void EigenvalueProblem<dim>::output_results() const
{
DataOut<dim> data_out;
data_out.attach_dof_handler(dof_handler);
for (size_t i = 0; i < eigenfunctions.size(); ++i) {
data_out.add_data_vector(eigenfunctions[i],
std::string("eigenfunction_") +
Utilities::int_to_string(i));
}
Vector<double> projected_potential (dof_handler.n_dofs());
{
FunctionParser<dim> potential;
potential.initialize (FunctionParser<dim>::default_variable_names (),
parameters.get ("Potential"),
typename FunctionParser<dim>::ConstMap());
VectorTools::interpolate (dof_handler, potential, projected_potential);
}
data_out.add_data_vector (projected_potential, "interpolated_potential");
data_out.build_patches ();
std::ofstream output ("eigenvectors.vtk");
data_out.write_vtk (output);
}
void EigenvalueProblem<dim>::assemble_system()
{
QGauss<dim> quadrature_formula(2);
FEValues<dim> fe_values(fe, quadrature_formula,
update_values | update_gradients |
update_quadrature_points | update_JxW_values);
const size_t dofs_per_cell = fe.dofs_per_cell;
const size_t n_q_points = quadrature_formula.size();
FullMatrix<double> cell_stiffness_matrix (dofs_per_cell, dofs_per_cell);
FullMatrix<double> cell_mass_matrix (dofs_per_cell, dofs_per_cell);
std::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);
FunctionParser<dim> potential;
potential.initialize(FunctionParser<dim>::default_variable_names(),
parameters.get("Potential"),
typename FunctionParser<dim>::ConstMap());
std::vector<double> potential_values(n_q_points);
for (auto cell : dof_handler.active_cell_iterators()) {
fe_values.reinit(cell);
cell_stiffness_matrix = 0;
cell_mass_matrix = 0;
potential.value_list(fe_values.get_quadrature_points(),
potential_values);
for (size_t q_point = 0; q_point < n_q_points; ++q_point) {
for (size_t i = 0; i < dofs_per_cell; ++i) {
for (size_t j = 0; j < dofs_per_cell; ++j) {
cell_stiffness_matrix(i, j) += (fe_values.shape_grad(i, q_point) *
fe_values.shape_grad(j, q_point)
+
potential_values[q_point] *
fe_values.shape_value(i, q_point) *
fe_values.shape_value(j, q_point)
) * fe_values.JxW(q_point);
cell_mass_matrix(i, j) += (fe_values.shape_value(i, q_point) *
fe_values.shape_value(j, q_point)
) * fe_values.JxW(q_point);
}
}
}
cell->get_dof_indices(local_dof_indices);
constraints.distribute_local_to_global(cell_stiffness_matrix,
local_dof_indices,
stiffness_matrix);
constraints.distribute_local_to_global(cell_mass_matrix,
local_dof_indices,
mass_matrix);
}
stiffness_matrix.compress(VectorOperation::add);
mass_matrix.compress(VectorOperation::add);
double min_spurious_eigenvalue = std::numeric_limits<double>::max(),
max_spurious_eigenvalue = -std::numeric_limits<double>::max();
for (size_t i = 0; i < dof_handler.n_dofs(); ++i) {
if (constraints.is_constrained(i)) {
const double ev = stiffness_matrix(i, i) / mass_matrix(i, i);
min_spurious_eigenvalue = std::min (min_spurious_eigenvalue, ev);
max_spurious_eigenvalue = std::max (max_spurious_eigenvalue, ev);
}
}
std::cout << " Spurious eigenvalues are all in the interval "
<< "[" << min_spurious_eigenvalue << "," << max_spurious_eigenvalue << "]"
<< std::endl;
}
