#include <deal.II/fe/fe_system.h>

Inheritance diagram for FESystem< dim, spacedim >:

Classes
class	InternalData

Public Member Functions
	FESystem (const FiniteElement< dim, spacedim > &fe, const unsigned int n_elements)

	FESystem (const FiniteElement< dim, spacedim > &fe1, const unsigned int n1, const FiniteElement< dim, spacedim > &fe2, const unsigned int n2)

	FESystem (const FiniteElement< dim, spacedim > &fe1, const unsigned int n1, const FiniteElement< dim, spacedim > &fe2, const unsigned int n2, const FiniteElement< dim, spacedim > &fe3, const unsigned int n3)

	FESystem (const FiniteElement< dim, spacedim > &fe1, const unsigned int n1, const FiniteElement< dim, spacedim > &fe2, const unsigned int n2, const FiniteElement< dim, spacedim > &fe3, const unsigned int n3, const FiniteElement< dim, spacedim > &fe4, const unsigned int n4)

	FESystem (const FiniteElement< dim, spacedim > &fe1, const unsigned int n1, const FiniteElement< dim, spacedim > &fe2, const unsigned int n2, const FiniteElement< dim, spacedim > &fe3, const unsigned int n3, const FiniteElement< dim, spacedim > &fe4, const unsigned int n4, const FiniteElement< dim, spacedim > &fe5, const unsigned int n5)

	FESystem (const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities)

template<class... FEPairs>
	FESystem (FEPairs &&...fe_pairs)

	FESystem (const std::initializer_list< std::pair< std::unique_ptr< FiniteElement< dim, spacedim >>, unsigned int >> &fe_systems)

	FESystem (const FESystem< dim, spacedim > &)=delete

	FESystem (FESystem< dim, spacedim > &&)=default

virtual	~FESystem () override=default

virtual std::string	get_name () const override

virtual std::unique_ptr< FiniteElement< dim, spacedim > >	clone () const override

virtual UpdateFlags	requires_update_flags (const UpdateFlags update_flags) const override

virtual const FiniteElement< dim, spacedim > &	get_sub_fe (const unsigned int first_component, const unsigned int n_selected_components) const override

virtual double	shape_value (const unsigned int i, const Point< dim > &p) const override

virtual double	shape_value_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override

virtual Tensor< 1, dim >	shape_grad (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 1, dim >	shape_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override

virtual Tensor< 2, dim >	shape_grad_grad (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 2, dim >	shape_grad_grad_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override

virtual Tensor< 3, dim >	shape_3rd_derivative (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 3, dim >	shape_3rd_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override

virtual Tensor< 4, dim >	shape_4th_derivative (const unsigned int i, const Point< dim > &p) const override

virtual Tensor< 4, dim >	shape_4th_derivative_component (const unsigned int i, const Point< dim > &p, const unsigned int component) const override

virtual void	get_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const override

virtual const FiniteElement< dim, spacedim > &	base_element (const unsigned int index) const override

virtual bool	has_support_on_face (const unsigned int shape_index, const unsigned int face_index) const override

virtual const FullMatrix< double > &	get_restriction_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const override

virtual const FullMatrix< double > &	get_prolongation_matrix (const unsigned int child, const RefinementCase< dim > &refinement_case=RefinementCase< dim >::isotropic_refinement) const override

virtual unsigned int	face_to_cell_index (const unsigned int face_dof_index, const unsigned int face, const bool face_orientation=true, const bool face_flip=false, const bool face_rotation=false) const override

virtual Point< dim >	unit_support_point (const unsigned int index) const override

virtual Point< dim-1 >	unit_face_support_point (const unsigned int index) const override

virtual std::pair< Table< 2, bool >, std::vector< unsigned int > >	get_constant_modes () const override

virtual void	convert_generalized_support_point_values_to_dof_values (const std::vector< Vector< double >> &support_point_values, std::vector< double > &dof_values) const override

virtual std::size_t	memory_consumption () const override

Functions to support hp
virtual bool	hp_constraints_are_implemented () const override

virtual void	get_face_interpolation_matrix (const FiniteElement< dim, spacedim > &source, FullMatrix< double > &matrix) const override

virtual void	get_subface_interpolation_matrix (const FiniteElement< dim, spacedim > &source, const unsigned int subface, FullMatrix< double > &matrix) const override

virtual std::vector< std::pair< unsigned int, unsigned int > >	hp_vertex_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const override

virtual std::vector< std::pair< unsigned int, unsigned int > >	hp_line_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const override

virtual std::vector< std::pair< unsigned int, unsigned int > >	hp_quad_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const override

virtual FiniteElementDomination::Domination	compare_for_face_domination (const FiniteElement< dim, spacedim > &fe_other) const override

Public Member Functions inherited from FiniteElement< dim, spacedim >
	FiniteElement (const FiniteElementData< dim > &fe_data, const std::vector< bool > &restriction_is_additive_flags, const std::vector< ComponentMask > &nonzero_components)

	FiniteElement (FiniteElement< dim, spacedim > &&)=default

	FiniteElement (const FiniteElement< dim, spacedim > &)=default

virtual	~FiniteElement () override=default

std::pair< std::unique_ptr< FiniteElement< dim, spacedim > >, unsigned int >	operator^ (const unsigned int multiplicity) const

const FiniteElement< dim, spacedim > &	operator[] (const unsigned int fe_index) const

virtual bool	operator== (const FiniteElement< dim, spacedim > &fe) const

bool	operator!= (const FiniteElement< dim, spacedim > &) const

bool	prolongation_is_implemented () const

bool	isotropic_prolongation_is_implemented () const

bool	restriction_is_implemented () const

bool	isotropic_restriction_is_implemented () const

bool	restriction_is_additive (const unsigned int index) const

const FullMatrix< double > &	constraints (const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const

bool	constraints_are_implemented (const ::internal::SubfaceCase< dim > &subface_case=::internal::SubfaceCase< dim >::case_isotropic) const

std::pair< unsigned int, unsigned int >	system_to_component_index (const unsigned int index) const

unsigned int	component_to_system_index (const unsigned int component, const unsigned int index) const

std::pair< unsigned int, unsigned int >	face_system_to_component_index (const unsigned int index) const

unsigned int	adjust_quad_dof_index_for_face_orientation (const unsigned int index, const bool face_orientation, const bool face_flip, const bool face_rotation) const

unsigned int	adjust_line_dof_index_for_line_orientation (const unsigned int index, const bool line_orientation) const

const ComponentMask &	get_nonzero_components (const unsigned int i) const

unsigned int	n_nonzero_components (const unsigned int i) const

bool	is_primitive () const

bool	is_primitive (const unsigned int i) const

unsigned int	n_base_elements () const

unsigned int	element_multiplicity (const unsigned int index) const

const FiniteElement< dim, spacedim > &	get_sub_fe (const ComponentMask &mask) const

std::pair< std::pair< unsigned int, unsigned int >, unsigned int >	system_to_base_index (const unsigned int index) const

std::pair< std::pair< unsigned int, unsigned int >, unsigned int >	face_system_to_base_index (const unsigned int index) const

types::global_dof_index	first_block_of_base (const unsigned int b) const

std::pair< unsigned int, unsigned int >	component_to_base_index (const unsigned int component) const

std::pair< unsigned int, unsigned int >	block_to_base_index (const unsigned int block) const

std::pair< unsigned int, types::global_dof_index >	system_to_block_index (const unsigned int component) const

unsigned int	component_to_block_index (const unsigned int component) const

ComponentMask	component_mask (const FEValuesExtractors::Scalar &scalar) const

ComponentMask	component_mask (const FEValuesExtractors::Vector &vector) const

ComponentMask	component_mask (const FEValuesExtractors::SymmetricTensor< 2 > &sym_tensor) const

ComponentMask	component_mask (const BlockMask &block_mask) const

BlockMask	block_mask (const FEValuesExtractors::Scalar &scalar) const

BlockMask	block_mask (const FEValuesExtractors::Vector &vector) const

BlockMask	block_mask (const FEValuesExtractors::SymmetricTensor< 2 > &sym_tensor) const

BlockMask	block_mask (const ComponentMask &component_mask) const

const std::vector< Point< dim > > &	get_unit_support_points () const

bool	has_support_points () const

const std::vector< Point< dim-1 > > &	get_unit_face_support_points () const

bool	has_face_support_points () const

const std::vector< Point< dim > > &	get_generalized_support_points () const

bool	has_generalized_support_points () const

const std::vector< Point< dim-1 > > &	get_generalized_face_support_points () const

bool	has_generalized_face_support_points () const

GeometryPrimitive	get_associated_geometry_primitive (const unsigned int cell_dof_index) const

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (const char *identifier=nullptr) const

void	unsubscribe (const char *identifier=nullptr) const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Public Member Functions inherited from FiniteElementData< dim >
	FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const BlockIndices &block_indices=BlockIndices())

unsigned int	n_dofs_per_vertex () const

unsigned int	n_dofs_per_line () const

unsigned int	n_dofs_per_quad () const

unsigned int	n_dofs_per_hex () const

unsigned int	n_dofs_per_face () const

unsigned int	n_dofs_per_cell () const

template<int structdim>
unsigned int	n_dofs_per_object () const

unsigned int	n_components () const

unsigned int	n_blocks () const

const BlockIndices &	block_indices () const

unsigned int	tensor_degree () const

bool	conforms (const Conformity) const

bool	operator== (const FiniteElementData &) const

Protected Member Functions
virtual std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase >	get_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim > &quadrature,::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override

virtual std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase >	get_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature,::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override

virtual std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase >	get_subface_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim-1 > &quadrature,::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const override

template<int dim_1>
void	compute_fill (const Mapping< dim, spacedim > &mapping, const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim_1 > &quadrature, const CellSimilarity::Similarity cell_similarity, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const typename FiniteElement< dim, spacedim >::InternalDataBase &fe_data, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const

Protected Member Functions inherited from FiniteElement< dim, spacedim >
void	reinit_restriction_and_prolongation_matrices (const bool isotropic_restriction_only=false, const bool isotropic_prolongation_only=false)

TableIndices< 2 >	interface_constraints_size () const

virtual void	fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal,::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0

virtual void	fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim-1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal,::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0

virtual void	fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int sub_no, const Quadrature< dim-1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal,::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const =0

Private Member Functions
void	initialize (const std::vector< const FiniteElement< dim, spacedim > * > &fes, const std::vector< unsigned int > &multiplicities)

void	build_interface_constraints ()

template<int structdim>
std::vector< std::pair< unsigned int, unsigned int > >	hp_object_dof_identities (const FiniteElement< dim, spacedim > &fe_other) const

Private Attributes
std::vector< std::pair< std::unique_ptr< const FiniteElement< dim, spacedim > >, unsigned int > >	base_elements

std::vector< std::vector< std::size_t > >	generalized_support_points_index_table

Static Private Attributes
static const unsigned int	invalid_face_number = numbers::invalid_unsigned_int

Friends
class	FE_Enriched< dim, spacedim >

Additional Inherited Members
Public Types inherited from FiniteElementData< dim >
Static Public Member Functions inherited from FiniteElement< dim, spacedim >
static::ExceptionBase &	ExcShapeFunctionNotPrimitive (int arg1)

static::ExceptionBase &	ExcFENotPrimitive ()

static::ExceptionBase &	ExcUnitShapeValuesDoNotExist ()

static::ExceptionBase &	ExcFEHasNoSupportPoints ()

static::ExceptionBase &	ExcEmbeddingVoid ()

static::ExceptionBase &	ExcProjectionVoid ()

static::ExceptionBase &	ExcWrongInterfaceMatrixSize (int arg1, int arg2)

static::ExceptionBase &	ExcInterpolationNotImplemented ()

Static Public Member Functions inherited from Subscriptor
static::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Public Attributes inherited from FiniteElementData< dim >
const unsigned int	dofs_per_vertex

const unsigned int	dofs_per_line

const unsigned int	dofs_per_quad

const unsigned int	dofs_per_hex

const unsigned int	first_line_index

const unsigned int	first_quad_index

const unsigned int	first_hex_index

const unsigned int	first_face_line_index

const unsigned int	first_face_quad_index

const unsigned int	dofs_per_face

const unsigned int	dofs_per_cell

const unsigned int	components

const unsigned int	degree

const Conformity	conforming_space

const BlockIndices	block_indices_data

Static Public Attributes inherited from FiniteElement< dim, spacedim >
static const unsigned int	space_dimension = spacedim

Static Public Attributes inherited from FiniteElementData< dim >
static const unsigned int	dimension = dim

Static Protected Member Functions inherited from FiniteElement< dim, spacedim >
static std::vector< unsigned int >	compute_n_nonzero_components (const std::vector< ComponentMask > &nonzero_components)

Protected Attributes inherited from FiniteElement< dim, spacedim >
std::vector< std::vector< FullMatrix< double > > >	restriction

std::vector< std::vector< FullMatrix< double > > >	prolongation

FullMatrix< double >	interface_constraints

std::vector< Point< dim > >	unit_support_points

std::vector< Point< dim-1 > >	unit_face_support_points

std::vector< Point< dim > >	generalized_support_points

std::vector< Point< dim-1 > >	generalized_face_support_points

Table< 2, int >	adjust_quad_dof_index_for_face_orientation_table

std::vector< int >	adjust_line_dof_index_for_line_orientation_table

std::vector< std::pair< unsigned int, unsigned int > >	system_to_component_table

std::vector< std::pair< unsigned int, unsigned int > >	face_system_to_component_table

std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > >	system_to_base_table

std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > >	face_system_to_base_table

BlockIndices	base_to_block_indices

std::vector< std::pair< std::pair< unsigned int, unsigned int >, unsigned int > >	component_to_base_table

const std::vector< bool >	restriction_is_additive_flags

const std::vector< ComponentMask >	nonzero_components

const std::vector< unsigned int >	n_nonzero_components_table

const bool	cached_primitivity

Detailed Description

template<int dim, int spacedim = dim>
class FESystem< dim, spacedim >

This class provides an interface to group several elements together into one. To the outside world, the resulting object looks just like a usual finite element object, which is composed of several other finite elements that are possibly of different type. The result is then a vector-valued finite element. An example is given in the documentation of namespace FETools::Compositing, when using the "tensor product" strategy.

Vector valued elements are discussed in a number of tutorial programs, for example step-8, step-20, step-21, and in particular in the Handling vector valued problems module.

Note: The material presented here is also discussed in video lecture 19, video lecture 20. (All video lectures are also available here.)

FESystem, components and blocks

An FESystem, except in the most trivial case, produces a vector-valued finite element with several components. The number of components n_components() corresponds to the dimension of the solution function in the PDE system, and correspondingly also to the number of equations your PDE system has. For example, the mixed Laplace system covered in step-20 has \(d+1\) components in \(d\) space dimensions: the scalar pressure and the \(d\) components of the velocity vector. Similarly, the elasticity equation covered in step-8 has \(d\) components in \(d\) space dimensions. In general, the number of components of a FESystem element is the accumulated number of components of all base elements times their multiplicities. A bit more on components is also given in the glossary entry on components.

While the concept of components is important from the viewpoint of a partial differential equation, the finite element side looks a bit different Since not only FESystem, but also vector-valued elements like FE_RaviartThomas, have several components. The concept needed here is a block. Each block encompasses the set of degrees of freedom associated with a single base element of an FESystem, where base elements with multiplicities count multiple times. These blocks are usually addressed using the information in DoFHandler::block_info(). The number of blocks of a FESystem object is simply the sum of all multiplicities of base elements and is given by n_blocks().

For example, the FESystem for the Taylor-Hood element for the three- dimensional Stokes problem can be built using the code

FE_Q<3> u(2);
FE_Q<3> p(1);
FESystem<3> sys1(u,3, p,1);

This example creates an FESystem sys1 with four components, three for the velocity components and one for the pressure, and also four blocks with the degrees of freedom of each of the velocity components and the pressure in a separate block each. The number of blocks is four since the first base element is repeated three times.

On the other hand, a Taylor-Hood element can also be constructed using

FESystem<3> U(u,3);

FESystem<3> sys2(U,1, p,1);

The FESystem sys2 created here has the same four components, but the degrees of freedom are distributed into only two blocks. The first block has all velocity degrees of freedom from U, while the second block contains the pressure degrees of freedom. Note that while U itself has 3 blocks, the FESystem sys2 does not attempt to split U into its base elements but considers it a block of its own. By blocking all velocities into one system first as in sys2, we achieve the same block structure that would be generated if instead of using a \(Q_2^3\) element for the velocities we had used vector-valued base elements, for instance like using a mixed discretization of Darcy's law using

FE_RaviartThomas<3> u(1);
FE_DGQ<3> p(1);
FESystem<3> sys3(u,1, p,1);

This example also produces a system with four components, but only two blocks.

In most cases, the composed element behaves as if it were a usual element. It just has more degrees of freedom than most of the "common" elements. However the underlying structure is visible in the restriction, prolongation and interface constraint matrices, which do not couple the degrees of freedom of the base elements. E.g. the continuity requirement is imposed for the shape functions of the subobjects separately; no requirement exist between shape functions of different subobjects, i.e. in the above example: on a hanging node, the respective value of the u velocity is only coupled to u at the vertices and the line on the larger cell next to this vertex, but there is no interaction with v and w of this or the other cell.

Internal information on numbering of degrees of freedom

The overall numbering of degrees of freedom is as follows: for each subobject (vertex, line, quad, or hex), the degrees of freedom are numbered such that we run over all subelements first, before turning for the next dof on this subobject or for the next subobject. For example, for an element of three components in one space dimension, the first two components being cubic lagrange elements and the third being a quadratic lagrange element, the ordering for the system s=(u,v,p) is:

First vertex: u0, v0, p0 = s0, s1, s2
Second vertex: u1, v1, p1 = s3, s4, s5
First component on the line: u2, u3 = s4, s5
Second component on the line: v2, v3 = s6, s7.
Third component on the line: p2 = s8.

That said, you should not rely on this numbering in your application as these internals might change in future. Rather use the functions system_to_component_index() and component_to_system_index().

For more information on the template parameter spacedim see the documentation of Triangulation.

Author: Wolfgang Bangerth, Guido Kanschat, 1999, 2002, 2003, 2006, Ralf Hartmann 2001.

Definition at line 42 of file fe.h.

Constructor & Destructor Documentation

template<int dim, int spacedim>

FESystem< dim, spacedim >::FESystem	(	const FiniteElement< dim, spacedim > &	fe,
		const unsigned int	n_elements
	)

Constructor. Take a finite element and the number of elements you want to group together using this class.

The object fe is not actually used for anything other than creating a copy that will then be owned by the current object. In other words, it is completely fine to call this constructor with a temporary object for the finite element, as in this code snippet:

FESystem<dim> fe (FE_Q<dim>(2), 2);

Here, FE_Q<dim>(2) constructs an unnamed, temporary object that is passed to the FESystem constructor to create a finite element that consists of two components, both of which are quadratic FE_Q elements. The temporary is destroyed again at the end of the code that corresponds to this line, but this does not matter because FESystem creates its own copy of the FE_Q object.

This constructor (or its variants below) is used in essentially all tutorial programs that deal with vector valued problems. See step-8, step-20, step-22 and others for use cases. Also see the module on Handling vector valued problems.

Note: The material presented here is also discussed in video lecture 19, video lecture 20. (All video lectures are also available here.)

Parameters

[in]	fe	The finite element that will be used to represent the components of this composed element.
[in]	n_elements	An integer denoting how many copies of `fe` this element should consist of.

Definition at line 112 of file fe_system.cc.

template<int dim, int spacedim>

FESystem< dim, spacedim >::FESystem	(	const FiniteElement< dim, spacedim > &	fe1,
		const unsigned int	n1,
		const FiniteElement< dim, spacedim > &	fe2,
		const unsigned int	n2
	)

Constructor for mixed discretizations with two base elements.

See the other constructor above for an explanation of the general idea of composing elements.

Definition at line 131 of file fe_system.cc.

template<int dim, int spacedim>

FESystem< dim, spacedim >::FESystem	(	const FiniteElement< dim, spacedim > &	fe1,
		const unsigned int	n1,
		const FiniteElement< dim, spacedim > &	fe2,
		const unsigned int	n2,
		const FiniteElement< dim, spacedim > &	fe3,
		const unsigned int	n3
	)

Constructor for mixed discretizations with three base elements.

See the other constructor above for an explanation of the general idea of composing elements.

Definition at line 156 of file fe_system.cc.

template<int dim, int spacedim>

FESystem< dim, spacedim >::FESystem	(	const FiniteElement< dim, spacedim > &	fe1,
		const unsigned int	n1,
		const FiniteElement< dim, spacedim > &	fe2,
		const unsigned int	n2,
		const FiniteElement< dim, spacedim > &	fe3,
		const unsigned int	n3,
		const FiniteElement< dim, spacedim > &	fe4,
		const unsigned int	n4
	)

Constructor for mixed discretizations with four base elements.

See the first of the other constructors above for an explanation of the general idea of composing elements.

Definition at line 192 of file fe_system.cc.

template<int dim, int spacedim>

FESystem< dim, spacedim >::FESystem	(	const FiniteElement< dim, spacedim > &	fe1,
		const unsigned int	n1,
		const FiniteElement< dim, spacedim > &	fe2,
		const unsigned int	n2,
		const FiniteElement< dim, spacedim > &	fe3,
		const unsigned int	n3,
		const FiniteElement< dim, spacedim > &	fe4,
		const unsigned int	n4,
		const FiniteElement< dim, spacedim > &	fe5,
		const unsigned int	n5
	)

Constructor for mixed discretizations with five base elements.

See the first of the other constructors above for an explanation of the general idea of composing elements.

Definition at line 243 of file fe_system.cc.

template<int dim, int spacedim>

FESystem< dim, spacedim >::FESystem	(	const std::vector< const FiniteElement< dim, spacedim > * > &	fes,
		const std::vector< unsigned int > &	multiplicities
	)

Same as above but for any number of base elements. Pointers to the base elements and their multiplicities are passed as vectors to this constructor. The lengths of these vectors are assumed to be equal.

As above, the finite element objects pointed to by the first argument are not actually used other than to create copies internally. Consequently, you can delete these pointers immediately again after calling this constructor.

How to use this constructor

Using this constructor is a bit awkward at times because you need to pass two vectors in a place where it may not be straightforward to construct such a vector – for example, in the member initializer list of a class with an FESystem member variable. For example, if your main class looks like this:

template <int dim>
class MySimulator {
public:
  MySimulator (const unsigned int polynomial_degree);
private:
  FESystem<dim> fe;
};
template <int dim>
MySimulator<dim>::MySimulator (const unsigned int polynomial_degree)
  :
  fe (...)  // what to pass here???
{}

Using the C++11 language standard (or later) you could do something like this to create an element with four base elements and multiplicities 1, 2, 3 and 4:

template <int dim>
MySimulator<dim>::MySimulator (const unsigned int polynomial_degree)
  :
  fe (std::vector<const FiniteElement<dim>*> { new FE_Q<dim>(1),
                                               new FE_Q<dim>(2),
                                               new FE_Q<dim>(3),
                                               new FE_Q<dim>(4) },
      std::vector<unsigned int> { 1, 2, 3, 4 })
{}

This creates two vectors in place and initializes them using the initializer list enclosed in braces { ... }.

This code has a problem: it creates four memory leaks because the first vector above is created with pointers to elements that are allocated with new but never destroyed.

The solution to the second of these problems is to create two static member functions that can create vectors. Here is an example:

template <int dim>
class MySimulator {
public:
  MySimulator (const unsigned int polynomial_degree);
private:
  FESystem<dim> fe;
  static std::vector<const FiniteElement<dim>*>
  create_fe_list (const unsigned int polynomial_degree);
  static std::vector<unsigned int>
  create_fe_multiplicities ();
};
template <int dim>
std::vector<const FiniteElement<dim>*>
MySimulator<dim>::create_fe_list (const unsigned int polynomial_degree)
{
  std::vector<const FiniteElement<dim>*> fe_list;
  fe_list.push_back (new FE_Q<dim>(1));
  fe_list.push_back (new FE_Q<dim>(2));
  fe_list.push_back (new FE_Q<dim>(3));
  fe_list.push_back (new FE_Q<dim>(4));
  return fe_list;
}
template <int dim>
std::vector<unsigned int>
MySimulator<dim>::create_fe_multiplicities ()
{
  std::vector<unsigned int> multiplicities;
  multiplicities.push_back (1);
  multiplicities.push_back (2);
  multiplicities.push_back (3);
  multiplicities.push_back (4);
  return multiplicities;
}
template <int dim>
MySimulator<dim>::MySimulator (const unsigned int polynomial_degree)
  :
  fe (create_fe_list (polynomial_degree),
      create_fe_multiplicities ())
{}

The way this works is that we have two static member functions that create the necessary vectors to pass to the constructor of the member variable fe. They need to be static because they are called during the constructor of MySimulator at a time when the *this object isn't fully constructed and, consequently, regular member functions cannot be called yet.

The code above does not solve the problem with the memory leak yet, though: the create_fe_list() function creates a vector of pointers, but nothing destroys these. This is the solution:

template <int dim>
class MySimulator
{
public:
  MySimulator (const unsigned int polynomial_degree);
private:
  FESystem<dim> fe;
  struct VectorElementDestroyer
  {
    const std::vector<const FiniteElement<dim>*> data;
    VectorElementDestroyer(
      const std::vector<const FiniteElement<dim>*> &pointers);
     // destructor to delete the pointers
    ~VectorElementDestroyer ();
    const std::vector<const FiniteElement<dim>*> & get_data () const;
  };
  static std::vector<const FiniteElement<dim>*>
  create_fe_list (const unsigned int polynomial_degree);
  static std::vector<unsigned int>
  create_fe_multiplicities ();
};
template <int dim>
MySimulator<dim>::VectorElementDestroyer::
VectorElementDestroyer(
  const std::vector<const FiniteElement<dim>*> &pointers)
  :
  data(pointers)
{}
template <int dim>
MySimulator<dim>::VectorElementDestroyer::
~VectorElementDestroyer ()
{
  for (unsigned int i=0; i<data.size(); ++i)
    delete data[i];
}
template <int dim>
const std::vector<const FiniteElement<dim>*> &
MySimulator<dim>::VectorElementDestroyer::
get_data () const
{
  return data;
}
template <int dim>
MySimulator<dim>::MySimulator (const unsigned int polynomial_degree)
:
fe (VectorElementDestroyer(create_fe_list (polynomial_degree)).get_data(),
    create_fe_multiplicities ())
{}

In other words, the vector we receive from the create_fe_list() is packed into a temporary object of type VectorElementDestroyer; we then get the vector from this temporary object immediately to pass it to the constructor of fe; and finally, the VectorElementDestroyer destructor is called at the end of the entire expression (after the constructor of fe has finished) and destroys the elements of the temporary vector. Voila: not short nor elegant, but it works!

Definition at line 296 of file fe_system.cc.

template<int dim, int spacedim = dim>

template<class... FEPairs>

FESystem< dim, spacedim >::FESystem ( FEPairs &&... fe_pairs )

Constructor taking an arbitrary number of parameters of type std::pair<std::unique_ptr<FiniteElement<dim, spacedim>>, unsigned int>. In combination with FiniteElement::operator^, this allows to construct FESystem objects as follows:

FiniteElementType1<dim,spacedim> fe_1;
FiniteElementType1<dim,spacedim> fe_2;
FESystem<dim,spacedim> fe_system = ( fe_1^dim, fe_2^1 );

The FiniteElement objects are not actually used for anything other than creating a copy that will then be owned by the current object. In other words, it is completely fine to call this constructor with a temporary object for the finite element, as in this code snippet:

FESystem<dim> fe (FE_Q<dim>(2)^2);

Here, FE_Q<dim>(2) constructs an unnamed, temporary object that is passed to the FESystem constructor to create a finite element that consists of two components, both of which are quadratic FE_Q elements. The temporary is destroyed again at the end of the code that corresponds to this line, but this does not matter because FESystem creates its own copy of the FE_Q object.

As a shortcut, this constructor also allows calling

FESystem<dim> fe (FE_Q<dim>(2)^dim, FE_Q<dim>(1));

instead of the more explicit

FESystem<dim> fe (FE_Q<dim>(2)^dim, FE_Q<dim>(1)^1);

In other words, if no multiplicity for an element is explicitly specified via the exponentiation operation, then it is assumed to be one (as one would have expected).

Warning: This feature is not available for Intel compilers prior to version 19.0. Defining this constructor leads to internal compiler errors for Intel compilers prior to 18.0.

template<int dim, int spacedim = dim>

FESystem< dim, spacedim >::FESystem ( const std::initializer_list< std::pair< std::unique_ptr< FiniteElement< dim, spacedim >>, unsigned int >> & fe_systems )

Same as above allowing the following syntax:

FiniteElementType1<dim,spacedim> fe_1;
FiniteElementType1<dim,spacedim> fe_2;
FESystem<dim,spacedim> fe_system = { fe_1^dim, fe_2^1 };

Warning: This feature is not available for Intel compilers prior to version 19.0. The constructor is just not selected for overload resolution.

template<int dim, int spacedim = dim>

FESystem< dim, spacedim >::FESystem ( const FESystem< dim, spacedim > & )

delete

Copy constructor. This constructor is deleted, i.e., copying FESystem objects is not allowed.

template<int dim, int spacedim = dim>

FESystem< dim, spacedim >::FESystem ( FESystem< dim, spacedim > && )

default

Move constructor.

template<int dim, int spacedim = dim>

virtual FESystem< dim, spacedim >::~FESystem ( )

overridevirtualdefault

Destructor.

Member Function Documentation

template<int dim, int spacedim>

std::string FESystem< dim, spacedim >::get_name ( ) const

overridevirtual

Return a string that uniquely identifies a finite element. This element returns a string that is composed of the strings name1...nameN returned by the basis elements. From these, we create a sequence FESystem<dim>[name1^m1-name2^m2-...-nameN^mN], where mi are the multiplicities of the basis elements. If a multiplicity is equal to one, then the superscript is omitted.

Implements FiniteElement< dim, spacedim >.

Definition at line 314 of file fe_system.cc.

template<int dim, int spacedim>

std::unique_ptr< FiniteElement< dim, spacedim > > FESystem< dim, spacedim >::clone ( ) const

overridevirtual

A sort of virtual copy constructor, this function returns a copy of the finite element object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.

Some places in the library, for example the constructors of FESystem as well as the hp::FECollection class, need to make copies of finite elements without knowing their exact type. They do so through this function.

Implements FiniteElement< dim, spacedim >.

Definition at line 343 of file fe_system.cc.

template<int dim, int spacedim>

UpdateFlags FESystem< dim, spacedim >::requires_update_flags ( const UpdateFlags update_flags ) const

overridevirtual

Given a set of update flags, compute which other quantities also need to be computed in order to satisfy the request by the given flags. Then return the combination of the original set of flags and those just computed.

As an example, if update_flags contains update_gradients a finite element class will typically require the computation of the inverse of the Jacobian matrix in order to rotate the gradient of shape functions on the reference cell to the real cell. It would then return not just update_gradients, but also update_covariant_transformation, the flag that makes the mapping class produce the inverse of the Jacobian matrix.

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module.

See also: UpdateFlags

Implements FiniteElement< dim, spacedim >.

Definition at line 914 of file fe_system.cc.

template<int dim, int spacedim>

const FiniteElement< dim, spacedim > & FESystem< dim, spacedim >::get_sub_fe	(	const unsigned int	first_component,
		const unsigned int	n_selected_components
	)		const

overridevirtual

Return a reference to a contained finite element that matches the components selected by the given ComponentMask mask.

For an arbitrarily nested FESystem, this function returns the inner-most FiniteElement that matches the given mask. The method fails if the mask does not exactly match one of the contained finite elements. It is most useful if the current object is an FESystem, as the return value can only be this in all other cases.

Note that the returned object can be an FESystem if the mask matches it but not any of the contained objects.

Let us illustrate the function with the an FESystem fe with 7 components:

FESystem<2> fe_velocity(FE_Q<2>(2), 2);
FE_Q<2> fe_pressure(1);
FE_DGP<2> fe_dg(0);
FE_BDM<2> fe_nonprim(1);
FESystem<2> fe(fe_velocity, 1, fe_pressure, 1, fe_dg, 2, fe_nonprim, 1);

The following table lists all possible component masks you can use:

ComponentMask	Result	Description
`[true,true,true,true,true,true,true]`	`FESystem<2>[FESystem<2>[FE_Q<2>(2)^2]-FE_Q<2>(1)-FE_DGP<2>(0)^2-FE_BDM<2>(1)]`	`fe` itself, the whole `FESystem`
`[true,true,false,false,false,false,false]`	`FESystem<2>[FE_Q<2>(2)^2]`	just the `fe_velocity`
`[true,false,false,false,false,false,false]`	`FE_Q<2>(2)`	The first component in `fe_velocity`
`[false,true,false,false,false,false,false]`	`FE_Q<2>(2)`	The second component in `fe_velocity`
`[false,false,true,false,false,false,false]`	`FE_Q<2>(1)`	`fe_pressure`
`[false,false,false,true,false,false,false]`	`FE_DGP<2>(0)`	first copy of `fe_dg`
`[false,false,false,false,true,false,false]`	`FE_DGP<2>(0)`	second copy of `fe_dg`
`[false,false,false,false,false,true,true]`	`FE_BDM<2>(1)`	both components of `fe_nonprim`

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 360 of file fe_system.cc.

template<int dim, int spacedim>

double FESystem< dim, spacedim >::shape_value	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Return the value of the ith shape function at the point p. p is a point on the reference element. Since this finite element is always vector-valued, we return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then throw an exception of type ExcShapeFunctionNotPrimitive.

An ExcUnitShapeValuesDoNotExist is thrown if the shape values of the FiniteElement (corresponding to the ith shape function) depend on the shape of the cell in real space.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 389 of file fe_system.cc.

template<int dim, int spacedim>

double FESystem< dim, spacedim >::shape_value_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

overridevirtual

Return the value of the componentth vector component of the ith shape function at the point p. See the FiniteElement base class for more information about the semantics of this function.

Since this element is vector valued in general, it relays the computation of these values to the base elements.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 405 of file fe_system.cc.

template<int dim, int spacedim>

Tensor< 1, dim > FESystem< dim, spacedim >::shape_grad	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Return the gradient of the ith shape function at the point p. p is a point on the reference element, and likewise the gradient is the gradient on the unit cell with respect to unit cell coordinates. Since this finite element is always vector-valued, we return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non-primitive), then throw an exception of type ExcShapeFunctionNotPrimitive.

An ExcUnitShapeValuesDoNotExist is thrown if the shape values of the FiniteElement (corresponding to the ith shape function) depend on the shape of the cell in real space.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 442 of file fe_system.cc.

template<int dim, int spacedim>

Tensor< 1, dim > FESystem< dim, spacedim >::shape_grad_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

overridevirtual

Return the gradient of the componentth vector component of the ith shape function at the point p. See the FiniteElement base class for more information about the semantics of this function.

Since this element is vector valued in general, it relays the computation of these values to the base elements.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 458 of file fe_system.cc.

template<int dim, int spacedim>

Tensor< 2, dim > FESystem< dim, spacedim >::shape_grad_grad	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Return the tensor of second derivatives of the ith shape function at point p on the unit cell. The derivatives are derivatives on the unit cell with respect to unit cell coordinates. Since this finite element is always vector-valued, we return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non- primitive), then throw an exception of type ExcShapeFunctionNotPrimitive.

An ExcUnitShapeValuesDoNotExist is thrown if the shape values of the FiniteElement (corresponding to the ith shape function) depend on the shape of the cell in real space.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 488 of file fe_system.cc.

template<int dim, int spacedim>

Tensor< 2, dim > FESystem< dim, spacedim >::shape_grad_grad_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

overridevirtual

Return the second derivatives of the componentth vector component of the ith shape function at the point p. See the FiniteElement base class for more information about the semantics of this function.

Since this element is vector valued in general, it relays the computation of these values to the base elements.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 504 of file fe_system.cc.

template<int dim, int spacedim>

Tensor< 3, dim > FESystem< dim, spacedim >::shape_3rd_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Return the tensor of third derivatives of the ith shape function at point p on the unit cell. The derivatives are derivatives on the unit cell with respect to unit cell coordinates. Since this finite element is always vector-valued, we return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non- primitive), then throw an exception of type ExcShapeFunctionNotPrimitive.

An ExcUnitShapeValuesDoNotExist is thrown if the shape values of the FiniteElement (corresponding to the ith shape function) depend on the shape of the cell in real space.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 534 of file fe_system.cc.

template<int dim, int spacedim>

Tensor< 3, dim > FESystem< dim, spacedim >::shape_3rd_derivative_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

overridevirtual

Return the third derivatives of the componentth vector component of the ith shape function at the point p. See the FiniteElement base class for more information about the semantics of this function.

Since this element is vector valued in general, it relays the computation of these values to the base elements.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 550 of file fe_system.cc.

template<int dim, int spacedim>

Tensor< 4, dim > FESystem< dim, spacedim >::shape_4th_derivative	(	const unsigned int	i,
		const Point< dim > &	p
	)		const

overridevirtual

Return the tensor of fourth derivatives of the ith shape function at point p on the unit cell. The derivatives are derivatives on the unit cell with respect to unit cell coordinates. Since this finite element is always vector-valued, we return the value of the only non-zero component of the vector value of this shape function. If the shape function has more than one non-zero component (which we refer to with the term non- primitive), then throw an exception of type ExcShapeFunctionNotPrimitive.

An ExcUnitShapeValuesDoNotExist is thrown if the shape values of the FiniteElement (corresponding to the ith shape function) depend on the shape of the cell in real space.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 580 of file fe_system.cc.

template<int dim, int spacedim>

Tensor< 4, dim > FESystem< dim, spacedim >::shape_4th_derivative_component	(	const unsigned int	i,
		const Point< dim > &	p,
		const unsigned int	component
	)		const

overridevirtual

Return the fourth derivatives of the componentth vector component of the ith shape function at the point p. See the FiniteElement base class for more information about the semantics of this function.

Since this element is vector valued in general, it relays the computation of these values to the base elements.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 596 of file fe_system.cc.

template<int dim, int spacedim>

void FESystem< dim, spacedim >::get_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source,
		FullMatrix< double > &	matrix
	)		const

overridevirtual

Return the matrix interpolating from the given finite element to the present one. The size of the matrix is then dofs_per_cell times source.dofs_per_cell.

These matrices are available if source and destination element are both FESystem elements, have the same number of base elements with same element multiplicity, and if these base elements also implement their get_interpolation_matrix functions. Otherwise, an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented is thrown.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 626 of file fe_system.cc.

template<int dim, int spacedim>

const FiniteElement< dim, spacedim > & FESystem< dim, spacedim >::base_element ( const unsigned int index ) const

overridevirtual

Access to a composing element. The index needs to be smaller than the number of base elements. Note that the number of base elements may in turn be smaller than the number of components of the system element, if the multiplicities are greater than one.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2293 of file fe_system.cc.

template<int dim, int spacedim>

bool FESystem< dim, spacedim >::has_support_on_face	(	const unsigned int	shape_index,
		const unsigned int	face_index
	)		const

overridevirtual

This function returns true, if the shape function shape_index has non-zero function values somewhere on the face face_index.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2304 of file fe_system.cc.

template<int dim, int spacedim>

const FullMatrix< double > & FESystem< dim, spacedim >::get_restriction_matrix	(	const unsigned int	child,
		const RefinementCase< dim > &	refinement_case = `RefinementCase<dim>::isotropic_refinement`
	)		const

overridevirtual

Projection from a fine grid space onto a coarse grid space. Overrides the respective method in FiniteElement, implementing lazy evaluation (initialize when requested).

If this projection operator is associated with a matrix P, then the restriction of this matrix P_i to a single child cell is returned here.

The matrix P is the concatenation or the sum of the cell matrices P_i, depending on the restriction_is_additive_flags. This distinguishes interpolation (concatenation) and projection with respect to scalar products (summation).

Row and column indices are related to coarse grid and fine grid spaces, respectively, consistent with the definition of the associated operator.

If projection matrices are not implemented in the derived finite element class, this function aborts with an exception of type FiniteElement::ExcProjectionVoid. You can check whether this would happen by first calling the restriction_is_implemented() or the isotropic_restriction_is_implemented() function.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 702 of file fe_system.cc.

template<int dim, int spacedim>

const FullMatrix< double > & FESystem< dim, spacedim >::get_prolongation_matrix	(	const unsigned int	child,
		const RefinementCase< dim > &	refinement_case = `RefinementCase<dim>::isotropic_refinement`
	)		const

overridevirtual

Embedding matrix between grids. Overrides the respective method in FiniteElement, implementing lazy evaluation (initialize when queried).

The identity operator from a coarse grid space into a fine grid space is associated with a matrix P. The restriction of this matrix P_i to a single child cell is returned here.

The matrix P is the concatenation, not the sum of the cell matrices P_i. That is, if the same non-zero entry j,k exists in two different child matrices P_i, the value should be the same in both matrices and it is copied into the matrix P only once.

Row and column indices are related to fine grid and coarse grid spaces, respectively, consistent with the definition of the associated operator.

These matrices are used by routines assembling the prolongation matrix for multi-level methods. Upon assembling the transfer matrix between cells using this matrix array, zero elements in the prolongation matrix are discarded and will not fill up the transfer matrix.

If prolongation matrices are not implemented in one of the base finite element classes, this function aborts with an exception of type FiniteElement::ExcEmbeddingVoid. You can check whether this would happen by first calling the prolongation_is_implemented() or the isotropic_prolongation_is_implemented() function.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 798 of file fe_system.cc.

template<int dim, int spacedim>

unsigned int FESystem< dim, spacedim >::face_to_cell_index	(	const unsigned int	face_dof_index,
		const unsigned int	face,
		const bool	face_orientation = `true`,
		const bool	face_flip = `false`,
		const bool	face_rotation = `false`
	)		const

overridevirtual

Given an index in the natural ordering of indices on a face, return the index of the same degree of freedom on the cell.

To explain the concept, consider the case where we would like to know whether a degree of freedom on a face, for example as part of an FESystem element, is primitive. Unfortunately, the is_primitive() function in the FiniteElement class takes a cell index, so we would need to find the cell index of the shape function that corresponds to the present face index. This function does that.

Code implementing this would then look like this:

for (i=0; i<dofs_per_face; ++i)
 if (fe.is_primitive(fe.face_to_cell_index(i, some_face_no)))
  ... do whatever

The function takes additional arguments that account for the fact that actual faces can be in their standard ordering with respect to the cell under consideration, or can be flipped, oriented, etc.

Parameters

face_dof_index	The index of the degree of freedom on a face. This index must be between zero and dofs_per_face.
face	The number of the face this degree of freedom lives on. This number must be between zero and GeometryInfo::faces_per_cell.
face_orientation	One part of the description of the orientation of the face. See GlossFaceOrientation.
face_flip	One part of the description of the orientation of the face. See GlossFaceOrientation.
face_rotation	One part of the description of the orientation of the face. See GlossFaceOrientation.

Returns: The index of this degree of freedom within the set of degrees of freedom on the entire cell. The returned value will be between zero and dofs_per_cell.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 869 of file fe_system.cc.

template<int dim, int spacedim>

Point< dim > FESystem< dim, spacedim >::unit_support_point ( const unsigned int index ) const

overridevirtual

Implementation of the respective function in the base class.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2317 of file fe_system.cc.

template<int dim, int spacedim>

Point< dim-1 > FESystem< dim, spacedim >::unit_face_support_point ( const unsigned int index ) const

overridevirtual

Implementation of the respective function in the base class.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2339 of file fe_system.cc.

template<int dim, int spacedim>

std::pair< Table< 2, bool >, std::vector< unsigned int > > FESystem< dim, spacedim >::get_constant_modes ( ) const

overridevirtual

Return a list of constant modes of the element. The returns table has as many rows as there are components in the element and dofs_per_cell columns. To each component of the finite element, the row in the returned table contains a basis representation of the constant function 1 on the element. Concatenates the constant modes of each base element.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2362 of file fe_system.cc.

template<int dim, int spacedim>

bool FESystem< dim, spacedim >::hp_constraints_are_implemented ( ) const

overridevirtual

Return whether this element implements its hanging node constraints in the new way, which has to be used to make elements "hp compatible".

This function returns true if and only if all its base elements return true for this function.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 1869 of file fe_system.cc.

template<int dim, int spacedim>

void FESystem< dim, spacedim >::get_face_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source,
		FullMatrix< double > &	matrix
	)		const

overridevirtual

Return the matrix interpolating from a face of one element to the face of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face.

Base elements of this element will have to implement this function. They may only provide interpolation matrices for certain source finite elements, for example those from the same family. If they don't implement interpolation from a given element, then they must throw an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented, which will get propagated out from this element.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 1882 of file fe_system.cc.

template<int dim, int spacedim>

void FESystem< dim, spacedim >::get_subface_interpolation_matrix	(	const FiniteElement< dim, spacedim > &	source,
		const unsigned int	subface,
		FullMatrix< double > &	matrix
	)		const

overridevirtual

Return the matrix interpolating from a face of one element to the subface of the neighboring element. The size of the matrix is then source.dofs_per_face times this->dofs_per_face.

Base elements of this element will have to implement this function. They may only provide interpolation matrices for certain source finite elements, for example those from the same family. If they don't implement interpolation from a given element, then they must throw an exception of type FiniteElement<dim,spacedim>::ExcInterpolationNotImplemented, which will get propagated out from this element.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 1991 of file fe_system.cc.

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FESystem< dim, spacedim >::hp_vertex_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

If, on a vertex, several finite elements are active, the hp code first assigns the degrees of freedom of each of these FEs different global indices. It then calls this function to find out which of them should get identical values, and consequently can receive the same global DoF index. This function therefore returns a list of identities between DoFs of the present finite element object with the DoFs of fe_other, which is a reference to a finite element object representing one of the other finite elements active on this particular vertex. The function computes which of the degrees of freedom of the two finite element objects are equivalent, both numbered between zero and the corresponding value of dofs_per_vertex of the two finite elements. The first index of each pair denotes one of the vertex dofs of the present element, whereas the second is the corresponding index of the other finite element.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2220 of file fe_system.cc.

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FESystem< dim, spacedim >::hp_line_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on lines.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2228 of file fe_system.cc.

template<int dim, int spacedim>

std::vector< std::pair< unsigned int, unsigned int > > FESystem< dim, spacedim >::hp_quad_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

Same as hp_vertex_dof_indices(), except that the function treats degrees of freedom on quads.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2238 of file fe_system.cc.

template<int dim, int spacedim>

FiniteElementDomination::Domination FESystem< dim, spacedim >::compare_for_face_domination ( const FiniteElement< dim, spacedim > & fe_other ) const

overridevirtual

Return whether this element dominates the one given as argument when they meet at a common face, whether it is the other way around, whether neither dominates, or if either could dominate.

For a definition of domination, see FiniteElementDomination::Domination and in particular the hp paper.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2248 of file fe_system.cc.

template<int dim, int spacedim>

void FESystem< dim, spacedim >::convert_generalized_support_point_values_to_dof_values	(	const std::vector< Vector< double >> &	support_point_values,
		std::vector< double > &	dof_values
	)		const

overridevirtual

Implementation of the FiniteElement::convert_generalized_support_point_values_to_dof_values() function.

This function simply calls FiniteElement::convert_generalized_support_point_values_to_dof_values of the base elements and re-assembles everything into the output argument. If a base element is non-interpolatory the corresponding dof values are filled with "signaling" NaNs instead.

The function fails if none of the base elements of the FESystem are interpolatory.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2419 of file fe_system.cc.

template<int dim, int spacedim>

std::size_t FESystem< dim, spacedim >::memory_consumption ( ) const

overridevirtual

Determine an estimate for the memory consumption (in bytes) of this object.

This function is made virtual, since finite element objects are usually accessed through pointers to their base class, rather than the class itself.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 2526 of file fe_system.cc.

template<int dim, int spacedim>

std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > FESystem< dim, spacedim >::get_data	(	const UpdateFlags	update_flags,
		const Mapping< dim, spacedim > &	mapping,
		const Quadrature< dim > &	quadrature,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

overrideprotectedvirtual

Create an internal data object and return a pointer to it of which the caller of this function then assumes ownership. This object will then be passed to the FiniteElement::fill_fe_values() every time the finite element shape functions and their derivatives are evaluated on a concrete cell. The object created here is therefore used by derived classes as a place for scratch objects that are used in evaluating shape functions, as well as to store information that can be pre-computed once and re-used on every cell (e.g., for evaluating the values and gradients of shape functions on the reference cell, for later re-use when transforming these values to a concrete cell).

This function is the first one called in the process of initializing a FEValues object for a given mapping and finite element object. The returned object will later be passed to FiniteElement::fill_fe_values() for a concrete cell, which will itself place its output into an object of type internal::FEValuesImplementation::FiniteElementRelatedData. Since there may be data that can already be computed in its final form on the reference cell, this function also receives a reference to the internal::FEValuesImplementation::FiniteElementRelatedData object as its last argument. This output argument is guaranteed to always be the same one when used with the InternalDataBase object returned by this function. In other words, the subdivision of scratch data and final data in the returned object and the output_data object is as follows: If data can be pre- computed on the reference cell in the exact form in which it will later be needed on a concrete cell, then this function should already emplace it in the output_data object. An example are the values of shape functions at quadrature points for the usual Lagrange elements which on a concrete cell are identical to the ones on the reference cell. On the other hand, if some data can be pre-computed to make computations on a concrete cell cheaper, then it should be put into the returned object for later re-use in a derive class's implementation of FiniteElement::fill_fe_values(). An example are the gradients of shape functions on the reference cell for Lagrange elements: to compute the gradients of the shape functions on a concrete cell, one has to multiply the gradients on the reference cell by the inverse of the Jacobian of the mapping; consequently, we cannot already compute the gradients on a concrete cell at the time the current function is called, but we can at least pre-compute the gradients on the reference cell, and store it in the object returned.

An extensive discussion of the interaction between this function and FEValues can be found in the How Mapping, FiniteElement, and FEValues work together documentation module. See also the documentation of the InternalDataBase class.

Parameters

[in]	update_flags	A set of UpdateFlags values that describe what kind of information the FEValues object requests the finite element to compute. This set of flags may also include information that the finite element can not compute, e.g., flags that pertain to data produced by the mapping. An implementation of this function needs to set up all data fields in the returned object that are necessary to produce the finite- element related data specified by these flags, and may already pre- compute part of this information as discussed above. Elements may want to store these update flags (or a subset of these flags) in InternalDataBase::update_each so they know at the time when FiniteElement::fill_fe_values() is called what they are supposed to compute
[in]	mapping	A reference to the mapping used for computing values and derivatives of shape functions.
[in]	quadrature	A reference to the object that describes where the shape functions should be evaluated.
[out]	output_data	A reference to the object that FEValues will use in conjunction with the object returned here and where an implementation of FiniteElement::fill_fe_values() will place the requested information. This allows the current function to already pre-compute pieces of information that can be computed on the reference cell, as discussed above. FEValues guarantees that this output object and the object returned by the current function will always be used together.

Returns: A pointer to an object of a type derived from InternalDataBase and that derived classes can use to store scratch data that can be pre- computed, or for scratch arrays that then only need to be allocated once. The calling site assumes ownership of this object and will delete it when it is no longer necessary.

Implements FiniteElement< dim, spacedim >.

Definition at line 928 of file fe_system.cc.

template<int dim, int spacedim>

std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > FESystem< dim, spacedim >::get_face_data	(	const UpdateFlags	update_flags,
		const Mapping< dim, spacedim > &	mapping,
		const Quadrature< dim-1 > &	quadrature,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

overrideprotectedvirtual

Like get_data(), but return an object that will later be used for evaluating shape function information at quadrature points on faces of cells. The object will then be used in calls to implementations of FiniteElement::fill_fe_face_values(). See the documentation of get_data() for more information.

The default implementation of this function converts the face quadrature into a cell quadrature with appropriate quadrature point locations, and with that calls the get_data() function above that has to be implemented in derived classes.

Parameters

[in]	update_flags	A set of UpdateFlags values that describe what kind of information the FEValues object requests the finite element to compute. This set of flags may also include information that the finite element can not compute, e.g., flags that pertain to data produced by the mapping. An implementation of this function needs to set up all data fields in the returned object that are necessary to produce the finite- element related data specified by these flags, and may already pre- compute part of this information as discussed above. Elements may want to store these update flags (or a subset of these flags) in InternalDataBase::update_each so they know at the time when FiniteElement::fill_fe_face_values() is called what they are supposed to compute
[in]	mapping	A reference to the mapping used for computing values and derivatives of shape functions.
[in]	quadrature	A reference to the object that describes where the shape functions should be evaluated.
[out]	output_data	A reference to the object that FEValues will use in conjunction with the object returned here and where an implementation of FiniteElement::fill_fe_face_values() will place the requested information. This allows the current function to already pre-compute pieces of information that can be computed on the reference cell, as discussed above. FEValues guarantees that this output object and the object returned by the current function will always be used together.

Returns: A pointer to an object of a type derived from InternalDataBase and that derived classes can use to store scratch data that can be pre- computed, or for scratch arrays that then only need to be allocated once. The calling site assumes ownership of this object and will delete it when it is no longer necessary.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 989 of file fe_system.cc.

template<int dim, int spacedim>

std::unique_ptr< typename FiniteElement< dim, spacedim >::InternalDataBase > FESystem< dim, spacedim >::get_subface_data	(	const UpdateFlags	update_flags,
		const Mapping< dim, spacedim > &	mapping,
		const Quadrature< dim-1 > &	quadrature,
		::internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

overrideprotectedvirtual

Like get_data(), but return an object that will later be used for evaluating shape function information at quadrature points on children of faces of cells. The object will then be used in calls to implementations of FiniteElement::fill_fe_subface_values(). See the documentation of get_data() for more information.

The default implementation of this function converts the face quadrature into a cell quadrature with appropriate quadrature point locations, and with that calls the get_data() function above that has to be implemented in derived classes.

Parameters

[in]	update_flags	A set of UpdateFlags values that describe what kind of information the FEValues object requests the finite element to compute. This set of flags may also include information that the finite element can not compute, e.g., flags that pertain to data produced by the mapping. An implementation of this function needs to set up all data fields in the returned object that are necessary to produce the finite- element related data specified by these flags, and may already pre- compute part of this information as discussed above. Elements may want to store these update flags (or a subset of these flags) in InternalDataBase::update_each so they know at the time when FiniteElement::fill_fe_subface_values() is called what they are supposed to compute
[in]	mapping	A reference to the mapping used for computing values and derivatives of shape functions.
[in]	quadrature	A reference to the object that describes where the shape functions should be evaluated.
[out]	output_data	A reference to the object that FEValues will use in conjunction with the object returned here and where an implementation of FiniteElement::fill_fe_subface_values() will place the requested information. This allows the current function to already pre-compute pieces of information that can be computed on the reference cell, as discussed above. FEValues guarantees that this output object and the object returned by the current function will always be used together.

Returns: A pointer to an object of a type derived from InternalDataBase and that derived classes can use to store scratch data that can be pre- computed, or for scratch arrays that then only need to be allocated once. The calling site assumes ownership of this object and will delete it when it is no longer necessary.

Reimplemented from FiniteElement< dim, spacedim >.

Definition at line 1050 of file fe_system.cc.

template<int dim, int spacedim>

template<int dim_1>

void FESystem< dim, spacedim >::compute_fill	(	const Mapping< dim, spacedim > &	mapping,
		const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const unsigned int	sub_no,
		const Quadrature< dim_1 > &	quadrature,
		const CellSimilarity::Similarity	cell_similarity,
		const typename Mapping< dim, spacedim >::InternalDataBase &	mapping_internal,
		const typename FiniteElement< dim, spacedim >::InternalDataBase &	fe_data,
		const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &	mapping_data,
		internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &	output_data
	)		const

protected

Do the work for the three fill_fe*_values functions.

Calls (among other things) fill_fe_([sub]face)_values of the base elements. Calls fill_fe_values if face_no==invalid_face_no and sub_no==invalid_face_no; calls fill_fe_face_values if face_no==invalid_face_no and sub_no!=invalid_face_no; and calls fill_fe_subface_values if face_no!=invalid_face_no and sub_no!=invalid_face_no.

Definition at line 1200 of file fe_system.cc.

template<int dim, int spacedim>

void FESystem< dim, spacedim >::initialize	(	const std::vector< const FiniteElement< dim, spacedim > * > &	fes,
		const std::vector< unsigned int > &	multiplicities
	)

private

This function is simply singled out of the constructors since there are several of them. It sets up the index table for the system as well as restriction and prolongation matrices.

Definition at line 1606 of file fe_system.cc.

template<int dim, int spacedim>

void FESystem< dim, spacedim >::build_interface_constraints ( )

private

Used by initialize.

Definition at line 1402 of file fe_system.cc.

template<int dim, int spacedim>

template<int structdim>

std::vector< std::pair< unsigned int, unsigned int > > FESystem< dim, spacedim >::hp_object_dof_identities ( const FiniteElement< dim, spacedim > & fe_other ) const

private

A function that computes the hp_vertex_dof_identities(), hp_line_dof_identities(), or hp_quad_dof_identities(), depending on the value of the template parameter.

Definition at line 2108 of file fe_system.cc.

Member Data Documentation

template<int dim, int spacedim = dim>

const unsigned int FESystem< dim, spacedim >::invalid_face_number = numbers::invalid_unsigned_int

staticprivate

Value to indicate that a given face or subface number is invalid.

Definition at line 1110 of file fe_system.h.

template<int dim, int spacedim = dim>

std::vector<std::pair<std::unique_ptr<const FiniteElement<dim, spacedim> >, unsigned int> > FESystem< dim, spacedim >::base_elements

private

Pointers to underlying finite element objects.

This object contains a pointer to each contributing element of a mixed discretization and its multiplicity. It is created by the constructor and constant afterwards.

Definition at line 1121 of file fe_system.h.

template<int dim, int spacedim = dim>

std::vector<std::vector<std::size_t> > FESystem< dim, spacedim >::generalized_support_points_index_table

private

An index table that maps generalized support points of a base element to the vector of generalized support points of the FE System. It holds true that

auto n = generalized_support_points_index_table[i][j];
generalized_support_points[n] ==
        base_elements[i].generalized_support_points[j];

for each base element (indexed by i) and each g. s. point of the base element (index by j).

Definition at line 1135 of file fe_system.h.

The documentation for this class was generated from the following files:

deal.II/fe/fe.h
deal.II/fe/fe_system.h
/mnt/data/darndt/Sources/dealii-clang-6.0.0/source/fe/fe_system.cc

Classes

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Protected Member Functions

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Private Attributes

Static Private Attributes

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Detailed Description

template<int dim, int spacedim = dim> class FESystem< dim, spacedim >

FESystem, components and blocks

Internal information on numbering of degrees of freedom

Constructor & Destructor Documentation

How to use this constructor

Member Function Documentation

Member Data Documentation

template<int dim, int spacedim = dim>
class FESystem< dim, spacedim >