Represents a reference element with all its properties. More...

#include <lf/base/ref_el.h>

Public Types
using	dim_t = unsigned int

template<RefElType type>
using	NodeCoordVector
	Type of the node coordinate iterator that is returned from NodeCoords()

Public Member Functions
constexpr	RefEl (RefElType type) noexcept
	Create a RefEl from a lf::base::RefElType enum.

constexpr	RefEl (const RefEl &)=default
	Default copy constructor.

constexpr	RefEl (RefEl &&)=default
	Default move constructor.

constexpr RefEl &	operator= (const RefEl &rhs)
	Default copy assignment operator.

constexpr RefEl &	operator= (RefEl &&rhs) noexcept
	Default move assignment operator.

constexpr dim_t	Dimension () const
	Return the dimension of this reference element.

constexpr size_type	NumNodes () const
	The number of nodes of this reference element.

const Eigen::MatrixXd &	NodeCoords () const
	Get the coordinates of the nodes of this reference element.

constexpr size_type	NumSubEntities (dim_t sub_codim) const
	Get the number of sub-entities of this RefEl with the given codimension.

constexpr RefEl	SubType (dim_t sub_codim, dim_t sub_index) const
	Return the RefEl of the sub-entity with codim `sub_codim` and index `sub_index`.

constexpr sub_idx_t	SubSubEntity2SubEntity (dim_t sub_codim, sub_idx_t sub_index, dim_t sub_rel_codim, sub_idx_t sub_rel_index) const
	Identifies sub-entities of sub-entities (so-called sub-sub-entities) with sub-entities.

std::string	ToString () const
	Return a string representation of this Reference element.

constexpr	operator RefElType () const
	Conversion operator, converts this RefEl to a lf::base::RefElType enum.

constexpr unsigned int	Id () const
	Return a unique id for this reference element.

	~RefEl ()=default

Static Public Member Functions
static constexpr RefEl	kPoint ()
	Returns the (0-dimensional) reference point.

static constexpr RefEl	kSegment ()
	Returns the (1-dimensional) reference segment.

static constexpr RefEl	kTria ()
	Returns the reference triangle.

static constexpr RefEl	kQuad ()
	Returns the reference quadrilateral.

template<RefElType type>
static const std::vector< NodeCoordVector< type > > &	NodeCoords ()
	Get the coordinates of the nodes of a reference element.

Private Attributes
RefElType	type_

Static Private Attributes
static const Eigen::MatrixXd	ncoords_point_dynamic_ = Eigen::VectorXd(0)

static const Eigen::MatrixXd	ncoords_segment_dynamic_

static const Eigen::MatrixXd	ncoords_tria_dynamic_

static const Eigen::MatrixXd	ncoords_quad_dynamic_

static const std::vector< Eigen::Matrix< double, 0, 1 > >	ncoords_point_static_

static const std::vector< Eigen::Matrix< double, 1, 1 > >	ncoords_segment_static_

static const std::vector< Eigen::Vector2d >	ncoords_tria_static_

static const std::vector< Eigen::Vector2d >	ncoords_quad_static_

static constexpr std::array< std::array< base::dim_t, 2 >, 3 >	sub_sub_entity_index_tria_ = {{{0, 1}, {1, 2}, {2, 0}}}

static constexpr std::array< std::array< base::dim_t, 2 >, 4 >	sub_sub_entity_index_quad_ = {{{0, 1}, {1, 2}, {2, 3}, {3, 0}}}

Related Symbols
(Note that these are not member symbols.)
void	PrintInfo (std::ostream &stream, const RefEl &ref_el, int output_ctrl=0)
	Diagnostic output operator. Prints info about a reference element.

Detailed Description

Represents a reference element with all its properties.

Every entity of a mesh in LehrFEM++ is the image of a reference element under an entity-specific (smooth) transformation (which is described by the lf::mesh::Geometry class). This transformation describes the shape of the actual entity, but also the algebraic relations between its sub-entities. For details consult Lecture Document Subsection 10.2.2

On a more fundamental level objects of this class distinguish the topological type of a mesh entity, see Lecture Document Paragraph 2.7.2.9.

Summing up, the reference element serves two main purposes:

it defines the local topology of the mesh in terms of incidence relations of the entities. For instance the reference element defines the number of edges of a cell.
it fixes the parameter domain for the mapping describing the shape of the entitiy.

There is a fixed number of reference elements. This class has a static member field for every type of reference element:

RefEl::kPoint() is the Reference element of every point/node in a mesh. The point itself doesn't have any sub-entities.
RefEl::kSegment() is the reference element of every edge in a mesh. It connects two points with each other.
RefEl::kTria() is the reference element of every triangular element in the mesh. It has three segments (codim=1) and three points (codim=2) as sub-entities.
RefEl::kQuad() is the reference element of every quadrilateral element in the mesh. It has four segments (codim=1) and four points (codim=2) as sub-entities.

Usage of this class

You can create arbitrary many instances of this class, but every instance is equal to one of the four types of reference elements that are exposed as static member fields (see above).
Instances of this class are copyable, moveable, assignable and have a number of member functions that give information about the reference element they represent.
This class is very lightweight, in fact sizeof(RefEl) == sizeof(char). It can be copied around as needed.

    // Example usage
    auto triangle = RefEl::kTria();
    assert(triangle.Dimension() == 2);
    assert(triangle.NumNodes() == 3);
    assert(triangle.NodeCoords().col(0) == Eigen::Vector2d(0, 0));
    assert(triangle.NumSubEntities(1) ==
           3);  // Triangle has 3 sub-entities with codim=1 (all segments)
 
    auto point =
        triangle.SubType(2, 0);  // RefEl of sub-entity with codim=2, index=0
    assert(point == RefEl::kPoint());

Definition at line 109 of file ref_el.h.

Member Typedef Documentation

◆ dim_t

using lf::base::RefEl::dim_t = unsigned int

Definition at line 132 of file ref_el.h.

◆ NodeCoordVector

template<RefElType type>

using lf::base::RefEl::NodeCoordVector

Initial value:

Eigen::Matrix<double, internal::DimensionImpl(type), 1>

Type of the node coordinate iterator that is returned from NodeCoords()

Definition at line 138 of file ref_el.h.

Constructor & Destructor Documentation

◆ RefEl() [1/3]

constexpr lf::base::RefEl::RefEl ( RefElType type )

inlineexplicitconstexprnoexcept

Create a RefEl from a lf::base::RefElType enum.

Parameters

type	The type of the Reference Element

Definition at line 175 of file ref_el.h.

Referenced by lf::assemble::DynamicFEDofHandler::GlobalDofIndices(), lf::assemble::DynamicFEDofHandler::InteriorGlobalDofIndices(), lf::mesh::test_utils::isWatertightMesh(), kPoint(), kQuad(), kSegment(), kTria(), lf::assemble::DynamicFEDofHandler::NumInteriorDofs(), lf::assemble::DynamicFEDofHandler::NumLocalDofs(), lf::mesh::Mesh::PrintInfo(), lf::mesh::Entity::PrintInfo(), lf::fe::test_utils::ComplexScalarReferenceFiniteElement< SCALAR >::RefEl(), lf::io::writeMatlab(), lf::io::writeMatplotlib(), and lf::io::writeTikZ().

◆ RefEl() [2/3]

constexpr lf::base::RefEl::RefEl ( const RefEl & )

constexprdefault

Default copy constructor.

◆ RefEl() [3/3]

constexpr lf::base::RefEl::RefEl ( RefEl && )

constexprdefault

Default move constructor.

◆ ~RefEl()

lf::base::RefEl::~RefEl ( )

default

Member Function Documentation

◆ Dimension()

constexpr dim_t lf::base::RefEl::Dimension ( ) const

inlineconstexpr

Return the dimension of this reference element.

0 for a RefEl::kPoint()
1 for a RefEl::kSegment()
2 for a RefEl::kTria()
2 for a RefEl::kQuad()

Definition at line 204 of file ref_el.h.

References type_.

Referenced by lf::mesh::hybrid2d::MeshFactory::AddEntity(), lf::mesh::test_utils::checkGeometryOrientation(), lf::mesh::test_utils::checkLocalTopology(), lf::mesh::test_utils::checkRelCodim(), lf::refinement::Hybrid2DRefinementPattern::ChildPolygons(), lf::fe::ScalarReferenceFiniteElement< SCALAR >::Dimension(), lf::refinement::Hybrid2DRefinementPattern::NumChildren(), NumSubEntities(), lf::fe::MeshFunctionGradFE< SCALAR_FE, SCALAR_COEFF >::operator()(), lf::mesh::utils::MeshFunctionGlobal< F >::operator()(), lf::mesh::Entity::PrintInfo(), PrintInfo(), lf::quad::QuadRule::QuadRule(), SubSubEntity2SubEntity(), and SubType().

◆ Id()

constexpr unsigned int lf::base::RefEl::Id ( ) const

inlineconstexpr

Return a unique id for this reference element.

The id numbers are contiguous over the known entity types starting from 0. Thus, this identification number can be used as an array index, if one wants to store information for (all) type of entities.

Usage example

    std::vector<quad::QuadRule> quad_rules(4);
    quad_rules[base::RefEl::kTria().Id()] = quad::make_QuadRule(base::RefEl::kTria(), 5);
    quad_rules[base::RefEl::kQuad().Id()] = quad::make_QuadRule(base::RefEl::kQuad(), 5);

Definition at line 494 of file ref_el.h.

References type_.

Referenced by lf::quad::QuadRuleCache::Get(), and lf::io::VtkWriter::WriteCellData().

◆ kPoint()

static constexpr RefEl lf::base::RefEl::kPoint ( )

inlinestaticconstexpr

Returns the (0-dimensional) reference point.

Definition at line 144 of file ref_el.h.

References lf::base::kPoint, and RefEl().

Referenced by lf::mesh::hybrid2d::MeshFactory::AddPoint(), lf::geometry::test_utils::checkChildGeometry(), lf::geometry::test_utils::checkSubGeometry(), lf::geometry::Point::ChildGeometry(), lf::refinement::Hybrid2DRefinementPattern::ChildPolygons(), lf::fe::HierarchicScalarFESpace< SCALAR >::HierarchicScalarFESpace(), lf::uscalfe::UniformScalarFESpace< SCALAR >::InitDofHandler(), lf::io::GmshReader::InitGmshFile(), lf::io::GmshReader::InitGmshFile(), lf::refinement::Hybrid2DRefinementPattern::NumChildren(), lf::assemble::UniformFEDofHandler::NumCoveredDofs(), lf::assemble::UniformFEDofHandler::NumInteriorDofs(), lf::uscalfe::UniformScalarFESpace< SCALAR >::NumRefShapeFunctions(), lf::refinement::EntityCenterPositionSelector< POSPRED >::operator()(), lf::refinement::MeshHierarchy::PerformRefinement(), lf::mesh::hybrid2d::Point::Point(), lf::uscalfe::PrintInfo(), lf::mesh::Entity::PrintInfo(), PrintInfo(), lf::fe::FePoint< SCALAR >::RefEl(), lf::geometry::Point::RefEl(), lf::mesh::hybrid2d::Point::RefEl(), lf::io::RefElOf(), lf::io::RefElOf(), lf::uscalfe::UniformScalarFESpace< SCALAR >::ShapeFunctionLayout(), SubType(), lf::assemble::UniformFEDofHandler::UniformFEDofHandler(), lf::geometry::Volume(), lf::io::VtkWriter::WriteCellData(), lf::io::writeMatplotlib(), and lf::io::writeTikZ().

◆ kQuad()

static constexpr RefEl lf::base::RefEl::kQuad ( )

inlinestaticconstexpr

Returns the reference quadrilateral.

Node numbering with (2D) node coordinates and segment orientation

Definition at line 169 of file ref_el.h.

References lf::base::kQuad, and RefEl().

Referenced by lf::mesh::utils::TorusMeshBuilder::Build(), lf::mesh::utils::TPQuadMeshBuilder::Build(), lf::geometry::test_utils::checkChildGeometry(), lf::geometry::QuadO1::ChildGeometry(), lf::geometry::Parallelogram::ChildGeometry(), lf::geometry::QuadO2::ChildGeometry(), lf::refinement::Hybrid2DRefinementPattern::ChildPolygons(), lf::uscalfe::LinearFELaplaceElementMatrix::Eval(), lf::uscalfe::LinearFELocalLoadVector< SCALAR, FUNCTOR >::Eval(), lf::mesh::test_utils::GenerateHybrid2DTestMesh(), lf::fe::HierarchicScalarFESpace< SCALAR >::Init(), lf::uscalfe::UniformScalarFESpace< SCALAR >::InitDofHandler(), lf::io::GmshReader::InitGmshFile(), lf::io::GmshReader::InitGmshFile(), lf::assemble::UniformFEDofHandler::initIndexArrays(), lf::quad::make_QuadQR_EdgeMidpointRule(), lf::quad::make_QuadQR_MidpointRule(), lf::quad::make_QuadQR_P4O4(), lf::quad::make_QuadRule(), lf::refinement::Hybrid2DRefinementPattern::NumChildren(), lf::assemble::UniformFEDofHandler::NumCoveredDofs(), lf::assemble::UniformFEDofHandler::NumInteriorDofs(), lf::uscalfe::UniformScalarFESpace< SCALAR >::NumRefShapeFunctions(), lf::refinement::EntityCenterPositionSelector< POSPRED >::operator()(), lf::uscalfe::PrintInfo(), lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider(), lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider(), lf::fe::FeHierarchicQuad< SCALAR >::RefEl(), lf::geometry::QuadO1::RefEl(), lf::geometry::Parallelogram::RefEl(), lf::geometry::QuadO2::RefEl(), lf::mesh::hybrid2d::Quadrilateral::RefEl(), lf::uscalfe::FeLagrangeO1Quad< SCALAR >::RefEl(), lf::uscalfe::FeLagrangeO2Quad< SCALAR >::RefEl(), lf::uscalfe::FeLagrangeO3Quad< SCALAR >::RefEl(), lf::io::RefElOf(), lf::io::RefElOf(), lf::refinement::MeshHierarchy::RefineMarked(), lf::uscalfe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ScalarLoadElementVectorProvider(), lf::uscalfe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ScalarLoadElementVectorProvider(), lf::uscalfe::UniformScalarFESpace< SCALAR >::ShapeFunctionLayout(), lf::assemble::UniformFEDofHandler::UniformFEDofHandler(), lf::geometry::Volume(), lf::io::VtkWriter::WriteCellData(), lf::io::writeMatlab(), lf::io::writeMatplotlib(), and lf::io::writeTikZ().

◆ kSegment()

static constexpr RefEl lf::base::RefEl::kSegment ( )

inlinestaticconstexpr

Returns the (1-dimensional) reference segment.

Node numbering with (1D) node coordinates

Definition at line 153 of file ref_el.h.

References lf::base::kSegment, and RefEl().

Referenced by lf::mesh::hybrid2d::MeshFactory::AddEntity(), lf::mesh::utils::TPTriagMeshBuilder::Build(), lf::geometry::test_utils::checkChildGeometry(), lf::geometry::SegmentO1::ChildGeometry(), lf::geometry::SegmentO2::ChildGeometry(), lf::refinement::Hybrid2DRefinementPattern::ChildPolygons(), lf::uscalfe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::Eval(), lf::uscalfe::ScalarLoadEdgeVectorProvider< SCALAR, FUNCTOR, EDGESELECTOR >::Eval(), lf::fe::FeHierarchicQuad< SCALAR >::FeHierarchicQuad(), lf::fe::FeHierarchicTria< SCALAR >::FeHierarchicTria(), lf::uscalfe::UniformScalarFESpace< SCALAR >::InitDofHandler(), lf::io::GmshReader::InitGmshFile(), lf::io::GmshReader::InitGmshFile(), lf::uscalfe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::isActive(), lf::fe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::isActive(), lf::quad::make_QuadRule(), lf::refinement::Hybrid2DRefinementPattern::NumChildren(), lf::assemble::UniformFEDofHandler::NumCoveredDofs(), lf::assemble::UniformFEDofHandler::NumInteriorDofs(), lf::uscalfe::UniformScalarFESpace< SCALAR >::NumRefShapeFunctions(), lf::refinement::EntityCenterPositionSelector< POSPRED >::operator()(), lf::uscalfe::PrintInfo(), lf::fe::FeHierarchicSegment< SCALAR >::RefEl(), lf::geometry::SegmentO1::RefEl(), lf::geometry::SegmentO2::RefEl(), lf::mesh::hybrid2d::Segment::RefEl(), lf::uscalfe::FeLagrangeO1Segment< SCALAR >::RefEl(), lf::uscalfe::FeLagrangeO2Segment< SCALAR >::RefEl(), lf::uscalfe::FeLagrangeO3Segment< SCALAR >::RefEl(), lf::io::RefElOf(), lf::io::RefElOf(), lf::refinement::MeshHierarchy::RefineMarked(), lf::uscalfe::UniformScalarFESpace< SCALAR >::ShapeFunctionLayout(), SubType(), lf::assemble::UniformFEDofHandler::UniformFEDofHandler(), lf::geometry::Volume(), lf::io::VtkWriter::WriteCellData(), lf::io::writeMatlab(), lf::io::writeMatplotlib(), and lf::io::writeTikZ().

◆ kTria()

static constexpr RefEl lf::base::RefEl::kTria ( )

inlinestaticconstexpr

Returns the reference triangle.

Node numbering with (2D) node coordinates and segment orientation.

Definition at line 161 of file ref_el.h.

References lf::base::kTria, and RefEl().

Referenced by lf::mesh::utils::TPTriagMeshBuilder::Build(), lf::geometry::test_utils::checkChildGeometry(), lf::geometry::TriaO1::ChildGeometry(), lf::geometry::TriaO2::ChildGeometry(), lf::refinement::Hybrid2DRefinementPattern::ChildPolygons(), lf::uscalfe::LinearFELaplaceElementMatrix::Eval(), lf::uscalfe::LinearFELocalLoadVector< SCALAR, FUNCTOR >::Eval(), lf::mesh::test_utils::GenerateHybrid2DTestMesh(), lf::fe::HierarchicScalarFESpace< SCALAR >::Init(), lf::uscalfe::UniformScalarFESpace< SCALAR >::InitDofHandler(), lf::io::GmshReader::InitGmshFile(), lf::io::GmshReader::InitGmshFile(), lf::assemble::UniformFEDofHandler::initIndexArrays(), lf::quad::make_QuadRule(), lf::quad::make_QuadRuleNodal(), lf::quad::make_TriaQR_EdgeMidpointRule(), lf::quad::make_TriaQR_MidpointRule(), lf::quad::make_TriaQR_P6O4(), lf::refinement::MeshHierarchy::MeshHierarchy(), lf::refinement::Hybrid2DRefinementPattern::NumChildren(), lf::assemble::UniformFEDofHandler::NumCoveredDofs(), lf::assemble::UniformFEDofHandler::NumInteriorDofs(), lf::uscalfe::UniformScalarFESpace< SCALAR >::NumRefShapeFunctions(), lf::refinement::EntityCenterPositionSelector< POSPRED >::operator()(), lf::uscalfe::PrintInfo(), lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider(), lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::ReactionDiffusionElementMatrixProvider(), lf::fe::FeHierarchicTria< SCALAR >::RefEl(), lf::geometry::TriaO1::RefEl(), lf::geometry::TriaO2::RefEl(), lf::mesh::hybrid2d::Triangle::RefEl(), lf::uscalfe::FeLagrangeO1Tria< SCALAR >::RefEl(), lf::uscalfe::FeLagrangeO2Tria< SCALAR >::RefEl(), lf::uscalfe::FeLagrangeO3Tria< SCALAR >::RefEl(), lf::io::RefElOf(), lf::io::RefElOf(), lf::refinement::MeshHierarchy::RefineMarked(), lf::uscalfe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ScalarLoadElementVectorProvider(), lf::uscalfe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ScalarLoadElementVectorProvider(), lf::uscalfe::UniformScalarFESpace< SCALAR >::ShapeFunctionLayout(), lf::assemble::UniformFEDofHandler::UniformFEDofHandler(), lf::geometry::Volume(), lf::io::VtkWriter::WriteCellData(), lf::io::writeMatlab(), lf::io::writeMatplotlib(), lf::io::VtkWriter::WritePointData(), and lf::io::writeTikZ().

◆ NodeCoords() [1/2]

template<RefElType type>

static const std::vector< NodeCoordVector< type > > & lf::base::RefEl::NodeCoords ( )

inlinestatic

Get the coordinates of the nodes of a reference element.

Template Parameters

type	The `RefElType` of the reference element for which the node coordinates should be returned, see usage below.

Returns: a std::vector with NumNodes() elements. Every Element is a fixed-size column vector (e.g. Eigen::Matrix<double,1,1> for a segment or Eigen::Matrix<double,2,1> for a triangle/quadrilateral)

Usage example:

  // If RefEl not known at compile time:
  auto nodeCoordsDynamic = RefEl::kTria().NodeCoords();
 
  // If RefEl known at compile time:
  std::vector<Eigen::Vector2d> nodeCoordsCompiletime =
      RefEl::NodeCoords<RefEl::kTria()>();

Remarks: This function template can only be called if the type of the reference element is known at compile time. The advantage of this method over NodeCoords() const is, that it returns a vector of fixed-size vectors that are allocated on the stack.

Definition at line 274 of file ref_el.h.

References lf::base::kPoint, lf::base::kQuad, lf::base::kSegment, lf::base::kTria, ncoords_point_static_, ncoords_quad_static_, ncoords_segment_static_, and ncoords_tria_static_.

◆ NodeCoords() [2/2]

const Eigen::MatrixXd & lf::base::RefEl::NodeCoords ( ) const

inline

Get the coordinates of the nodes of this reference element.

Returns: a matrix of size Dimension() x NumNodes() that contains the the coordinates of every node as a column vector.

Remarks: This method is not optimal from a performance point of view because the matrix is allocated on the heap. If the type of the RefEl is known at compile time, use the static NodeCoords() function instead.

  // If RefEl not known at compile time:
  auto nodeCoordsDynamic = RefEl::kTria().NodeCoords();
 
  // If RefEl known at compile time:
  std::vector<Eigen::Vector2d> nodeCoordsCompiletime =
      RefEl::NodeCoords<RefEl::kTria()>();

Definition at line 241 of file ref_el.h.

References lf::base::kPoint, lf::base::kQuad, lf::base::kSegment, lf::base::kTria, ncoords_point_dynamic_, ncoords_quad_dynamic_, ncoords_segment_dynamic_, ncoords_tria_dynamic_, and type_.

Referenced by lf::mesh::test_utils::checkGeometryOrientation(), lf::geometry::test_utils::checkSubGeometry(), lf::geometry::Corners(), lf::fe::DiffusionElementMatrixProvider< SCALAR, DIFF_COEFF >::Eval(), lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::Eval(), lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::Eval(), lf::uscalfe::FeLagrangeO1Tria< SCALAR >::EvaluationNodes(), lf::uscalfe::FeLagrangeO1Quad< SCALAR >::EvaluationNodes(), lf::uscalfe::FeLagrangeO1Segment< SCALAR >::EvaluationNodes(), lf::mesh::test_utils::isWatertightMesh(), lf::quad::make_QuadRuleNodal(), lf::geometry::Geometry::PrintInfo(), lf::mesh::Mesh::PrintInfo(), lf::mesh::Entity::PrintInfo(), PrintInfo(), lf::io::VtkWriter::WriteCellData(), lf::io::writeMatplotlib(), and lf::io::writeTikZ().

◆ NumNodes()

constexpr size_type lf::base::RefEl::NumNodes ( ) const

inlineconstexpr

The number of nodes of this reference element.

Remarks: This is a shortcut for calling NumSubEntities(Dimension())

Definition at line 213 of file ref_el.h.

References lf::base::kPoint, lf::base::kQuad, lf::base::kSegment, lf::base::kTria, and type_.

Referenced by lf::mesh::hybrid2d::MeshFactory::AddEntity(), lf::uscalfe::LinearFELocalLoadVector< SCALAR, FUNCTOR >::Eval(), lf::mesh::test_utils::isWatertightMesh(), lf::quad::make_QuadRuleNodal(), lf::uscalfe::FeLagrangeO1Tria< SCALAR >::NumEvaluationNodes(), lf::uscalfe::FeLagrangeO1Quad< SCALAR >::NumEvaluationNodes(), lf::uscalfe::FeLagrangeO1Segment< SCALAR >::NumEvaluationNodes(), PrintInfo(), and lf::io::writeTikZ().

◆ NumSubEntities()

constexpr size_type lf::base::RefEl::NumSubEntities ( dim_t sub_codim ) const

inlineconstexpr

Get the number of sub-entities of this RefEl with the given codimension.

Parameters

sub_codim The codimension of the subEntities that should be counted.

Examples

a segment has two points as codim=1 sub-entities, therefore RefEl::kSegment().NumSubEntities(1) == 2
a Triangle has three subentities of codim=1 (all Segments), therefore RefEl::kTria().NumSubEntities(1) == 3
a Triangle has three subEntities of codim=2 (all Points), therefore RefEl::kTria().NumSubEntities(2) == 3

Definition at line 308 of file ref_el.h.

References Dimension(), lf::base::kQuad, lf::base::kSegment, lf::base::kTria, and type_.

Referenced by lf::refinement::Hybrid2DRefinementPattern::Hybrid2DRefinementPattern(), lf::fe::ScalarReferenceFiniteElement< SCALAR >::NumRefShapeFunctions(), lf::mesh::Entity::PrintInfo(), PrintInfo(), lf::refinement::Hybrid2DRefinementPattern::setAnchor(), SubSubEntity2SubEntity(), and SubType().

◆ operator RefElType()

constexpr lf::base::RefEl::operator RefElType ( ) const

inlineconstexpr

Conversion operator, converts this RefEl to a lf::base::RefElType enum.

Usage example

Definition at line 481 of file ref_el.h.

References type_.

◆ operator=() [1/2]

constexpr RefEl & lf::base::RefEl::operator= ( const RefEl & rhs )

inlineconstexpr

Default copy assignment operator.

Definition at line 185 of file ref_el.h.

References type_.

◆ operator=() [2/2]

constexpr RefEl & lf::base::RefEl::operator= ( RefEl && rhs )

inlineconstexprnoexcept

Default move assignment operator.

Definition at line 191 of file ref_el.h.

References type_.

◆ SubSubEntity2SubEntity()

constexpr sub_idx_t lf::base::RefEl::SubSubEntity2SubEntity	(	dim_t	sub_codim,
		sub_idx_t	sub_index,
		dim_t	sub_rel_codim,
		sub_idx_t	sub_rel_index ) const

inlineconstexpr

Identifies sub-entities of sub-entities (so-called sub-sub-entities) with sub-entities.

Parameters

sub_codim	The codimension of the sub-entity.
sub_index	The zero-based index of the sub-entity.
sub_rel_codim	The codimension of the sub-sub-entity w.r.t. the sub-entity identified by `sub_codim` and `sub_index`.
sub_rel_index	The index of the sub-sub-entity w.r.t. the sub-entity identified by `sub_codim` and `sub_index`.

Returns: The index of the sub-sub-entity w.r.t. this RefEl.

Note: the argument sub_rel_codim is a relative co-dimension.; the argument sub_rel_index is a local index in the sub-entity.

Conventions

For a triangle (the arrow indicates the induced orientation of the edge)
- edge 0 connects vertices 0 -> 1
- edge 1 connects vertices 1 -> 2
- edge 2 connects vertices 2 -> 0
For a quadrilateral
- edge 0 connects vertices 0 -> 1
- edge 1 connects vertices 1 -> 2
- edge 2 connects vertices 2 -> 3
- edge 3 connects vertices 3 -> 0

Examples

The sub-entity of a RefEl::kTria() with sub_codim=1, sub_index=1 is a RefEl::kSegment() that connects node 1 with node 2. The (sub-)sub-entity of this segment with codim sub_rel_codim=1 and sub-index sub_rel_index=0 (both w.r.t. to the segment) is the first point of the segment, i.e. node 1. Therefore SubSubEntity2SubEntity(1,1,1,0) == 1
Similarly, for sub_rel_index=1: SubSubEntity2SubEntity(1,1,1,1) == 2

Definition at line 412 of file ref_el.h.

References Dimension(), lf::base::kPoint, lf::base::kQuad, lf::base::kTria, NumSubEntities(), sub_sub_entity_index_quad_, sub_sub_entity_index_tria_, SubType(), and type_.

◆ SubType()

constexpr RefEl lf::base::RefEl::SubType	(	dim_t	sub_codim,
		dim_t	sub_index ) const

inlineconstexpr

Return the RefEl of the sub-entity with codim sub_codim and index sub_index.

Parameters

sub_codim	The codimension of the sub-entity (w.r.t. `Dimension()`). Should be `<= Dimension()`.
sub_index	The zero-based index of the sub-entity. `sub_index` should be smaller than `NumSumEntities(sub_codim)`

Examples:

A triangle has three codim=2 entities which are all points, therefore RefEl::kTria().SubType(2,i) == RefEl::kPoint() for i=0,1,2.
A quadrilateral has four codim=1 entities which are all segments, therefore RefEl::kQuad().SubType(1,i) == RefEl::kSegment() for i=0,1,2,3.
The codim=0 subEntity of a triangle is the triangle itself, therefore RefEl::kTria().SubType(0,0) == RefEl::kTria().

See also: NumSubEntities() const to get the number of sub entities of a given codimension

Definition at line 351 of file ref_el.h.

References Dimension(), kPoint(), kSegment(), and NumSubEntities().

Referenced by PrintInfo(), and SubSubEntity2SubEntity().

◆ ToString()

std::string lf::base::RefEl::ToString ( ) const

inline

Return a string representation of this Reference element.

This string is supposed to described the topological type of the entity: NODE, EDGE (2 nodes), TRIA (3-node triangle), QUAD (4-node quadrilateral)

Definition at line 458 of file ref_el.h.

References lf::base::kPoint, lf::base::kQuad, lf::base::kSegment, lf::base::kTria, and type_.

Friends And Related Symbol Documentation

◆ PrintInfo()

void PrintInfo	(	std::ostream &	stream,
		const RefEl &	ref_el,
		int	output_ctrl = 0 )

Parameters

ref_el	The reference element to print info about
stream	The stream to which this function should output
output_ctrl	Determines the level of detail with which the output is printed to `o`

Output levels

output_ctrl = 0: Type of reference element, dimension and number of nodes
output_ctrl > 0: The above and number of subentities and their types for each codimension
output_ctrl > 10: The above and type of subentity for each subentities in each codimension.
output_ctrl > 20: The above and coordinates of the points of the reference element

Definition at line 17 of file ref_el.cc.

References Dimension(), kPoint(), NodeCoords(), NumNodes(), NumSubEntities(), SubType(), and ToString().

Member Data Documentation

◆ ncoords_point_dynamic_

const Eigen::MatrixXd lf::base::RefEl::ncoords_point_dynamic_ = Eigen::VectorXd(0)

staticprivate

Definition at line 111 of file ref_el.h.

Referenced by NodeCoords().

◆ ncoords_point_static_

const std::vector<Eigen::Matrix<double, 0, 1> > lf::base::RefEl::ncoords_point_static_

staticprivate

Definition at line 117 of file ref_el.h.

Referenced by NodeCoords().

◆ ncoords_quad_dynamic_

const Eigen::MatrixXd lf::base::RefEl::ncoords_quad_dynamic_

staticprivate

Initial value:

=

(Eigen::MatrixXd{2, 4} << 0, 1, 1, 0, 0, 0, 1, 1).finished()

Definition at line 114 of file ref_el.h.

Referenced by NodeCoords().

◆ ncoords_quad_static_

const std::vector<Eigen::Vector2d> lf::base::RefEl::ncoords_quad_static_

staticprivate

Definition at line 120 of file ref_el.h.

Referenced by NodeCoords().

◆ ncoords_segment_dynamic_

const Eigen::MatrixXd lf::base::RefEl::ncoords_segment_dynamic_

staticprivate

Initial value:

=

Eigen::Vector2d(0, 1).transpose()

Definition at line 112 of file ref_el.h.

Referenced by NodeCoords().

◆ ncoords_segment_static_

const std::vector<Eigen::Matrix<double, 1, 1> > lf::base::RefEl::ncoords_segment_static_

staticprivate

Definition at line 118 of file ref_el.h.

Referenced by NodeCoords().

◆ ncoords_tria_dynamic_

const Eigen::MatrixXd lf::base::RefEl::ncoords_tria_dynamic_

staticprivate

Initial value:

=

(Eigen::MatrixXd{2, 3} << 0, 1, 0, 0, 0, 1).finished()

Definition at line 113 of file ref_el.h.

Referenced by NodeCoords().

◆ ncoords_tria_static_

const std::vector<Eigen::Vector2d> lf::base::RefEl::ncoords_tria_static_

staticprivate

Definition at line 119 of file ref_el.h.

Referenced by NodeCoords().

◆ sub_sub_entity_index_quad_

constexpr std::array<std::array<base::dim_t, 2>, 4> lf::base::RefEl::sub_sub_entity_index_quad_ = {{{0, 1}, {1, 2}, {2, 3}, {3, 0}}}

staticconstexprprivate

Definition at line 129 of file ref_el.h.

Referenced by SubSubEntity2SubEntity().

◆ sub_sub_entity_index_tria_

constexpr std::array<std::array<base::dim_t, 2>, 3> lf::base::RefEl::sub_sub_entity_index_tria_ = {{{0, 1}, {1, 2}, {2, 0}}}

staticconstexprprivate

Definition at line 127 of file ref_el.h.

Referenced by SubSubEntity2SubEntity().

◆ type_

RefElType lf::base::RefEl::type_

private

Definition at line 123 of file ref_el.h.

Referenced by Dimension(), Id(), NodeCoords(), NumNodes(), NumSubEntities(), operator RefElType(), operator=(), operator=(), SubSubEntity2SubEntity(), and ToString().

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

/__w/lehrfempp/lehrfempp/lib/lf/base/ref_el.h
/__w/lehrfempp/lehrfempp/lib/lf/base/ref_el.cc

Public Types

Public Member Functions

Static Public Member Functions

Private Attributes

Static Private Attributes

Related Symbols

Detailed Description

Usage of this class

Member Typedef Documentation

◆ dim_t

◆ NodeCoordVector

Constructor & Destructor Documentation

◆ RefEl() [1/3]

◆ RefEl() [2/3]

◆ RefEl() [3/3]

◆ ~RefEl()

Member Function Documentation

◆ Dimension()

◆ Id()

Usage example

◆ kPoint()

◆ kQuad()

Node numbering with (2D) node coordinates and segment orientation

◆ kSegment()

Node numbering with (1D) node coordinates

◆ kTria()

Node numbering with (2D) node coordinates and segment orientation.

◆ NodeCoords() [1/2]

Usage example:

◆ NodeCoords() [2/2]

◆ NumNodes()

◆ NumSubEntities()

Examples

◆ operator RefElType()

Usage example

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ SubSubEntity2SubEntity()

Conventions

Examples

◆ SubType()

Examples:

◆ ToString()

Friends And Related Symbol Documentation

◆ PrintInfo()

Output levels

Member Data Documentation

◆ ncoords_point_dynamic_

◆ ncoords_point_static_

◆ ncoords_quad_dynamic_

◆ ncoords_quad_static_

◆ ncoords_segment_dynamic_

◆ ncoords_segment_static_

◆ ncoords_tria_dynamic_

◆ ncoords_tria_static_

◆ sub_sub_entity_index_quad_

◆ sub_sub_entity_index_tria_

◆ type_