I am trying to implement example 26 using Newton's method and Sacado, in
order to get a better feeling for the method. As mentioned before, I had
problems with retaining the old solution when remeshing. Thus I rewrote my
remeshing sequence as
template <int dim>
void HeatEquation<dim>::refine_mesh ()
{
Vector<float> estimated_error_per_cell (triangulation.n_active_cells
());
KellyErrorEstimator<dim>::estimate (dof_handler,
QGauss<dim-1>(fe.degree+1),
typename FunctionMap<dim>::type
(),
present_solution,
estimated_error_per_cell);
GridRefinement::refine_and_coarsen_fixed_number (triangulation,
estimated_error_per_cell,
0.6, 0.4);
if (triangulation.n_levels() > max_grid_level)
for (auto cell = triangulation.begin_active(max_grid_level);
cell != triangulation.end(); ++cell)
cell->clear_refine_flag ();
for (auto cell = triangulation.begin_active(min_grid_level); cell !=
triangulation.end_active(min_grid_level); ++cell)
cell->clear_coarsen_flag ();
triangulation.prepare_coarsening_and_refinement ();
SolutionTransfer<dim> solution_transfer(dof_handler);
solution_transfer.prepare_for_coarsening_and_refinement(
present_solution);
triangulation.execute_coarsening_and_refinement();
dof_handler.distribute_dofs(fe);
Vector<double> tmp(dof_handler.n_dofs());
solution_transfer.interpolate(present_solution, tmp);
present_solution = tmp;
solution_transfer.interpolate(old_solution, tmp);
old_solution = tmp;
set_boundary_values ();
constraint_matrix.clear();
DoFTools::make_hanging_node_constraints(dof_handler,
constraint_matrix);
constraint_matrix.close();
constraint_matrix.distribute (present_solution);
constraint_matrix.distribute(old_solution);
setup_system (false);
}
and then I use the same grid both for the new and the old solution for the
fe_values.grad_values(). Is that approach correct? I assume it still
introduces some errors, but I am not sure if they are responsible for my
(wrong) results:
It appears as if the heat is never spreading out, but also the maximum
temperature is way below the example results, even though I used exactly
the same boundary/Input values.
<https://lh3.googleusercontent.com/-859t-dJsZwc/WaUo7F_lmKI/AAAAAAAACSs/OsEfEFuTjGU8QGM8k4Z30QjVxfSc8IaFQCLcBGAs/s1600/heat_sacado.gif>
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