#include <deal.II/fe/mapping_q1.h>

Inheritance diagram for MappingQ1< dim, spacedim >:

Public Member Functions
	MappingQ1 ()

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

Public Member Functions inherited from MappingQGeneric< dim, dim >
	MappingQGeneric (const unsigned int polynomial_degree)

	MappingQGeneric (const MappingQGeneric< dim, spacedim > &mapping)

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

unsigned int	get_degree () const

virtual bool	preserves_vertex_locations () const override

virtual Point< spacedim >	transform_unit_to_real_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< dim > &p) const override

virtual Point< dim >	transform_real_to_unit_cell (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p) const override

virtual void	transform (const ArrayView< const Tensor< 1, dim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 1, spacedim >> &output) const override

virtual void	transform (const ArrayView< const DerivativeForm< 1, dim, spacedim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 2, spacedim >> &output) const override

virtual void	transform (const ArrayView< const Tensor< 2, dim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 2, spacedim >> &output) const override

virtual void	transform (const ArrayView< const DerivativeForm< 2, dim, spacedim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 3, spacedim >> &output) const override

virtual void	transform (const ArrayView< const Tensor< 3, dim >> &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 3, spacedim >> &output) const override

virtual UpdateFlags	requires_update_flags (const UpdateFlags update_flags) const override

virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase >	get_data (const UpdateFlags, const Quadrature< dim > &quadrature) const override

virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase >	get_face_data (const UpdateFlags flags, const Quadrature< dim - 1 > &quadrature) const override

virtual std::unique_ptr< typename Mapping< dim, spacedim >::InternalDataBase >	get_subface_data (const UpdateFlags flags, const Quadrature< dim - 1 > &quadrature) const override

virtual CellSimilarity::Similarity	fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const CellSimilarity::Similarity cell_similarity, const Quadrature< dim > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override

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 typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override

virtual void	fill_fe_subface_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const Quadrature< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, ::internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const override

Public Member Functions inherited from Mapping< dim, spacedim >
virtual	~Mapping () override=default

virtual std::array< Point< spacedim >, GeometryInfo< dim >::vertices_per_cell >	get_vertices (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const

virtual Point< spacedim >	get_center (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const bool map_center_of_reference_cell=true) const

virtual BoundingBox< spacedim >	get_bounding_box (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const

virtual bool	preserves_vertex_locations () const =0

Point< dim - 1 >	project_real_point_to_unit_point_on_face (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Point< spacedim > &p) 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 (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

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

void	list_subscribers () const

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

Additional Inherited Members
Static Public Member Functions inherited from Mapping< dim, spacedim >
static ::ExceptionBase &	ExcInvalidData ()

static ::ExceptionBase &	ExcTransformationFailed ()

static ::ExceptionBase &	ExcDistortedMappedCell (Point< spacedim > arg1, double arg2, int arg3)

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)

Protected Member Functions inherited from MappingQGeneric< dim, dim >
virtual std::vector< Point< spacedim > >	compute_mapping_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell) const

Point< dim >	transform_real_to_unit_cell_internal (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Point< spacedim > &p, const Point< dim > &initial_p_unit) const

Point< 1 >	transform_real_to_unit_cell_internal (const Triangulation< 1, 1 >::cell_iterator &cell, const Point< 1 > &p, const Point< 1 > &initial_p_unit) const

Point< 2 >	transform_real_to_unit_cell_internal (const Triangulation< 2, 2 >::cell_iterator &cell, const Point< 2 > &p, const Point< 2 > &initial_p_unit) const

Point< 3 >	transform_real_to_unit_cell_internal (const Triangulation< 3, 3 >::cell_iterator &cell, const Point< 3 > &p, const Point< 3 > &initial_p_unit) const

Point< 1 >	transform_real_to_unit_cell_internal (const Triangulation< 1, 2 >::cell_iterator &cell, const Point< 2 > &p, const Point< 1 > &initial_p_unit) const

Point< 2 >	transform_real_to_unit_cell_internal (const Triangulation< 2, 3 >::cell_iterator &cell, const Point< 3 > &p, const Point< 2 > &initial_p_unit) const

Point< 1 >	transform_real_to_unit_cell_internal (const Triangulation< 1, 3 >::cell_iterator &, const Point< 3 > &, const Point< 1 > &) const

virtual void	add_line_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim >> &a) const

virtual void	add_quad_support_points (const typename Triangulation< dim, spacedim >::cell_iterator &cell, std::vector< Point< spacedim >> &a) const

void	add_quad_support_points (const Triangulation< 3, 3 >::cell_iterator &cell, std::vector< Point< 3 >> &a) const

void	add_quad_support_points (const Triangulation< 2, 3 >::cell_iterator &cell, std::vector< Point< 3 >> &a) const

Interface with FEValues
Protected Attributes inherited from MappingQGeneric< dim, dim >
const unsigned int	polynomial_degree

QGaussLobatto< 1 >	line_support_points

std::vector< Table< 2, double > >	support_point_weights_perimeter_to_interior

Table< 2, double >	support_point_weights_cell

Detailed Description

template<int dim, int spacedim = dim>
class MappingQ1< dim, spacedim >

Implementation of a \(d\)-linear mapping from the reference cell to a general quadrilateral/hexahedron.

The mapping implemented by this class maps the reference (unit) cell to a general grid cell with straight lines in \(d\) dimensions. (Note, however, that in 3D the faces of a general, trilinearly mapped cell may be curved, even if the edges are not). This is the standard mapping used for polyhedral domains. It is also the mapping used throughout deal.II for many functions that come in two variants, one that allows to pass a mapping argument explicitly and one that simply falls back to the MappingQ1 class declared here. (Or, in fact, to an object of kind MappingQGeneric(1), which implements exactly the functionality of this class.)

The shape functions for this mapping are the same as for the finite element FE_Q of polynomial degree 1. Therefore, coupling these two yields an isoparametric element.

Note: This class is, in all reality, nothing more than a different name for calling MappingQGeneric with a polynomial degree of one as argument.

Author: Guido Kanschat, 2000, 2001; Ralf Hartmann, 2000, 2001, 2005, Wolfgang Bangerth, 2015

Definition at line 57 of file mapping_q1.h.

Constructor & Destructor Documentation

◆ MappingQ1()

template<int dim, int spacedim>

MappingQ1< dim, spacedim >::MappingQ1

Default constructor.

Definition at line 48 of file mapping_q1.cc.

Member Function Documentation

◆ clone()

template<int dim, int spacedim>

std::unique_ptr< Mapping< dim, spacedim > > MappingQ1< dim, spacedim >::clone ( ) const

overridevirtual

Return a pointer to a copy of the present object. The caller of this copy then assumes ownership of it.

The function is declared abstract virtual in this base class, and derived classes will have to implement it.

This function is mainly used by the hp::MappingCollection class.

Implements Mapping< dim, spacedim >.

Definition at line 56 of file mapping_q1.cc.

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

include/deal.II/fe/mapping_q1.h
source/fe/mapping_q1.cc

Public Member Functions