formula. This will lead to Jc being of the type Tensor
and not SymmetricTensor. Now there's a function symmetrize() to symmetrize
the type Tensor<2,dim>, but not for higher-order tensor types. One could
manually do this, but is there a better way? If not, would it be a good
idea to extend the symmetrize() function to Tensor<4,dim> since this type
is often used to represent many quantities, such as the elasticity tensors?
Thanks & regards
Vinayak
On Thursday, July 18, 2024 at 11:31:51 PM UTC+5:30 Wolfgang Bangerth wrote:
> On 7/18/24 00:22, Vinayak Vijay wrote:
> >
> > But here, it looks like the information about the composition of the
> functions
> > is not being stored somehow, maybe because it reduces the expressions to
> the
> > independent variables ("x" in this case). What change should I make to
> obtain
> > dg_dy? The independent variable remains "x" of course.
>
> I do not actually know enough about SD to help with this. The way I read
> the
> code is that you declare x to be an independent variable, whereas y is
> not.
> Intuitively, I would have expected the underlying library to raise an
> exception when you try to compute the derivative with regard to anything
> other
> than an independent variable.
>
> I think you'll have to find out what underlying SD library your example is
> using, and then read through the documentation of that library to see how
> to
> approach the issue. Alternatively, you can of course define a function
> g_of_x
> and another g_of_y, and depending on whether you want to compute the
> derivative with regard to x or y, you choose one or the other.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> www: http://www.math.colostate.edu/~bangerth/
>
>
>
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