Reference documentation for deal.II version GIT relicensing31gf283a0fc39 20240229 06:50:02+00:00

#include <deal.II/dofs/dof_handler.h>
Classes  
struct  ActiveFEIndexTransfer 
class  MGVertexDoFs 
Public Types  
using  cell_accessor = typename ActiveSelector::CellAccessor 
using  face_accessor = typename ActiveSelector::FaceAccessor 
using  line_iterator = typename ActiveSelector::line_iterator 
using  active_line_iterator = typename ActiveSelector::active_line_iterator 
using  quad_iterator = typename ActiveSelector::quad_iterator 
using  active_quad_iterator = typename ActiveSelector::active_quad_iterator 
using  hex_iterator = typename ActiveSelector::hex_iterator 
using  active_hex_iterator = typename ActiveSelector::active_hex_iterator 
using  active_cell_iterator = typename ActiveSelector::active_cell_iterator 
using  cell_iterator = typename ActiveSelector::cell_iterator 
using  face_iterator = typename ActiveSelector::face_iterator 
using  active_face_iterator = typename ActiveSelector::active_face_iterator 
using  level_cell_accessor = typename LevelSelector::CellAccessor 
using  level_face_accessor = typename LevelSelector::FaceAccessor 
using  level_cell_iterator = typename LevelSelector::cell_iterator 
using  level_face_iterator = typename LevelSelector::face_iterator 
using  active_fe_index_type = types::fe_index 
using  offset_type = unsigned int 
Public Member Functions  
DoFHandler ()  
DoFHandler (const Triangulation< dim, spacedim > &tria)  
DoFHandler (const DoFHandler &)=delete  
virtual  ~DoFHandler () override 
DoFHandler &  operator= (const DoFHandler &)=delete 
void  set_active_fe_indices (const std::vector< types::fe_index > &active_fe_indices) 
void  set_active_fe_indices (const std::vector< unsigned int > &active_fe_indices) 
std::vector< types::fe_index >  get_active_fe_indices () const 
void  get_active_fe_indices (std::vector< unsigned int > &active_fe_indices) const 
void  set_future_fe_indices (const std::vector< types::fe_index > &future_fe_indices) 
std::vector< types::fe_index >  get_future_fe_indices () const 
void  reinit (const Triangulation< dim, spacedim > &tria) 
void  distribute_dofs (const FiniteElement< dim, spacedim > &fe) 
void  distribute_dofs (const hp::FECollection< dim, spacedim > &fe) 
void  distribute_mg_dofs () 
bool  has_hp_capabilities () const 
bool  has_level_dofs () const 
bool  has_active_dofs () const 
void  initialize_local_block_info () 
void  clear () 
void  renumber_dofs (const std::vector< types::global_dof_index > &new_numbers) 
void  renumber_dofs (const unsigned int level, const std::vector< types::global_dof_index > &new_numbers) 
unsigned int  max_couplings_between_dofs () const 
unsigned int  max_couplings_between_boundary_dofs () const 
types::global_dof_index  n_dofs () const 
types::global_dof_index  n_dofs (const unsigned int level) const 
types::global_dof_index  n_boundary_dofs () const 
template<typename number >  
types::global_dof_index  n_boundary_dofs (const std::map< types::boundary_id, const Function< spacedim, number > * > &boundary_ids) const 
types::global_dof_index  n_boundary_dofs (const std::set< types::boundary_id > &boundary_ids) const 
const BlockInfo &  block_info () const 
types::global_dof_index  n_locally_owned_dofs () const 
const IndexSet &  locally_owned_dofs () const 
const IndexSet &  locally_owned_mg_dofs (const unsigned int level) const 
const FiniteElement< dim, spacedim > &  get_fe (const types::fe_index index=0) const 
const hp::FECollection< dim, spacedim > &  get_fe_collection () const 
const Triangulation< dim, spacedim > &  get_triangulation () const 
MPI_Comm  get_communicator () const 
void  prepare_for_serialization_of_active_fe_indices () 
void  deserialize_active_fe_indices () 
virtual std::size_t  memory_consumption () const 
template<class Archive >  
void  save (Archive &ar, const unsigned int version) const 
template<class Archive >  
void  load (Archive &ar, const unsigned int version) 
template<class Archive >  
void  serialize (Archive &archive, const unsigned int version) 
Cell iterator functions  
cell_iterator  begin (const unsigned int level=0) const 
active_cell_iterator  begin_active (const unsigned int level=0) const 
cell_iterator  end () const 
cell_iterator  end (const unsigned int level) const 
active_cell_iterator  end_active (const unsigned int level) const 
level_cell_iterator  begin_mg (const unsigned int level=0) const 
level_cell_iterator  end_mg (const unsigned int level) const 
level_cell_iterator  end_mg () const 
Cell iterator functions returning ranges of iterators  
IteratorRange< cell_iterator >  cell_iterators () const 
IteratorRange< active_cell_iterator >  active_cell_iterators () const 
IteratorRange< level_cell_iterator >  mg_cell_iterators () const 
IteratorRange< cell_iterator >  cell_iterators_on_level (const unsigned int level) const 
IteratorRange< active_cell_iterator >  active_cell_iterators_on_level (const unsigned int level) const 
IteratorRange< level_cell_iterator >  mg_cell_iterators_on_level (const unsigned int level) const 
Subscriptor functionality  
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.  
void  subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const 
void  unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const 
unsigned int  n_subscriptions () const 
template<typename StreamType >  
void  list_subscribers (StreamType &stream) const 
void  list_subscribers () const 
Static Public Member Functions  
static ::ExceptionBase &  ExcNoFESelected () 
static ::ExceptionBase &  ExcInvalidBoundaryIndicator () 
static ::ExceptionBase &  ExcInvalidLevel (int arg1) 
static ::ExceptionBase &  ExcNewNumbersNotConsecutive (types::global_dof_index arg1) 
static ::ExceptionBase &  ExcInvalidFEIndex (int arg1, int arg2) 
static ::ExceptionBase &  ExcOnlyAvailableWithHP () 
static ::ExceptionBase &  ExcNotImplementedWithHP () 
static ::ExceptionBase &  ExcInUse (int arg1, std::string arg2, std::string arg3) 
static ::ExceptionBase &  ExcNoSubscriber (std::string arg1, std::string arg2) 
Static Public Attributes  
static constexpr unsigned int  dimension = dim 
static constexpr unsigned int  space_dimension = spacedim 
static const types::fe_index  default_fe_index = 0 
static const unsigned int  invalid_fe_index 
static const types::fe_index  invalid_active_fe_index 
Private Types  
using  ActiveSelector = ::internal::DoFHandlerImplementation::Iterators< dim, spacedim, false > 
using  LevelSelector = ::internal::DoFHandlerImplementation::Iterators< dim, spacedim, true > 
using  map_value_type = decltype(counter_map)::value_type 
using  map_iterator = decltype(counter_map)::iterator 
Private Member Functions  
void  clear_space () 
void  clear_mg_space () 
void  setup_policy () 
void  connect_to_triangulation_signals () 
void  create_active_fe_table () 
void  update_active_fe_table () 
void  pre_transfer_action () 
void  post_transfer_action () 
void  pre_distributed_transfer_action () 
void  post_distributed_transfer_action () 
void  check_no_subscribers () const noexcept 
Static Private Attributes  
static std::mutex  mutex 
Friends  
template<int , int , int , bool >  
class  ::DoFAccessor 
template<int , int , bool >  
class  ::DoFCellAccessor 
struct  ::internal::DoFAccessorImplementation::Implementation 
struct  ::internal::DoFCellAccessorImplementation::Implementation 
struct  ::internal::DoFHandlerImplementation::Implementation 
struct  ::internal::hp::DoFHandlerImplementation::Implementation 
struct  ::internal::DoFHandlerImplementation::Policy::Implementation 
Given a triangulation and a description of a finite element, this class enumerates degrees of freedom on all vertices, edges, faces, and cells of the triangulation. As a result, it also provides a basis for a discrete space \(V_h\) whose elements are finite element functions defined on each cell by a FiniteElement object. This class satisfies the MeshType concept requirements.
It is first used in the step2 tutorial program.
For each 0d, 1d, 2d, and 3d subobject, this class stores a list of the indices of degrees of freedom defined on this DoFHandler. These indices refer to the unconstrained degrees of freedom, i.e. constrained degrees of freedom are numbered in the same way as unconstrained ones, and are only later eliminated. This leads to the fact that indices in global vectors and matrices also refer to all degrees of freedom and some kind of condensation is needed to restrict the systems of equations to the unconstrained degrees of freedom only. The actual layout of storage of the indices is described in the internal::DoFHandlerImplementation::DoFLevel class documentation.
The class offers iterators to traverse all cells, in much the same way as the Triangulation class does. Using the begin() and end() functions (and companions, like begin_active()), one can obtain iterators to walk over cells, and query the degree of freedom structures as well as the triangulation data. These iterators are built on top of those of the Triangulation class, but offer the additional information on degrees of freedom functionality compared to pure triangulation iterators. The order in which dof iterators are presented by the ++
and 
operators is the same as that for the corresponding iterators traversing the triangulation on which this DoFHandler is constructed.
The spacedim
parameter has to be used if one wants to solve problems on surfaces. If not specified, this parameter takes the default value =dim
implying that we want to solve problems in a domain whose dimension equals the dimension of the space in which it is embedded.
The degrees of freedom (‘dofs’) are distributed on the given triangulation by the function distribute_dofs(). It gets passed a finite element object describing how many degrees of freedom are located on vertices, lines, etc. It traverses the triangulation cell by cell and numbers the dofs of that cell if not yet numbered. For nonmultigrid algorithms, only active cells are considered. Active cells are defined to be those cells which have no children, i.e. they are the most refined ones.
Since the triangulation is traversed starting with the cells of the coarsest active level and going to more refined levels, the lowest numbers for dofs are given to the largest cells as well as their bounding lines and vertices, with the dofs of more refined cells getting higher numbers.
This numbering implies very large bandwidths of the resulting matrices and is thus vastly suboptimal for some solution algorithms. For this reason, the DoFRenumbering class offers several algorithms to reorder the dof numbering according. See there for a discussion of the implemented algorithms.
Upon construction, this class takes a reference to a triangulation object. In most cases, this will be a reference to an object of type Triangulation, i.e. the class that represents triangulations that entirely reside on a single processor. However, it can also be of type parallel::distributed::Triangulation (see, for example, step32, step40 and in particular the Parallel computing with multiple processors using distributed memory module) in which case the DoFHandler object will proceed to only manage degrees of freedom on locally owned and ghost cells. This process is entirely transparent to the used.
The DoFRenumbering class offers a number of renumbering schemes like the CuthillMcKee scheme. Basically, the function sets up an array in which for each degree of freedom we store the new index this DoF should have after renumbering. Using this array, the renumber_dofs() function of the present class is called, which actually performs the change from old DoF indices to the ones given in the array. In some cases, however, a user may want to compute their own renumbering order; in this case, one can allocate an array with one element per degree of freedom and fill it with the number that the respective degree of freedom shall be assigned. This number may, for example, be obtained by sorting the support points of the degrees of freedom in downwind direction. Then call the renumber_dofs(vector<types::global_dof_index>)
function with the array, which converts old into new degree of freedom indices.
Like many other classes in deal.II, the DoFHandler class can stream its contents to an archive using BOOST's serialization facilities. The data so stored can later be retrieved again from the archive to restore the contents of this object. This facility is frequently used to save the state of a program to disk for possible later resurrection, often in the context of checkpoint/restart strategies for long running computations or on computers that aren't very reliable (e.g. on very large clusters where individual nodes occasionally fail and then bring down an entire MPI job).
The model for doing so is similar for the DoFHandler class as it is for the Triangulation class (see the section in the general documentation of that class). In particular, the load() function does not exactly restore the same state as was stored previously using the save() function. Rather, the function assumes that you load data into a DoFHandler object that is already associated with a triangulation that has a content that matches the one that was used when the data was saved. Likewise, the load() function assumes that the current object is already associated with a finite element object that matches the one that was associated with it when data was saved; the latter can be achieved by calling DoFHandler::distribute_dofs() using the same kind of finite element before reloading data from the serialization archive.
Instead of only using one particular FiniteElement on all cells, this class also allows for an enumeration of degrees of freedom on different finite elements on every cells. To this end, one assigns an active_fe_index
to every cell that indicates which element within a collection of finite elements (represented by an object of type hp::FECollection) is the one that lives on this cell. The class then enumerates the degree of freedom associated with these finite elements on each cell of a triangulation and, if possible, identifies degrees of freedom at the interfaces of cells if they match. If neighboring cells have degrees of freedom along the common interface that do not immediate match (for example, if you have \(Q_2\) and \(Q_3\) elements meeting at a common face), then one needs to compute constraints to ensure that the resulting finite element space on the mesh remains conforming.
The whole process of working with objects of this type is explained in step27. Many of the algorithms this class implements are described in the hppaper.
The typical workflow for using this class is to create a mesh, assign an active FE index to every active cell, call DoFHandler::distribute_dofs(), and then assemble a linear system and solve a problem on this finite element space.
Active FE indices will be automatically transferred during mesh adaptation from the old to the new mesh. Future FE indices are meant to determine the active FE index after mesh adaptation, and are used to prepare data on the old mesh for the new one. If no future FE index is specified, the finite element prevails.
In particular, the following rules apply during adaptation:
Strategies for automatic hpadaptation which will set future FE indices based on criteria are available in the hp::Refinement namespace.
When this class is used with either a parallel::shared::Triangulation or a parallel::distributed::Triangulation, you can only set active FE indices on cells that are locally owned, using a call such as cell>set_active_fe_index(...)
. On the other hand, setting the active FE index on ghost or artificial cells is not allowed.
Ghost cells do acquire the information what element is active on them, however: whenever you call DoFHandler::distribute_dofs(), all processors that participate in the parallel mesh exchange information in such a way that the active FE index on ghost cells equals the active FE index that was set on that processor that owned that particular ghost cell. Consequently, one can query the active_fe_index
on ghost cells, just not set it by hand.
On artificial cells, no information is available about the active_fe_index
used there. That's because we don't even know whether these cells exist at all, and even if they did, the current processor does not know anything specific about them. See the glossary entry on artificial cells for more information.
During refinement and coarsening, information about the active_fe_index
of each cell will be automatically transferred.
However, using a parallel::distributed::Triangulation with a DoFHandler in hpmode requires additional attention during serialization, since no information on active FE indices will be automatically transferred. This has to be done manually using the prepare_for_serialization_of_active_fe_indices() and deserialize_active_fe_indices() functions. The former has to be called before parallel::distributed::Triangulation::save() is invoked, and the latter needs to be run after parallel::distributed::Triangulation::load(). If further data will be attached to the triangulation via the parallel::distributed::CellDataTransfer, parallel::distributed::SolutionTransfer, or Particles::ParticleHandler classes, all corresponding preparation and deserialization function calls need to happen in the same order. Consult the documentation of parallel::distributed::SolutionTransfer for more information.
Definition at line 316 of file dof_handler.h.

private 
Definition at line 318 of file dof_handler.h.

private 
Definition at line 320 of file dof_handler.h.
using DoFHandler< dim, spacedim >::level_cell_accessor = typename LevelSelector::CellAccessor 
Definition at line 501 of file dof_handler.h.
using DoFHandler< dim, spacedim >::level_face_accessor = typename LevelSelector::FaceAccessor 
Definition at line 502 of file dof_handler.h.
using DoFHandler< dim, spacedim >::level_cell_iterator = typename LevelSelector::cell_iterator 
Definition at line 504 of file dof_handler.h.
using DoFHandler< dim, spacedim >::level_face_iterator = typename LevelSelector::face_iterator 
Definition at line 505 of file dof_handler.h.
using DoFHandler< dim, spacedim >::active_fe_index_type = types::fe_index 
The type in which we store the active FE index.
Definition at line 536 of file dof_handler.h.
using DoFHandler< dim, spacedim >::offset_type = unsigned int 
The type in which we store the offsets in the CRS data structures.
Definition at line 541 of file dof_handler.h.

privateinherited 
The data type used in counter_map.
Definition at line 229 of file subscriptor.h.

privateinherited 
The iterator type used in counter_map.
Definition at line 234 of file subscriptor.h.
DoFHandler< dim, spacedim >::DoFHandler  (  ) 
Standard constructor, not initializing any data. After constructing an object with this constructor, use reinit() to get a valid DoFHandler.

explicit 
Constructor. Take tria
as the triangulation to work on.

delete 
Copy constructor. DoFHandler objects are large and expensive. They should not be copied, in particular not by accident, but rather deliberately constructed. As a consequence, this constructor is explicitly removed from the interface of this class.

overridevirtual 
Destructor.

delete 
Copy operator. DoFHandler objects are large and expensive. They should not be copied, in particular not by accident, but rather deliberately constructed. As a consequence, this operator is explicitly removed from the interface of this class.
void DoFHandler< dim, spacedim >::set_active_fe_indices  (  const std::vector< types::fe_index > &  active_fe_indices  ) 
For each locally owned cell, set the active finite element index to the corresponding value given in active_fe_indices
.
The vector active_fe_indices
needs to have as many entries as there are active cells. The FE indices must be in the order in which we iterate over active cells. Vector entries corresponding to active cells that are not locally owned are ignored.
Active FE indices will only be set for locally owned cells. Ghost and artificial cells will be ignored; no active FE index will be assigned to them. To exchange active FE indices on ghost cells, call distribute_dofs() afterwards.
void DoFHandler< dim, spacedim >::set_active_fe_indices  (  const std::vector< unsigned int > &  active_fe_indices  ) 
For each locally owned cell, set the active finite element index to the corresponding value given in active_fe_indices
.
The vector active_fe_indices
needs to have as many entries as there are active cells. The FE indices must be in the order in which we iterate over active cells. Vector entries corresponding to active cells that are not locally owned are ignored.
Active FE indices will only be set for locally owned cells. Ghost and artificial cells will be ignored; no active FE index will be assigned to them. To exchange active FE indices on ghost cells, call distribute_dofs() afterwards.
std::vector< types::fe_index > DoFHandler< dim, spacedim >::get_active_fe_indices  (  )  const 
For each locally relevant cell, extract the active finite element index and return them in the order in which we iterate over active cells.
As we do not know the active FE index on artificial cells, they are set to the invalid value numbers::invalid_fe_index.
For DoFHandler objects without hpcapabilities, the vector will consist of zeros, indicating that all cells use the same finite element. In hpmode, the values may be different, though.
The returned vector has as many entries as there are active cells.
void DoFHandler< dim, spacedim >::get_active_fe_indices  (  std::vector< unsigned int > &  active_fe_indices  )  const 
For each locally relevant cell, extract the active finite element index and fill the vector active_fe_indices
in the order in which we iterate over active cells. This vector is resized, if necessary.
As we do not know the active FE index on artificial cells, they are set to the invalid value numbers::invalid_fe_index.
For DoFHandler objects without hpcapabilities, the vector will consist of zeros, indicating that all cells use the same finite element. In hpmode, the values may be different, though.
The returned vector has as many entries as there are active cells.
void DoFHandler< dim, spacedim >::set_future_fe_indices  (  const std::vector< types::fe_index > &  future_fe_indices  ) 
For each locally owned cell, set the future finite element index to the corresponding value given in future_fe_indices
.
The vector future_fe_indices
needs to have as many entries as there are active cells. The FE indices must be in the order in which we iterate over active cells. Vector entries corresponding to active cells that are not locally owned are ignored.
Future FE indices will only be set for locally owned cells. Ghost and artificial cells will be ignored; no future FE index will be assigned to them.
std::vector< types::fe_index > DoFHandler< dim, spacedim >::get_future_fe_indices  (  )  const 
For each locally owned cell, extract the future finite element index and return them in the order in which we iterate over active cells.
As we do not know the future FE index on ghost and artificial cells, they are set to the invalid value numbers::invalid_fe_index. The same applies to locally owned cells that have no future FE index assigned.
The returned vector has as many entries as there are active cells.
void DoFHandler< dim, spacedim >::reinit  (  const Triangulation< dim, spacedim > &  tria  ) 
Assign a Triangulation to the DoFHandler.
Remove all associations with the previous Triangulation object and establish connections with the new one. All information about previous degrees of freedom will be removed. Activates hpmode.
void DoFHandler< dim, spacedim >::distribute_dofs  (  const FiniteElement< dim, spacedim > &  fe  ) 
Go through the triangulation and "distribute" the degrees of freedom needed for the given finite element. "Distributing" degrees of freedom involves allocating memory to store the indices on all entities on which degrees of freedom can be located (e.g., vertices, edges, faces, etc.) and to then enumerate all degrees of freedom. In other words, while the mesh and the finite element object by themselves simply define a finite element space \(V_h\), the process of distributing degrees of freedom makes sure that there is a basis for this space and that the shape functions of this basis are enumerated in an indexable, predictable way.
The exact order in which degrees of freedom on a mesh are ordered, i.e., the order in which basis functions of the finite element space are enumerated, is something that deal.II treats as an implementation detail. By and large, degrees of freedom are enumerated in the same order in which we traverse cells, but you should not rely on any specific numbering. In contrast, if you want a particular ordering, use the functions in namespace DoFRenumbering.
This function is first discussed in the introduction to the step2 tutorial program.
void DoFHandler< dim, spacedim >::distribute_dofs  (  const hp::FECollection< dim, spacedim > &  fe  ) 
Same as above but taking an hp::FECollection object.
void DoFHandler< dim, spacedim >::distribute_mg_dofs  (  ) 
Distribute level degrees of freedom on each level for geometric multigrid. The active DoFs need to be distributed using distribute_dofs() before calling this function.
bool DoFHandler< dim, spacedim >::has_hp_capabilities  (  )  const 
Returns whether this DoFHandler has hpcapabilities.
bool DoFHandler< dim, spacedim >::has_level_dofs  (  )  const 
This function returns whether this DoFHandler has DoFs distributed on each multigrid level or in other words if distribute_mg_dofs() has been called.
bool DoFHandler< dim, spacedim >::has_active_dofs  (  )  const 
This function returns whether this DoFHandler has active DoFs. This is equivalent to asking whether (i) distribute_dofs() has been called and (ii) the finite element for which degrees of freedom have been distributed actually has degrees of freedom (which is not the case for FE_Nothing, for example).
If this object is based on a parallel::distributed::Triangulation, then the current function returns true if any partition of the parallel DoFHandler object has any degrees of freedom. In other words, the function returns true even if the Triangulation does not own any active cells on the current MPI process, but at least one process owns cells and at least this one process has any degrees of freedom associated with it.
void DoFHandler< dim, spacedim >::initialize_local_block_info  (  ) 
After distribute_dofs() with an FESystem element, the block structure of global and level vectors is stored in a BlockInfo object accessible with block_info(). This function initializes the local block structure on each cell in the same object.
void DoFHandler< dim, spacedim >::clear  (  ) 
Clear all data of this object.
void DoFHandler< dim, spacedim >::renumber_dofs  (  const std::vector< types::global_dof_index > &  new_numbers  ) 
Renumber degrees of freedom based on a list of new DoF indices for each of the degrees of freedom.
This function is called by the functions in DoFRenumbering function after computing a new ordering of the degree of freedom indices. However, it can of course also be called from user code.
i
is currently locally owned, then new_numbers[locally_owned_dofs().index_within_set(i)]
returns the new global DoF index of i
. Since the IndexSet of locally_owned_dofs() is complete in the sequential case, the latter convention for the content of the array reduces to the former in the case that only one processor participates in the mesh.true
) are of course affected by the exact renumbering performed here. For example, while the initial numbering of DoF indices done in distribute_dofs() yields a contiguous numbering, the renumbering performed by DoFRenumbering::component_wise() will, in general, not yield contiguous locally owned DoF indices. void DoFHandler< dim, spacedim >::renumber_dofs  (  const unsigned int  level, 
const std::vector< types::global_dof_index > &  new_numbers  
) 
The same function as above, but renumber the degrees of freedom of a single level of a multigrid hierarchy.
unsigned int DoFHandler< dim, spacedim >::max_couplings_between_dofs  (  )  const 
Return the maximum number of degrees of freedom a degree of freedom in the given triangulation with the given finite element may couple with. This is the maximum number of entries per line in the system matrix; this information can therefore be used upon construction of the SparsityPattern object.
The returned number is not really the maximum number but an estimate based on the finite element and the maximum number of cells meeting at a vertex. The number holds for the constrained matrix as well.
The determination of the number of couplings can be done by simple picture drawing. An example can be found in the implementation of this function.
unsigned int DoFHandler< dim, spacedim >::max_couplings_between_boundary_dofs  (  )  const 
Return the number of degrees of freedom located on the boundary another dof on the boundary can couple with.
The number is the same as for max_couplings_between_dofs() in one dimension less.
cell_iterator DoFHandler< dim, spacedim >::begin  (  const unsigned int  level = 0  )  const 
Iterator to the first used cell on level level
.
active_cell_iterator DoFHandler< dim, spacedim >::begin_active  (  const unsigned int  level = 0  )  const 
Iterator to the first active cell on level level
. If the given level does not contain any active cells (i.e., all cells on this level are further refined), then this function returns end_active(level)
so that loops of the kind
have zero iterations, as may be expected if there are no active cells on this level.
cell_iterator DoFHandler< dim, spacedim >::end  (  )  const 
Iterator past the end; this iterator serves for comparisons of iterators with pasttheend or beforethebeginning states.
cell_iterator DoFHandler< dim, spacedim >::end  (  const unsigned int  level  )  const 
Return an iterator which is the first iterator not on the given level. If level
is the last level, then this returns end()
.
active_cell_iterator DoFHandler< dim, spacedim >::end_active  (  const unsigned int  level  )  const 
Return an active iterator which is the first active iterator not on the given level. If level
is the last level, then this returns end()
.
level_cell_iterator DoFHandler< dim, spacedim >::begin_mg  (  const unsigned int  level = 0  )  const 
Iterator to the first used cell on level level
. This returns a level_cell_iterator that returns level dofs when dof_indices() is called.
level_cell_iterator DoFHandler< dim, spacedim >::end_mg  (  const unsigned int  level  )  const 
Iterator past the last cell on level level
. This returns a level_cell_iterator that returns level dofs when dof_indices() is called.
level_cell_iterator DoFHandler< dim, spacedim >::end_mg  (  )  const 
Iterator past the end; this iterator serves for comparisons of iterators with pasttheend or beforethebeginning states.
types::global_dof_index DoFHandler< dim, spacedim >::n_dofs  (  )  const 
Return the global number of degrees of freedom. If the current object handles all degrees of freedom itself (even if you may intend to solve your linear system in parallel, such as in step17 or step18), then this number equals the number of locally owned degrees of freedom since this object doesn't know anything about what you want to do with it and believes that it owns every degree of freedom it knows about.
On the other hand, if this object operates on a parallel::distributed::Triangulation object, then this function returns the global number of degrees of freedom, accumulated over all processors.
In either case, included in the returned number are those DoFs which are constrained by hanging nodes, see Constraints on degrees of freedom.
Mathematically speaking, the number returned by this function equals the dimension of the finite element space (without taking into account constraints) that corresponds to (i) the mesh on which it is defined, and (ii) the finite element that is used by the current object. It also, of course, equals the number of shape functions that span this space.
types::global_dof_index DoFHandler< dim, spacedim >::n_dofs  (  const unsigned int  level  )  const 
The (global) number of multilevel degrees of freedom on a given level.
If no level degrees of freedom have been assigned to this level, returns numbers::invalid_dof_index. Else returns the number of degrees of freedom on this level.
types::global_dof_index DoFHandler< dim, spacedim >::n_boundary_dofs  (  )  const 
Return the number of locally owned degrees of freedom located on the boundary.
types::global_dof_index DoFHandler< dim, spacedim >::n_boundary_dofs  (  const std::map< types::boundary_id, const Function< spacedim, number > * > &  boundary_ids  )  const 
Return the number of locally owned degrees of freedom located on those parts of the boundary which have a boundary indicator listed in the given set. The reason that a map
rather than a set
is used is the same as described in the documentation of that variant of DoFTools::make_boundary_sparsity_pattern() that takes a map.
There is, however, another overload of this function that takes a set
argument (see below).
types::global_dof_index DoFHandler< dim, spacedim >::n_boundary_dofs  (  const std::set< types::boundary_id > &  boundary_ids  )  const 
Return the number of degrees of freedom located on those parts of the boundary which have a boundary indicator listed in the given set. The
const BlockInfo & DoFHandler< dim, spacedim >::block_info  (  )  const 
Access to an object informing of the block structure of the dof handler.
If an FESystem is used in distribute_dofs(), degrees of freedom naturally split into several blocks. For each base element as many blocks appear as its multiplicity.
At the end of distribute_dofs(), the number of degrees of freedom in each block is counted, and stored in a BlockInfo object, which can be accessed here. If you have previously called distribute_mg_dofs(), the same is done on each level of the multigrid hierarchy. Additionally, the block structure on each cell can be generated in this object by calling initialize_local_block_info().
types::global_dof_index DoFHandler< dim, spacedim >::n_locally_owned_dofs  (  )  const 
Return the number of degrees of freedom that belong to this process.
If this is a sequential DoFHandler, then the result equals that produced by n_dofs(). (Here, "sequential" means that either the whole program does not use MPI, or that it uses MPI but only uses a single MPI process, or that there are multiple MPI processes but the Triangulation on which this DoFHandler builds works only on one MPI process.) On the other hand, if we are operating on a parallel::distributed::Triangulation or parallel::shared::Triangulation, then it includes only the degrees of freedom that the current processor owns. Note that in this case this does not include all degrees of freedom that have been distributed on the current processor's image of the mesh: in particular, some of the degrees of freedom on the interface between the cells owned by this processor and cells owned by other processors may be theirs, and degrees of freedom on ghost cells are also not necessarily included.
const IndexSet & DoFHandler< dim, spacedim >::locally_owned_dofs  (  )  const 
Return an IndexSet describing the set of locally owned DoFs as a subset of 0..n_dofs(). The number of elements of this set equals n_locally_owned_dofs().
const IndexSet & DoFHandler< dim, spacedim >::locally_owned_mg_dofs  (  const unsigned int  level  )  const 
Return an IndexSet describing the set of locally owned DoFs used for the given multigrid level as a subset of 0..n_dofs(level).
const FiniteElement< dim, spacedim > & DoFHandler< dim, spacedim >::get_fe  (  const types::fe_index  index = 0  )  const 
Return a constant reference to the indexth finite element object that is used by this object.
const hp::FECollection< dim, spacedim > & DoFHandler< dim, spacedim >::get_fe_collection  (  )  const 
Return a constant reference to the set of finite element objects that are used by this object.
const Triangulation< dim, spacedim > & DoFHandler< dim, spacedim >::get_triangulation  (  )  const 
Return a constant reference to the triangulation underlying this object.
MPI_Comm DoFHandler< dim, spacedim >::get_communicator  (  )  const 
Return MPI communicator used by the underlying triangulation.
void DoFHandler< dim, spacedim >::prepare_for_serialization_of_active_fe_indices  (  ) 
Whenever serialization with a parallel::distributed::Triangulation as the underlying triangulation is considered, we also need to consider storing the active FE indices on all active cells as well.
This function registers that these indices are to be stored whenever the parallel::distributed::Triangulation::save() function is called on the underlying triangulation.
void DoFHandler< dim, spacedim >::deserialize_active_fe_indices  (  ) 
Whenever serialization with a parallel::distributed::Triangulation as the underlying triangulation is considered, we also need to consider storing the active FE indices on all active cells as well.
This function deserializes and distributes the previously stored active FE indices on all active cells.

virtual 
Determine an estimate for the memory consumption (in bytes) of this object.
This function is made virtual, since a dof handler object might be accessed through a pointers to this base class, although the actual object might be a derived class.
void DoFHandler< dim, spacedim >::save  (  Archive &  ar, 
const unsigned int  version  
)  const 
Write the data of this object to a stream for the purpose of serialization using the BOOST serialization library.
void DoFHandler< dim, spacedim >::load  (  Archive &  ar, 
const unsigned int  version  
) 
Read the data of this object from a stream for the purpose of serialization using the BOOST serialization library.
void DoFHandler< dim, spacedim >::serialize  (  Archive &  archive, 
const unsigned int  version  
) 
Write and read the data of this object from a stream for the purpose of serialization using the BOOST serialization library.

private 
Free all memory used for nonmultigrid data structures.

private 
Free all memory used for multigrid data structures.

private 
Set up DoFHandler policy.

private 
Set up connections to signals of the underlying triangulation.

private 
Create default tables for the active and future fe_indices.
Active indices are initialized with a zero indicator, meaning that fe[0] is going to be used by default. Future indices are initialized with an invalid indicator, meaning that no padaptation is scheduled by default.
This method is called upon construction and whenever the underlying triangulation gets created. This ensures that each cell has a valid active and future fe_index.

private 
Update tables for active and future fe_indices.
Whenever the underlying triangulation changes (either by adaptation or deserialization), active and future FE index tables will be adjusted to the current structure of the triangulation. Missing values of active and future indices will be initialized with their defaults (see create_active_fe_table()).
This method is called post refinement and post deserialization. This ensures that each cell has a valid active and future fe_index.

private 
A function that will be triggered through a triangulation signal just before the associated Triangulation or parallel::shared::Triangulation is modified.
The function that stores the active FE indices of all cells that will be refined or coarsened before the refinement happens, so that they can be set again after refinement.

private 
A function that will be triggered through a triangulation signal just after the associated Triangulation or parallel::shared::Triangulation is modified.
The function that restores the active FE indices of all cells that were refined or coarsened.

private 
A function that will be triggered through a triangulation signal just before the associated parallel::distributed::Triangulation is modified.
The function that stores all active FE indices on locally owned cells for distribution over all participating processors.

private 
A function that will be triggered through a triangulation signal just after the associated parallel::distributed::Triangulation is modified.
The function that restores all active FE indices on locally owned cells that have been communicated.

inherited 
Subscribes a user of the object by storing the pointer validity
. The subscriber may be identified by text supplied as identifier
.
Definition at line 135 of file subscriptor.cc.

inherited 
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 155 of file subscriptor.cc.

inlineinherited 
Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.
Definition at line 300 of file subscriptor.h.

inlineinherited 
List the subscribers to the input stream
.
Definition at line 317 of file subscriptor.h.

inherited 
List the subscribers to deallog
.
Definition at line 203 of file subscriptor.cc.

privatenoexceptinherited 
Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.
Definition at line 52 of file subscriptor.cc.

friend 
Definition at line 1724 of file dof_handler.h.

friend 
Definition at line 1726 of file dof_handler.h.

friend 
Definition at line 1727 of file dof_handler.h.

friend 
Definition at line 1728 of file dof_handler.h.

friend 
Definition at line 1732 of file dof_handler.h.

friend 
Definition at line 1733 of file dof_handler.h.

friend 
Definition at line 1734 of file dof_handler.h.

staticconstexpr 
Make the dimension available in function templates.
Definition at line 511 of file dof_handler.h.

staticconstexpr 
Make the space dimension available in function templates.
Definition at line 516 of file dof_handler.h.

static 
The default index of the finite element to be used on a given cell.
Definition at line 521 of file dof_handler.h.

static 
Invalid index of the finite element to be used on a given cell.
Definition at line 528 of file dof_handler.h.

static 
Invalid active FE index which will be used as a default value to determine whether a future FE index has been set or not.
Definition at line 549 of file dof_handler.h.

private 
An object containing information on the block structure.
Definition at line 1497 of file dof_handler.h.

private 
Boolean indicating whether or not the current DoFHandler has hpcapabilities.
Definition at line 1503 of file dof_handler.h.

private 
Address of the triangulation to work on.
Definition at line 1509 of file dof_handler.h.

private 
Store a hp::FECollection object. If only a single FiniteElement is used during initialization of this object, it contains the (one) FiniteElement.
Definition at line 1516 of file dof_handler.h.

private 
An object that describes how degrees of freedom should be distributed and renumbered.
Definition at line 1524 of file dof_handler.h.

private 
A structure that contains all sorts of numbers that characterize the degrees of freedom this object works on.
For most members of this structure, there is an accessor function in this class that returns its value.
Definition at line 1533 of file dof_handler.h.

private 
Data structure like number_cache, but for each multigrid level.
Definition at line 1539 of file dof_handler.h.

mutableprivate 
Indices of degree of freedom of each d+1 geometric object (3d: vertex, line, quad, hex) for all relevant active finite elements. Identification of the appropriate position is done via object_dof_ptr (CRS scheme).
Definition at line 1547 of file dof_handler.h.

mutableprivate 
Pointer to the first cached degree of freedom of a geometric object for all relevant active finite elements.
Definition at line 1558 of file dof_handler.h.

mutableprivate 
Active FE indices of each geometric object. Identification of the appropriate position of a cell in the vectors is done via hp_object_fe_ptr (CRS scheme).
Definition at line 1566 of file dof_handler.h.

mutableprivate 
Pointer to the first FE index of a geometric object.
Definition at line 1571 of file dof_handler.h.

mutableprivate 
Active FE index of an active cell (identified by level and level index). This vector is only used in hpmode.
Definition at line 1577 of file dof_handler.h.

mutableprivate 
Future FE index of an active cell (identified by level and level index). This vector is only used in hpmode.
Definition at line 1583 of file dof_handler.h.

private 
An array to store the indices for level degrees of freedom located at vertices.
Definition at line 1589 of file dof_handler.h.

private 
Space to store the DoF numbers for the different multigrid levels.
Definition at line 1596 of file dof_handler.h.

private 
Space to store DoF numbers of faces in the multigrid context.
Definition at line 1602 of file dof_handler.h.

private 
We embed our data structure into a pointer to control that all transfer related data only exists during the actual transfer process.
Definition at line 1608 of file dof_handler.h.

private 
A list of connections with which this object connects to the triangulation to get information about when the triangulation changes.
Definition at line 1614 of file dof_handler.h.

private 
A list of connections with which this object connects to the triangulation. They get triggered specifically when data needs to be transferred due to refinement or repartitioning. Only active in hpmode.
Definition at line 1621 of file dof_handler.h.

mutableprivateinherited 
Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).
The creator (and owner) of an object is counted in the map below if HE manages to supply identification.
We use the mutable
keyword in order to allow subscription to constant objects also.
This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic
class template.
Definition at line 218 of file subscriptor.h.

mutableprivateinherited 
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 224 of file subscriptor.h.

mutableprivateinherited 
In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.
Definition at line 240 of file subscriptor.h.

mutableprivateinherited 
Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.
Definition at line 248 of file subscriptor.h.

staticprivateinherited 
A mutex used to ensure data consistency when accessing the mutable
members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers()
.
Definition at line 271 of file subscriptor.h.