const Coefficient<dim> coefficient;
std::vector<double> coefficient_values (n_q_points);
- // Next a few things that are specific to
- // building the multigrid data structures
- // (since we only need them in the current
- // function, rather than also elsewhere, we
- // build them here instead of the
- // <code>setup_system</code>
- // function). Some of the following may be
- // a bit obscure if you're not familiar
- // with the algorithm actually implemented
- // in deal.II to support multilevel
- // algorithms on adaptive meshes; if some
- // of the things below seem strange, take a
- // look at the @ref mg_paper.
+ // Next a few things that are specific to building the multigrid
+ // data structures (since we only need them in the current
+ // function, rather than also elsewhere, we build them here
+ // instead of the <code>setup_system</code> function). Some of the
+ // following may be a bit obscure if you're not familiar with the
+ // algorithm actually implemented in deal.II to support multilevel
+ // algorithms on adaptive meshes; if some of the things below seem
+ // strange, take a look at the @ref mg_paper.
//
- // Our first job is to identify those
- // degrees of freedom on each level that
- // are located on interfaces between
- // adaptively refined levels, and those
- // that lie on the interface but also on
- // the exterior boundary of the domain. As
- // in many other parts of the library, we
- // do this by using boolean masks,
- // i.e. vectors of booleans each element of
- // which indicates whether the
- // corresponding degree of freedom index is
- // an interface DoF or not. The <code>MGConstraints</code>
- // already computed the information for us
- // when we called initialize in <code>setup_system()</code>.
+ // Our first job is to identify those degrees of freedom on each
+ // level that are located on interfaces between adaptively refined
+ // levels, and those that lie on the interface but also on the
+ // exterior boundary of the domain. As in many other parts of the
+ // library, we do this by using boolean masks, i.e. vectors of
+ // booleans each element of which indicates whether the
+ // corresponding degree of freedom index is an interface DoF or
+ // not. The <code>MGConstraints</code> already computed the
+ // information for us when we called initialize in
+ // <code>setup_system()</code>.
std::vector<std::vector<bool> > interface_dofs
= mg_constrained_dofs.get_refinement_edge_indices ();
std::vector<std::vector<bool> > boundary_interface_dofs
= mg_constrained_dofs.get_refinement_edge_boundary_indices ();
- // The indices just identified will later
- // be used to decide where the assembled value
- // has to be added into on each level.
- // On the other hand,
- // we also have to impose zero boundary
- // conditions on the external boundary of
- // each level. But this the <code>MGConstraints</code>
- // knows it. So we simply ask for them by calling
- // <code>get_boundary_indices ()</code>.
- // The third step is to construct
- // constraints on all those degrees of
- // freedom: their value should be zero
- // after each application of the level
- // operators. To this end, we construct
- // ConstraintMatrix objects for each level,
- // and add to each of these constraints for
- // each degree of freedom. Due to the way
- // the ConstraintMatrix stores its data,
- // the function to add a constraint on a
- // single degree of freedom and force it to
- // be zero is called
- // Constraintmatrix::add_line(); doing so
- // for several degrees of freedom at once
- // can be done using
+ // The indices just identified will later be used to decide where
+ // the assembled value has to be added into on each level. On the
+ // other hand, we also have to impose zero boundary conditions on
+ // the external boundary of each level. But this the
+ // <code>MGConstraints</code> knows it. So we simply ask for them
+ // by calling <code>get_boundary_indices ()</code>. The third
+ // step is to construct constraints on all those degrees of
+ // freedom: their value should be zero after each application of
+ // the level operators. To this end, we construct ConstraintMatrix
+ // objects for each level, and add to each of these constraints
+ // for each degree of freedom. Due to the way the ConstraintMatrix
+ // stores its data, the function to add a constraint on a single
+ // degree of freedom and force it to be zero is called
+ // Constraintmatrix::add_line(); doing so for several degrees of
+ // freedom at once can be done using
// Constraintmatrix::add_lines():
std::vector<ConstraintMatrix> boundary_constraints (triangulation.n_global_levels());
std::vector<ConstraintMatrix> boundary_interface_constraints (triangulation.n_global_levels());
boundary_interface_constraints[level].close ();
}
- // Now that we're done with most of our
- // preliminaries, let's start the
- // integration loop. It looks mostly like
- // the loop in
- // <code>assemble_system</code>, with two
- // exceptions: (i) we don't need a right
- // hand side, and more significantly (ii) we
- // don't just loop over all active cells,
- // but in fact all cells, active or
- // not. Consequently, the correct iterator
- // to use is MGDoFHandler::cell_iterator
- // rather than
- // MGDoFHandler::active_cell_iterator. Let's
- // go about it:
+ // Now that we're done with most of our preliminaries, let's start
+ // the integration loop. It looks mostly like the loop in
+ // <code>assemble_system</code>, with two exceptions: (i) we don't
+ // need a right hand side, and more significantly (ii) we don't
+ // just loop over all active cells, but in fact all cells, active
+ // or not. Consequently, the correct iterator to use is
+ // MGDoFHandler::cell_iterator rather than
+ // MGDoFHandler::active_cell_iterator. Let's go about it:
typename DoFHandler<dim>::cell_iterator cell = mg_dof_handler.begin(),
endc = mg_dof_handler.end();
fe_values.shape_grad(j,q_point) *
fe_values.JxW(q_point));
- // The rest of the assembly is again
- // slightly different. This starts with
- // a gotcha that is easily forgotten:
- // The indices of global degrees of
- // freedom we want here are the ones
- // for current level, not for the
- // global matrix. We therefore need the
- // function
- // MGDoFAccessorLLget_mg_dof_indices,
- // not MGDoFAccessor::get_dof_indices
- // as used in the assembly of the
- // global system:
+ // The rest of the assembly is again slightly
+ // different. This starts with a gotcha that is easily
+ // forgotten: The indices of global degrees of freedom we
+ // want here are the ones for current level, not for the
+ // global matrix. We therefore need the function
+ // MGDoFAccessorLLget_mg_dof_indices, not
+ // MGDoFAccessor::get_dof_indices as used in the assembly of
+ // the global system:
cell->get_mg_dof_indices (local_dof_indices);
- // Next, we need to copy local
- // contributions into the level
- // objects. We can do this in the same
- // way as in the global assembly, using
- // a constraint object that takes care
- // of constrained degrees (which here
- // are only boundary nodes, as the
- // individual levels have no hanging
- // node constraints). Note that the
- // <code>boundary_constraints</code>
- // object makes sure that the level
- // matrices contains no contributions
- // from degrees of freedom at the
- // interface between cells of different
+ // Next, we need to copy local contributions into the level
+ // objects. We can do this in the same way as in the global
+ // assembly, using a constraint object that takes care of
+ // constrained degrees (which here are only boundary nodes,
+ // as the individual levels have no hanging node
+ // constraints). Note that the
+ // <code>boundary_constraints</code> object makes sure that
+ // the level matrices contains no contributions from degrees
+ // of freedom at the interface between cells of different
// refinement level.
boundary_constraints[cell->level()]
.distribute_local_to_global (cell_matrix,
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