Interface class representing a topological entity in a cellular complex More...

#include <lf/mesh/entity.h>

Inheritance diagram for lf::mesh::Entity:

Public Member Functions
virtual unsigned	Codim () const =0
	The codimension of this entity w.r.t. the Mesh.dimMesh() of the owning mesh manager.

virtual std::span< const Entity *const >	SubEntities (unsigned rel_codim) const =0
	Return all sub entities of this entity that have the given codimension (w.r.t. this entity!)

virtual std::span< const Orientation >	RelativeOrientations () const =0
	return span of relative orientations of sub-entities of the next higher co-dimension.

virtual const geometry::Geometry *	Geometry () const =0
	Describes the geometry of this entity.

virtual base::RefEl	RefEl () const =0
	Describes the reference element type of this entity.

virtual bool	operator== (const Entity &rhs) const =0
	Check if two entities are the same.

bool	operator!= (const Entity &rhs) const
	Check if two entities are different.

virtual	~Entity ()=default
	Virtual Destructor.

Protected Member Functions
	Entity ()=default

	Entity (const Entity &)=default

	Entity (Entity &&)=default

Entity &	operator= (const Entity &)=default

Entity &	operator= (Entity &&)=default

Related Symbols
(Note that these are not member symbols.)
void	PrintInfo (std::ostream &stream, const lf::mesh::Entity &e, int output_ctrl=0)
	Prints info about an entity.

Detailed Description

Interface class representing a topological entity in a cellular complex

Example: a 2D hybrid mesh consists of cells (entities of co-dimension 0), edges (entities of co-dimension 1), and nodes (entities of co-dimension 2). The set of these entities endowed with incidence relations defines the topology of the mesh.

The core purpose of this class is to provide interface definitions for accessing incidence relations and geometry information. This interface applies to all (topological) types of entities.

Further information can be found in Subsection 2.7.2.2 of the Lecture Document

Definition at line 42 of file entity.h.

Constructor & Destructor Documentation

◆ Entity() [1/3]

lf::mesh::Entity::Entity ( )

protecteddefault

◆ Entity() [2/3]

lf::mesh::Entity::Entity ( const Entity & )

protecteddefault

◆ Entity() [3/3]

lf::mesh::Entity::Entity ( Entity && )

protecteddefault

◆ ~Entity()

virtual lf::mesh::Entity::~Entity ( )

virtualdefault

Virtual Destructor.

Member Function Documentation

◆ Codim()

virtual unsigned lf::mesh::Entity::Codim ( ) const

pure virtual

The codimension of this entity w.r.t. the Mesh.dimMesh() of the owning mesh manager.

Implemented in lf::mesh::hybrid2d::Point, lf::mesh::hybrid2d::Quadrilateral, lf::mesh::hybrid2d::Segment, and lf::mesh::hybrid2d::Triangle.

Referenced by lf::mesh::utils::CodimMeshDataSet< T >::DefinedOn(), and lf::mesh::utils::AllCodimMeshDataSet< T >::operator()().

◆ Geometry()

virtual const geometry::Geometry * lf::mesh::Entity::Geometry ( ) const

pure virtual

Describes the geometry of this entity.

Returns: A pointer to a Geometry object that will remain valid for as long as the Mesh remains valid.

Why does this member function return a pointer instead of a reference? One reason is that entities without a geometric shape are conceivable as building block of a "mesh graph", where only topological information matters. Another reason is that during the construction of a mesh, it turns out to be convenient to build entities "without geometry" first and then endow them with geometric information. A nullptr is a good way to indicate missing geometric information.

Implemented in lf::mesh::hybrid2d::Point, lf::mesh::hybrid2d::Quadrilateral, lf::mesh::hybrid2d::Segment, and lf::mesh::hybrid2d::Triangle.

Referenced by lf::mesh::test_utils::checkGeometryOrientation(), lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::Eval(), lf::uscalfe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::Eval(), lf::fe::DiffusionElementMatrixProvider< SCALAR, DIFF_COEFF >::Eval(), lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::Eval(), lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::Eval(), lf::uscalfe::LinearFELaplaceElementMatrix::Eval(), lf::uscalfe::LinearFELocalLoadVector< SCALAR, FUNCTOR >::Eval(), lf::uscalfe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::Eval(), lf::uscalfe::ScalarLoadEdgeVectorProvider< SCALAR, FUNCTOR, EDGESELECTOR >::Eval(), lf::fe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::Eval(), lf::fe::ScalarLoadEdgeVectorProvider< SCALAR, FUNCTOR, EDGESELECTOR >::Eval(), lf::fe::MeshFunctionGradFE< SCALAR_FE, SCALAR_COEFF >::operator()(), lf::refinement::EntityCenterPositionSelector< POSPRED >::operator()(), lf::mesh::utils::MeshFunctionGlobal< F >::operator()(), and PrintInfo().

◆ operator!=()

bool lf::mesh::Entity::operator!= ( const Entity & rhs ) const

inline

Check if two entities are different.

See also: Entity::operator==

Definition at line 141 of file entity.h.

References operator==().

◆ operator=() [1/2]

Entity & lf::mesh::Entity::operator= ( const Entity & )

protecteddefault

◆ operator=() [2/2]

Entity & lf::mesh::Entity::operator= ( Entity && )

protecteddefault

◆ operator==()

virtual bool lf::mesh::Entity::operator== ( const Entity & rhs ) const

pure virtual

Check if two entities are the same.

Parameters

rhs	Check if this entity is the same as the rhs entity.

Note: The behavior of this method is undefined if the rhs entity belongs to a different Mesh.

Implemented in lf::mesh::hybrid2d::Point, lf::mesh::hybrid2d::Quadrilateral, lf::mesh::hybrid2d::Segment, and lf::mesh::hybrid2d::Triangle.

Referenced by operator!=().

◆ RefEl()

virtual base::RefEl lf::mesh::Entity::RefEl ( ) const

pure virtual

Describes the reference element type of this entity.

Returns: An object of type lf::base::RefEl.

Implemented in lf::mesh::hybrid2d::Point, lf::mesh::hybrid2d::Quadrilateral, lf::mesh::hybrid2d::Segment, and lf::mesh::hybrid2d::Triangle.

Referenced by lf::mesh::test_utils::checkGeometryOrientation(), lf::mesh::test_utils::checkLocalTopology(), lf::mesh::test_utils::checkRelCodim(), lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >::Eval(), lf::uscalfe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::Eval(), lf::fe::DiffusionElementMatrixProvider< SCALAR, DIFF_COEFF >::Eval(), lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >::Eval(), lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::Eval(), lf::uscalfe::LinearFELaplaceElementMatrix::Eval(), lf::uscalfe::LinearFELocalLoadVector< SCALAR, FUNCTOR >::Eval(), lf::uscalfe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::Eval(), lf::uscalfe::ScalarLoadEdgeVectorProvider< SCALAR, FUNCTOR, EDGESELECTOR >::Eval(), lf::fe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::Eval(), lf::fe::ScalarLoadEdgeVectorProvider< SCALAR, FUNCTOR, EDGESELECTOR >::Eval(), lf::uscalfe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::isActive(), lf::fe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >::isActive(), lf::uscalfe::UniformScalarFESpace< SCALAR >::NumRefShapeFunctions(), lf::fe::MeshFunctionGradFE< SCALAR_FE, SCALAR_COEFF >::operator()(), lf::refinement::EntityCenterPositionSelector< POSPRED >::operator()(), lf::mesh::utils::MeshFunctionGlobal< F >::operator()(), lf::mesh::operator<<(), PrintInfo(), and lf::uscalfe::UniformScalarFESpace< SCALAR >::ShapeFunctionLayout().

◆ RelativeOrientations()

virtual std::span< const Orientation > lf::mesh::Entity::RelativeOrientations ( ) const

pure virtual

return span of relative orientations of sub-entities of the next higher co-dimension.

The corners of every entity are numbered and, thus, define a local orientation of the sub-entitites of co-dimension+1 as explained in Lecture Document Remark 2.7.2.15. This local orientation need not agree with the intrinsic orientation of that sub-entity as given by its own numbering of corners. Such a possible mismatch is detected by this function.

Implemented in lf::mesh::hybrid2d::Point, lf::mesh::hybrid2d::Quadrilateral, lf::mesh::hybrid2d::Segment, and lf::mesh::hybrid2d::Triangle.

◆ SubEntities()

virtual std::span< const Entity *const > lf::mesh::Entity::SubEntities ( unsigned rel_codim ) const

pure virtual

Return all sub entities of this entity that have the given codimension (w.r.t. this entity!)

Parameters

rel_codim The relative co-dimension w.r.t. this entity

Returns: A span of pointers to the sub-entities with the specified relative co-dimension

Implicitly this function defines the numbering of sub-entities, see lf::base::RefEl and Lecture Document Paragraph 2.7.2.14.

Note

For a mesh covering a manifold of dimension 2, we have the following cases

For a cell (co-dimension 0 entity), the cell itself is a subentity of relative co-dimension 0, the edges have relative co-dimension 1, and the vertices relative co-dimension 2: in this case the usual co-dimension agrees with the relative co-dimension.
For an edge (co-dimension 1 entity), the edge itself is the only sub-entity with relative co-dimension 0, and the endpoints are the sub-entitities of relative co-dimension 1.

The lifetime of the returned span equals the lifetime of the Parent Entity.

Demonstration of usage

bool checkLocalTopology(const Entity &e) {
  // Obtain basic information about current Entity
  const lf::base::RefEl ref_el = e.RefEl();
  const lf::base::dim_t dimension = ref_el.Dimension();
  // What this function does in the case of a 2D cell entity (dimension = 2):
  // It runs through all edges (co-dimension = 1), fetches their endnodes
  // (co-dimension again 1 relative to an edge) and test whether they
  // are also sub-entities of co-dimension 2 of the cell.
 
  // Co-dimensions of sub-entities run from 1 to dimension
  for (lf::base::dim_t sub_codim = 1; sub_codim <= dimension; sub_codim++) {
    // Number of sub-entities with relative co-dimensjon sub_codim
    const lf::base::size_type num_sub_entities =
        ref_el.NumSubEntities(sub_codim);
    // Obtain sequence of pointers to sub-entities of co-dimension sub_codim
    std::span<const Entity *const> sub_ent_range = e.SubEntities(sub_codim);
    // Run through sub-entities
    lf::base::size_type sub_ent_cnt{0};
    for (const lf::mesh::Entity *sub_ent : sub_ent_range) {
      const lf::base::RefEl sub_ref_el = sub_ent->RefEl();
      const lf::base::dim_t sub_dim = sub_ref_el.Dimension();
      if (sub_dim != dimension - sub_codim) return false;
      // The sub-entity has further sub-entities of codimension 1 to sub_dim
      for (lf::base::dim_t sub_sub_codim = 1; sub_sub_codim <= sub_dim;
           sub_sub_codim++) {
        std::span<const Entity *const> sub_sub_ent_range =
            sub_ent->SubEntities(sub_sub_codim);
        for (const lf::mesh::Entity *sub_sub_ent : sub_sub_ent_range) {
          // The entity pointed to by sub_sub_ent has co-dimension
          // sub_codim + sub_sub_codim w.r.t. the entity referenced by e
          // Hence get all corresponding sub-entities of e
          std::span<const Entity *const> e_sub_sub_range =
              e.SubEntities(sub_codim + sub_sub_codim);
          // See whether we find sub_sub_ent in this range
          int found = 0;  // Count how many times we find the sub-entity
          for (const Entity *e_sub_sub : e_sub_sub_range) {
            if (e_sub_sub == sub_sub_ent) found++;
          }
          // Any sub-entity should occur exactly once.
          if (found != 1) return false;
        }
      }
      sub_ent_cnt++;
    }  // end loop over sub-entities
    if (num_sub_entities != sub_ent_cnt) return false;
  }
  return true;
}  // end checklocalTopology

Use of this method is also shown in Lecture Document Example 2.7.2.12.

Implemented in lf::mesh::hybrid2d::Point, lf::mesh::hybrid2d::Quadrilateral, lf::mesh::hybrid2d::Segment, and lf::mesh::hybrid2d::Triangle.

Referenced by lf::mesh::test_utils::checkGeometryOrientation(), lf::mesh::test_utils::checkLocalTopology(), lf::mesh::test_utils::checkRelCodim(), and PrintInfo().

Friends And Related Symbol Documentation

◆ PrintInfo()

void PrintInfo	(	std::ostream &	stream,
		const lf::mesh::Entity &	e,
		int	output_ctrl = 0 )

Parameters

e	The entity to print info about
output_ctrl	controls the level of output (see below)
stream	The stream to which this function should output

Output levels

output_ctrl == 0: Entity type is printed
output_ctrl > 10: The above and information of codimensions
output_ctrl > 50: The above and information about subentities
output_ctrl > 90: The above and coordinates

Definition at line 74 of file print_info.cc.

References lf::base::RefEl::Dimension(), Geometry(), lf::geometry::Geometry::Global(), lf::base::RefEl::kPoint(), lf::base::RefEl::NodeCoords(), lf::base::RefEl::NumSubEntities(), RefEl(), lf::base::RefEl::RefEl(), and SubEntities().

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

/__w/lehrfempp/lehrfempp/lib/lf/mesh/entity.h
/__w/lehrfempp/lehrfempp/lib/lf/mesh/utils/print_info.h

Public Member Functions

Protected Member Functions

Related Symbols

Detailed Description

Constructor & Destructor Documentation

◆ Entity() [1/3]

◆ Entity() [2/3]

◆ Entity() [3/3]

◆ ~Entity()

Member Function Documentation

◆ Codim()

◆ Geometry()

◆ operator!=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ RefEl()

◆ RelativeOrientations()

◆ SubEntities()

Demonstration of usage

Friends And Related Symbol Documentation

◆ PrintInfo()

Output levels