Dear Benhour,
I'm afraid that your question falls out of the scope of those suitable for
the forum (please see this post
<https://groups.google.com/forum/#!topic/dealii/GRZMUTLIm2I>). It is too
vague and abstract, and to be honest you could spend some time constructing
a small case to work this out for yourself.
What I will say is that (to the best of my knowledge) this expression will
differ if you're working in 3d or in 2d (i.e. axisymmetric). Your grid is
constructed in a Cartesian basis, so the gradients returned by the deal.II
functions will be those taken with respect to this basis. You therefore
need to account for this. In 2-d, you could (I think) directly interpret
the radial and e_{1} directions as being aligned with one another, and the
same for the e_{2} and z-direction. In 3-d this no longer holds, and you
need to compute the equivalent expression for the radial (and azimuthal)
derivatives with respect to the Cartesian directions; i.e. you should apply
the chain rule.
Regards,
J-P
On Saturday, September 3, 2016 at 1:56:32 AM UTC+2,
benhour.amiria...@gmail.com wrote:
>
> Dear All,
> I have a question. I want to define a tensor with components like the
> below expression, where eta is a scalar function in cylindrical coordinate
> system. I defined this component in dealii like this:
> FE_Q<dim> fe
> const QGauss<dim> quadrature_formula(3)
> FEValues<dim> fe_values (fe, quadrature_formula,
> update_gradients|
> update_quadrature_points);
> const unsigned int n_q_points =
> quadrature_formula.size();
> std::vector< Tensor<1, dim> >
> eta_gradients(n_q_points);
> std::vector< Tensor<2, dim> >
> eta_hessians(n_q_points);
> fe_values.get_function_gradients(eta_gradients);
> fe_values.get_function_hessians(eta_hessians);
> for(unsigned int q_point = 0; q_point <
> n_q_points; ++q_point)
>
> const double comp11 = std::pow(eta, 2)*
> std::pow((1-eta), 2)+(eta_hessians[q_point][0] +
> eta_hessians[q_point][1]) - eta_gradients[q_point][0] *
> eta_gradients[q_point][0];
> I do really appreciate it if you let me know whether this part of code for
> the following component is true or not.
>
> .
> <https://lh3.googleusercontent.com/-ki-xrwAfxYc/V8oOoAsTsmI/AAAAAAAAACo/uWArz5VCC1UsAWC4s9EcvnKVzMzp2P_5ACLcB/s1600/2.PNG>
>
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