Dear all,
I was wondering how to get the vector-valued gradient of solution vector.
If I have my solution f (a scalar field, from the Poisson equation for
example), I would like to get u = \nabla f. I started by adding this weak
form to the assemble_system, but I got stuck. This is what I got so for:
template <int dim>
void Step4<dim>::assemble_system ()
{
QGauss<dim> quadrature_formula(dof_handler.get_fe().degree+1);
FEValues<dim> fe_values (fe, quadrature_formula,
update_values | update_gradients |
update_quadrature_points | update_JxW_values);
std::vector<Tensor<1, dim>> fe_function_grad(quadrature_formula.size());
const unsigned int dofs_per_cell = fe.dofs_per_cell;
const unsigned int n_q_points = quadrature_formula.size();
FullMatrix<double> cell_matrix (dofs_per_cell, dofs_per_cell);
Vector<double> cell_rhs (dofs_per_cell);
std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);
typename DoFHandler<dim>::active_cell_iterator
cell = dof_handler.begin_active(),
endc = dof_handler.end();
for (; cell!=endc; ++cell)
{
fe_values.reinit (cell);
fe_values.get_function_gradients(solution,fe_function_grad);
cell_matrix = 0;
cell_rhs = 0;
for (unsigned int q_index=0; q_index<n_q_points; ++q_index)
for (unsigned int i=0; i<dofs_per_cell; ++i)
{
for (unsigned int j=0; j<dofs_per_cell; ++j)
cell_matrix(i,j) += ((fe_values.shape_value(i, q_index) *
fe_values.shape_value (j, q_index))*
fe_values.JxW (q_index));
cell_rhs(i) += ((fe_values.shape_value (i, q_index) *
fe_function_grad[q_index])*
fe_values.JxW (q_index));
}
cell->get_dof_indices (local_dof_indices);
constraints.distribute_local_to_global (cell_matrix,
cell_rhs,
local_dof_indices,
system_matrix,
system_rhs);
}
}
But this do not compile. The error is that fe_function_grad is a Tensor,
not a double. How do I fix this? How do I set up the right-hand side
from get_function_gradients?
Best,
Joel
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