P.S. Here is the equation. Sorry it did not attach last time around:
On Tuesday, September 28, 2021 at 6:24:38 PM UTC+1 Morris Jowas wrote:
> Hello everyone,
>
>
>
> I am solving the heat equation with the Laplacian expressed in terms of
> spatially varying thermal conductivities (k_x, k_y and k_z) as shown below:
>
> Can I please request your suggestions on how I may go about assigning the
> three thermal conductivities to every cell in the assemble loop? The
> examples I have seen in dealii provide sufficient guidance for a
> homogeneous problem where k is the same in all three directions per cell.
>
> For example, in the below loop I solve a version of the problem where
> there are two materials in the domain each with material properties k1 and
> k2 which I assign based on the cell number contained in the vector geomDef
> assuming that each cell is homogenous. However, if the cell is anisotropic,
> how can I set up the condition so that dealii knows the direction in which
> I am pointing so I can assign the correct thermal conductivity accordingly?
>
> Here is the code
>
> for (const auto& cell : dof_handler.active_cell_iterators())
>
> {
>
> cell_matrix = 0;
>
> cell_rhs = 0;
>
> fe_values.reinit(cell);
>
> for (const unsigned int q_index :
> fe_values.quadrature_point_indices())
>
> for (const unsigned int i : fe_values.dof_indices())
>
> {
>
> for (const unsigned int j : fe_values.dof_indices())
>
>
>
> if (geomDef[curr_cell] == 1)
>
> {
>
> cell_matrix(i, j) +=
>
> (k1 * fe_values.shape_grad(i, q_index) * //
> assigning k1, thermal conductivity for material 1. Help needed here for
> allocating the thermal conductivity correctly
>
> fe_values.shape_grad(j, q_index) *
>
> fe_values.JxW(q_index));
>
> }
>
> else
>
> {
>
> cell_matrix(i, j) +=
>
> (k2 * fe_values.shape_grad(i, q_index) * //
> assigning k2, thermal conductivity for material 2
>
> fe_values.shape_grad(j, q_index) *
>
> fe_values.JxW(q_index));
>
> }
>
> }
>
> }
>
>
>
> Thank you in advance for your help with this.
>
>
>
> MJ
>
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