cartesian/prodcut space of finite element functions on a hybrid 2D mesh. More...

#include <projects/dpg/product_fe_space.h>

Public Types
using	scalar = SCALAR

Public Member Functions
	ProductUniformFESpace ()=default

	ProductUniformFESpace (const ProductUniformFESpace &)=delete

	ProductUniformFESpace (ProductUniformFESpace &&) noexcept=default

ProductUniformFESpace &	operator= (const ProductUniformFESpace &)=delete

ProductUniformFESpace &	operator= (ProductUniformFESpace &&) noexcept=default

	ProductUniformFESpace (std::shared_ptr< const lf::mesh::Mesh > mesh_p, std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > > rfs_tria_v, std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > > rfs_quad_v, std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > > rfs_edge_v, std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > > rfs_point_v)
	Main construcotr: sets up the local-to-global index mapping (dofhandler) More...

std::shared_ptr< const lf::mesh::Mesh >	Mesh () const
	acess to underlying mesh More...

const ProductUniformFEDofHandler &	LocGlobMap () const
	access to associated local-to-global map More...

lf::fe::ScalarReferenceFiniteElement< SCALAR > const *	ShapeFunctionLayout (lf::base::RefEl ref_el_type, size_type component) const
	access to shape function layout More...

size_type	NumRefShapeFunctions (lf::base::RefEl ref_el_type, size_type component) const
	number of interior shape functions associated to entities of various types for a given component More...

size_type	NumComponents () const
	number of components of the product space More...

std::shared_ptr< const lf::uscalfe::UniformScalarFESpace< SCALAR > >	ComponentFESpace (size_type component) const
	Constructs a lf::uscalfe::UniformScalarFESpace that describes the finite element space associated to a certain component. More...

virtual	~ProductUniformFESpace ()=default
	no special destructor More...

Private Member Functions
void	init ()

Private Attributes
std::shared_ptr< const lf::mesh::Mesh >	mesh_p_

std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > >	rfs_tria_v_

std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > >	rfs_quad_v_

std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > >	rfs_edge_v_

std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > >	rfs_point_v_

std::vector< size_type >	num_rsf_node_

std::vector< size_type >	num_rsf_edge_

std::vector< size_type >	num_rsf_tria_

std::vector< size_type >	num_rsf_quad_

std::unique_ptr< ProductUniformFEDofHandler >	dofh_p_

size_type	numComponents_ = 0

Detailed Description

template<typename SCALAR>
class projects::dpg::ProductUniformFESpace< SCALAR >

cartesian/prodcut space of finite element functions on a hybrid 2D mesh.

Template Parameters

SCALAR underlying scalar type for all components, usually 'double'

This class provides functionality similar to the class lf::uscalfe::UniformScalarFESpace for product/cartesian finite element spaces. These spaces are of the form

\[ U = U_0 \times U_1 \times \dots \times U_{n-1} \]

where each of the \( U_i \) is a function space of scalar valued functions (see the description in ProductUniformFEDofHandler).

To allow this, this class provides some further member functions that give extra information about the contained FE spaces. It furthermore uses a ProductUniformFEDofHandler internally resulting in a different dof ordering.

Furthermore, this class also weakens some constraints on the shape function layouts compared to the lf::uscalfe::UniformScalarFESpace in order to represent function spaces as they occur in the description of DPG methods:

There may be multiple global shape functions associated with the same vertex (usually they will belong to different components)
Some components may not specify any local shape functions on triangles or quadrilaterals, but only on segments.

Note: Some of the pointers may be NULL, which indicates that the shape function descriptions are missing.

Definition at line 58 of file product_fe_space.h.

Member Typedef Documentation

◆ scalar

template<typename SCALAR >

using projects::dpg::ProductUniformFESpace< SCALAR >::scalar = SCALAR

Definition at line 60 of file product_fe_space.h.

Constructor & Destructor Documentation

◆ ProductUniformFESpace() [1/4]

template<typename SCALAR >

projects::dpg::ProductUniformFESpace< SCALAR >::ProductUniformFESpace ( )

default

default constructor

Note: creates an invalid object that can not be used.

◆ ProductUniformFESpace() [2/4]

template<typename SCALAR >

projects::dpg::ProductUniformFESpace< SCALAR >::ProductUniformFESpace ( const ProductUniformFESpace< SCALAR > & )

delete

◆ ProductUniformFESpace() [3/4]

template<typename SCALAR >

projects::dpg::ProductUniformFESpace< SCALAR >::ProductUniformFESpace ( ProductUniformFESpace< SCALAR > && )

defaultnoexcept

◆ ProductUniformFESpace() [4/4]

template<typename SCALAR >

projects::dpg::ProductUniformFESpace< SCALAR >::ProductUniformFESpace	(	std::shared_ptr< const lf::mesh::Mesh >	mesh_p,
		std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > >	rfs_tria_v,
		std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > >	rfs_quad_v,
		std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > >	rfs_edge_v,
		std::vector< std::shared_ptr< const lf::fe::ScalarReferenceFiniteElement< SCALAR > > >	rfs_point_v
	)

inline

Main construcotr: sets up the local-to-global index mapping (dofhandler)

Parameters

mesh_p	shared pointer to underlying mesh (imutable)
rfs_tria_v	vector of shared pointers to layout description of reference shape functions on triangular cells for each component.
rfs_quad_v	vector of shared pointers to layout description of reference shape functions on quadrilateral cells for each component.
rfs_edge_v	vector of shared pointers to layout description of reference shape functions on the edges for each component.

The schemes for local shape functions belonging to some component have to satisfy the following compatibility conditions.

The number of interior shape functions for edges of triangles and quadrilaterals must agree.

Note: none of the shape function layouts needs to be specified; just pass a null pointer. This will restrict the applicability of the resulting finite element space object.

Definition at line 92 of file product_fe_space.h.

References projects::dpg::ProductUniformFESpace< SCALAR >::init(), projects::dpg::ProductUniformFESpace< SCALAR >::numComponents_, and projects::dpg::ProductUniformFESpace< SCALAR >::rfs_tria_v_.

◆ ~ProductUniformFESpace()

template<typename SCALAR >

virtual projects::dpg::ProductUniformFESpace< SCALAR >::~ProductUniformFESpace ( )

virtualdefault

no special destructor

Member Function Documentation

◆ ComponentFESpace()

template<typename SCALAR >

std::shared_ptr< const lf::uscalfe::UniformScalarFESpace< SCALAR > > projects::dpg::ProductUniformFESpace< SCALAR >::ComponentFESpace ( size_type component ) const

inline

Constructs a lf::uscalfe::UniformScalarFESpace that describes the finite element space associated to a certain component.

Note: The resulting FESpace has no more information about the other components

Warning: For some components the construction of the lf::uscalfe::UniformScalarFESpace may be impossible, since some of the constraints regarding the shape function layouts were weakened.

Definition at line 163 of file product_fe_space.h.

References projects::dpg::ProductUniformFESpace< SCALAR >::mesh_p_, projects::dpg::ProductUniformFESpace< SCALAR >::rfs_edge_v_, projects::dpg::ProductUniformFESpace< SCALAR >::rfs_point_v_, projects::dpg::ProductUniformFESpace< SCALAR >::rfs_quad_v_, and projects::dpg::ProductUniformFESpace< SCALAR >::rfs_tria_v_.

Referenced by projects::dpg::InitEssentialConditionsFromFunctions().

◆ init()

template<typename SCALAR >

void projects::dpg::ProductUniformFESpace< SCALAR >::init

private

Initialization of class member variables and consistency checks

Definition at line 210 of file product_fe_space.h.

References lf::base::RefEl::kPoint(), lf::base::RefEl::kQuad(), lf::base::RefEl::kSegment(), and lf::base::RefEl::kTria().

Referenced by projects::dpg::ProductUniformFESpace< SCALAR >::ProductUniformFESpace().

◆ LocGlobMap()

template<typename SCALAR >

const ProductUniformFEDofHandler & projects::dpg::ProductUniformFESpace< SCALAR >::LocGlobMap ( ) const

inline

access to associated local-to-global map

Returns: a reference to the ProductUniformFEDofHandler object (immutable)

Definition at line 126 of file product_fe_space.h.

References projects::dpg::ProductUniformFESpace< SCALAR >::dofh_p_, and projects::dpg::ProductUniformFESpace< SCALAR >::mesh_p_.

Referenced by projects::dpg::InitEssentialConditionsFromFunctions().

◆ Mesh()

template<typename SCALAR >

std::shared_ptr< const lf::mesh::Mesh > projects::dpg::ProductUniformFESpace< SCALAR >::Mesh ( ) const

inline

acess to underlying mesh

Returns: a shared pointer to the mesh

Definition at line 118 of file product_fe_space.h.

References projects::dpg::ProductUniformFESpace< SCALAR >::mesh_p_.

◆ NumComponents()

template<typename SCALAR >

size_type projects::dpg::ProductUniformFESpace< SCALAR >::NumComponents ( ) const

inline

number of components of the product space

Definition at line 152 of file product_fe_space.h.

References projects::dpg::ProductUniformFESpace< SCALAR >::numComponents_.

◆ NumRefShapeFunctions()

template<typename SCALAR >

size_type projects::dpg::ProductUniformFESpace< SCALAR >::NumRefShapeFunctions	(	lf::base::RefEl	ref_el_type,
		size_type	component
	)		const

number of interior shape functions associated to entities of various types for a given component

Definition at line 380 of file product_fe_space.h.

References lf::base::RefEl::kPoint(), lf::base::RefEl::kQuad(), lf::base::RefEl::kSegment(), and lf::base::RefEl::kTria().

◆ operator=() [1/2]

template<typename SCALAR >

ProductUniformFESpace & projects::dpg::ProductUniformFESpace< SCALAR >::operator= ( const ProductUniformFESpace< SCALAR > & )

delete

◆ operator=() [2/2]

template<typename SCALAR >

ProductUniformFESpace & projects::dpg::ProductUniformFESpace< SCALAR >::operator= ( ProductUniformFESpace< SCALAR > && )

defaultnoexcept

◆ ShapeFunctionLayout()

template<typename SCALAR >

lf::fe::ScalarReferenceFiniteElement< SCALAR > const * projects::dpg::ProductUniformFESpace< SCALAR >::ShapeFunctionLayout	(	lf::base::RefEl	ref_el_type,
		size_type	component
	)		const

access to shape function layout

Parameters

ref_el_type	type of entit, can be anything except for lf::base::RefEl::kPoint()
component	index of the component whose shape function layout is returned.

Warning: NULL pointers may be returned by this method in case a finite element specification was not given for a particular topological type of entity and e particular component.

Definition at line 348 of file product_fe_space.h.

References lf::base::RefEl::kPoint(), lf::base::RefEl::kQuad(), lf::base::RefEl::kSegment(), and lf::base::RefEl::kTria().