Metin,
I understand that the components are in space (x/y/z),
> and (*shape_gradient_ptr++)[d] would be derivative of phi in each
> direction; is that correct?
>
Yes, that is the derivative of the dth component in direction d.
>
> (compared to vectors) the implementation of divergence function for the
> tensors is as following;
>
> *if* (snc != -1)
>
> {
>
> *const* *unsigned* *int* comp =
>
>
> shape_function_data[shape_function].single_nonzero_component_index;
>
>
> *const* dealii::Tensor < 1, *spacedim*> *shape_gradient_ptr
> =
>
> &shape_gradients[snc][0];
>
>
> *const* TableIndices<2> indices = dealii::Tensor<2,
> *spacedim*>::unrolled_to_component_indices(comp);
>
> *const* *unsigned* *int* ii = indices[0];
>
> *const* *unsigned* *int* jj = indices[1];
>
>
> *for* (*unsigned* *int* q_point = 0; q_point <
> n_quadrature_points;
>
> ++q_point, ++shape_gradient_ptr)
>
> {
>
> divergences[q_point][jj] += value *
> (*shape_gradient_ptr)[ii];
>
> }
>
> }
>
This is similar to the previous one. Note that the ith component of the
divergence of a rank-2-tensor is defined as sum_i \partial_i T_{ij}.
This is what is implemented for the general (non-symmetric) Tensor class.
You have to compare this to the Vector implementation for primitive shape
functions.
Basically, ii corresponds to the first index of the non-zero component and
jj corresponds to the second index of the non-zero component.
We figure the correct component of the divergence add add the appropriate
derivative to it.
For a SymmetricTensor, only T_{ij} for i\leq j is stored.Therefore, we need
to have the line
if (ii != jj)
divergences[q_point][jj] += value * (*shape_gradient_ptr)[ii];
additionally to account for the contribution of T_{ji} add the same time.
> There is only the "snc != 1" case, and it seems that the component now
> means the tensor components and not the directions in space. Is this
> function (for tensors) not yet implemented? or is it sth related to
> non-primitive shape functions (I would appreciate if you could comment on
> this as well)?
>
This is only implemented for primitive shape functions.
Best,
Daniel
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