Metin,
[...]
> For the vectors, the implementation (for the else case) is as following;
>
> *for* (*unsigned* *int* shape_function=0;
>
> shape_function<dofs_per_cell; ++shape_function)
>
> {
>
> *for* (*unsigned* *int* d=0; d<*spacedim*; ++d)
>
> *if*
> (shape_function_data[shape_function].is_nonzero_shape_function_component[d])
>
> {
>
> *const* dealii::Tensor<1,*spacedim*>
> *shape_gradient_ptr =
>
> &shape_gradients[shape_function_data[shape_function].
>
> row_index[d]][0];
>
> *for* (*unsigned* *int* q_point=0;
> q_point<n_quadrature_points; ++q_point)
>
> divergences[q_point] += value *
> (*shape_gradient_ptr++)[d];
>
> }
>
> }
>
> To me, it's not clear how the "value and shape_gradient_ptr" is used or in
> general how the (e.g.) u_x+v_y+w_z is done..
>
Let me just comment on this:
The divergence at a quadrature point is decomposed into a sum over all
shape functions and all of their components.
Since the value at a certain quadrature point q_p of a FE function u can be
written as u(q_p)=\sum_i u_i \phi_i(q_p),
it holds \nabla \cdot u(q_p) = \sum_i u_i \nabla \cdot \phi_i(q_p) = \sum_i
u_i \sum_c \partial_c \phi_i^c(q_p) where \phi_i^c is the cth component of
the ith shape function.
This is exactly what is done in the last line.
shape_gradient_ptr is initialized with the gradient of the dth component of
the considered shape_function at the first quadrature point.
By "*shape_gradient_ptr++", the gradient at this quadrature point is
returned and the pointer incremented such that it points to the
gradient at the next quadrature point.
Best,
Daniel
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