#include <mapping_q1.h>

Inheritance diagram for MappingQ1< dim, spacedim >:

Classes
class	InternalData

Public Types
typedef QProjector< dim > ::DataSetDescriptor	DataSetDescriptor

Public Member Functions
	MappingQ1 ()

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

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

virtual void	transform (const VectorSlice< const std::vector< Tensor< 1, dim > > > input, VectorSlice< std::vector< Tensor< 1, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const

virtual void	transform (const VectorSlice< const std::vector< DerivativeForm< 1, dim, spacedim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const

virtual void	transform (const VectorSlice< const std::vector< Tensor< 2, dim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const

virtual Mapping< dim, spacedim > *	clone () const

virtual void	fill_fe_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const Quadrature< dim > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, typename std::vector< Point< spacedim > > &quadrature_points, std::vector< double > &JxW_values, std::vector< DerivativeForm< 1, dim, spacedim > > &jacobians, std::vector< DerivativeForm< 2, dim, spacedim > > &jacobian_grads, std::vector< DerivativeForm< 1, spacedim, dim > > &inverse_jacobians, std::vector< Point< spacedim > > &cell_normal_vectors, CellSimilarity::Similarity &cell_similarity) const

virtual void	fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim-1 > &quadrature, typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, typename std::vector< Point< spacedim > > &quadrature_points, std::vector< double > &JxW_values, typename std::vector< Tensor< 1, spacedim > > &boundary_form, typename std::vector< Point< spacedim > > &normal_vectors) const

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, typename Mapping< dim, spacedim >::InternalDataBase &mapping_data, typename std::vector< Point< spacedim > > &quadrature_points, std::vector< double > &JxW_values, typename std::vector< Tensor< 1, spacedim > > &boundary_form, typename std::vector< Point< spacedim > > &normal_vectors) const

void	compute_shapes (const std::vector< Point< dim > > &unit_points, InternalData &data) const

void	compute_data (const UpdateFlags flags, const Quadrature< dim > &quadrature, const unsigned int n_orig_q_points, InternalData &data) const

void	compute_face_data (const UpdateFlags flags, const Quadrature< dim > &quadrature, const unsigned int n_orig_q_points, InternalData &data) const

void	compute_fill (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int npts, const DataSetDescriptor data_set, const CellSimilarity::Similarity cell_similarity, InternalData &data, std::vector< Point< spacedim > > &quadrature_points) const

void	compute_fill_face (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const unsigned int subface_no, const unsigned int npts, const DataSetDescriptor data_set, const std::vector< double > &weights, InternalData &mapping_data, std::vector< Point< spacedim > > &quadrature_points, std::vector< double > &JxW_values, std::vector< Tensor< 1, spacedim > > &boundary_form, std::vector< Point< spacedim > > &normal_vectors) const

virtual void	compute_shapes_virtual (const std::vector< Point< dim > > &unit_points, InternalData &data) const

Point< spacedim >	transform_unit_to_real_cell_internal (const InternalData &mdata) 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, InternalData &mdata) const

virtual bool	preserves_vertex_locations () const

template<>
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, InternalData &mdata) const

template<>
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, InternalData &mdata) const

template<>
Point< 1 >	transform_real_to_unit_cell_internal (const Triangulation< 1, 3 >::cell_iterator &cell, const Point< 3 > &p, const Point< 1 > &initial_p_unit, InternalData &mdata) const

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

virtual void	transform (const VectorSlice< const std::vector< Tensor< 1, dim > > > input, VectorSlice< std::vector< Tensor< 1, spacedim > > > output, const InternalDataBase &internal, const MappingType type) const =0

virtual void	transform (const VectorSlice< const std::vector< DerivativeForm< 1, dim, spacedim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const InternalDataBase &internal, const MappingType type) const =0

virtual void	transform (const VectorSlice< const std::vector< Tensor< 2, dim > > > input, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const InternalDataBase &internal, const MappingType type) const =0

void	transform_covariant (const VectorSlice< const std::vector< Tensor< 1, dim > > > input, const unsigned int offset, VectorSlice< std::vector< Tensor< 1, spacedim > > > output, const InternalDataBase &internal) const DEAL_II_DEPRECATED

void	transform_covariant (const VectorSlice< const std::vector< DerivativeForm< 1, dim, spacedim > > > input, const unsigned int offset, VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const InternalDataBase &internal) const DEAL_II_DEPRECATED

void	transform_contravariant (const VectorSlice< const std::vector< Tensor< 1, dim > > > input, const unsigned int offset, VectorSlice< std::vector< Tensor< 1, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const DEAL_II_DEPRECATED

void	transform_contravariant (const VectorSlice< const std::vector< DerivativeForm< 1, dim, spacedim > > > input, const unsigned int offset, const VectorSlice< std::vector< Tensor< 2, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const DEAL_II_DEPRECATED

const Point< spacedim > &	support_point_value (const unsigned int index, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const

const Tensor< 2, spacedim > &	support_point_gradient (const unsigned int index, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const

const Tensor< 2, spacedim > &	support_point_inverse_gradient (const unsigned int index, const typename Mapping< dim, spacedim >::InternalDataBase &internal) const

	DeclException0 (ExcInvalidData)

	DeclException0 (ExcTransformationFailed)

	DeclException3 (ExcDistortedMappedCell, Point< spacedim >, double, int,<< "The image of the mapping applied to cell with center ["<< arg1<< "] is distorted. The cell geometry or the "<< "mapping are invalid, giving a non-positive volume "<< "fraction of "<< arg2<< " in quadrature point "<< arg3<< ".")

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

void	subscribe (const char *identifier=0) const

void	unsubscribe (const char *identifier=0) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

	DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")

	DeclException2 (ExcNoSubscriber, char , char ,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)

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

Protected Member Functions
template<int rank>
void	transform_fields (const VectorSlice< const std::vector< Tensor< rank, dim > > > input, VectorSlice< std::vector< Tensor< rank, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const

template<int rank>
void	transform_gradients (const VectorSlice< const std::vector< Tensor< rank, dim > > > input, VectorSlice< std::vector< Tensor< rank, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const

template<int rank>
void	transform_differential_forms (const VectorSlice< const std::vector< DerivativeForm< rank, dim, spacedim > > > input, VectorSlice< std::vector< DerivativeForm< rank, spacedim, spacedim > > > output, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const MappingType type) const

template<int dim_>
Point< dim_ >	transform_real_to_unit_cell_internal_codim1 (const typename Triangulation< dim_, dim_+1 >::cell_iterator &cell, const Point< dim_+1 > &p, const Point< dim_ > &initial_p_unit, InternalData &mdata) const

Point< dim >	transform_real_to_unit_cell_initial_guess (const std::vector< Point< spacedim > > &vertex, const Point< spacedim > &p) const

Private Member Functions
virtual UpdateFlags	update_once (const UpdateFlags flags) const

virtual UpdateFlags	update_each (const UpdateFlags flags) const

virtual Mapping< dim, spacedim > ::InternalDataBase *	get_data (const UpdateFlags, const Quadrature< dim > &quadrature) const

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

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

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

Static Private Attributes
static const unsigned int	n_shape_functions = GeometryInfo<dim>::vertices_per_cell

Detailed Description

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

Mapping of general quadrilateral/hexahedra by d-linear shape functions.

This function maps the unit cell to a general grid cell with straight lines in $d$ dimensions (remark that in 3D the surfaces may be curved, even if the edges are not). This is the well-known mapping for polyhedral domains.

Shape function for this mapping are the same as for the finite element FE_Q of order 1. Therefore, coupling these two yields an isoparametric element.

For more information about the spacedim template parameter check the documentation of FiniteElement or the one of Triangulation.

Author: Guido Kanschat, 2000, 2001; Ralf Hartmann, 2000, 2001, 2005

Definition at line 57 of file mapping_q1.h.

Member Typedef Documentation

template<int dim, int spacedim = dim>

typedef QProjector<dim>::DataSetDescriptor MappingQ1< dim, spacedim >::DataSetDescriptor

Declare a convenience typedef for the class that describes offsets into quadrature formulas projected onto faces and subfaces.

Definition at line 391 of file mapping_q1.h.

Constructor & Destructor Documentation

template<int dim, int spacedim = dim>

MappingQ1< dim, spacedim >::MappingQ1 ( )

Default constructor.

Member Function Documentation

template<int dim, int spacedim = dim>

virtual Point<spacedim> MappingQ1< dim, spacedim >::transform_unit_to_real_cell	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const Point< dim > &	p
	)		const

virtual

Transforms the point p on the unit cell to the point p_real on the real cell cell and returns p_real.

Implements Mapping< dim, spacedim >.

Reimplemented in MappingQ< dim, spacedim >.

template<int dim, int spacedim = dim>

virtual Point<dim> MappingQ1< dim, spacedim >::transform_real_to_unit_cell	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const Point< spacedim > &	p
	)		const

virtual

Transforms the point p on the real cell to the point p_unit on the unit cell cell and returns p_unit.

Uses Newton iteration and the transform_unit_to_real_cell function.

In the codimension one case, this function returns the normal projection of the real point p on the curve or surface identified by the cell.

Note: Polynomial mappings from the reference (unit) cell coordinates to the coordinate system of a real cell are not always invertible if the point for which the inverse mapping is to be computed lies outside the cell's boundaries. In such cases, the current function may fail to compute a point on the reference cell whose image under the mapping equals the given point p. If this is the case then this function throws an exception of type Mapping::ExcTransformationFailed . Whether the given point p lies outside the cell can therefore be determined by checking whether the return reference coordinates lie inside of outside the reference cell (e.g., using GeometryInfo::is_inside_unit_cell) or whether the exception mentioned above has been thrown.

Implements Mapping< dim, spacedim >.

Reimplemented in MappingQ< dim, spacedim >.

template<int dim, int spacedim = dim>

template<int rank>

void MappingQ1< dim, spacedim >::transform_fields	(	const VectorSlice< const std::vector< Tensor< rank, dim > > >	input,
		VectorSlice< std::vector< Tensor< rank, spacedim > > >	output,
		const typename Mapping< dim, spacedim >::InternalDataBase &	internal,
		const MappingType	type
	)		const

protected

This function and the next allow to generate the transform require by the virtual transform() in mapping, but unfortunately in C++ one cannot declare a virtual template function.

template<int dim, int spacedim = dim>

template<int rank>

void MappingQ1< dim, spacedim >::transform_gradients	(	const VectorSlice< const std::vector< Tensor< rank, dim > > >	input,
		VectorSlice< std::vector< Tensor< rank, spacedim > > >	output,
		const typename Mapping< dim, spacedim >::InternalDataBase &	internal,
		const MappingType	type
	)		const

protected

see doc in transform_fields

template<int dim, int spacedim = dim>

template<int rank>

void MappingQ1< dim, spacedim >::transform_differential_forms	(	const VectorSlice< const std::vector< DerivativeForm< rank, dim, spacedim > > >	input,
		VectorSlice< std::vector< DerivativeForm< rank, spacedim, spacedim > > >	output,
		const typename Mapping< dim, spacedim >::InternalDataBase &	internal,
		const MappingType	type
	)		const

protected

see doc in transform_fields

template<int dim, int spacedim = dim>

virtual Mapping<dim,spacedim>* MappingQ1< dim, spacedim >::clone ( ) const

virtual

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

Implements Mapping< dim, spacedim >.

Reimplemented in MappingQ< dim, spacedim >, MappingQ1Eulerian< dim, VECTOR, spacedim >, MappingQEulerian< dim, VECTOR, spacedim >, and MappingC1< dim, spacedim >.

template<int dim, int spacedim = dim>

virtual void MappingQ1< dim, spacedim >::fill_fe_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const Quadrature< dim > &	quadrature,
		typename Mapping< dim, spacedim >::InternalDataBase &	mapping_data,
		typename std::vector< Point< spacedim > > &	quadrature_points,
		std::vector< double > &	JxW_values,
		std::vector< DerivativeForm< 1, dim, spacedim > > &	jacobians,
		std::vector< DerivativeForm< 2, dim, spacedim > > &	jacobian_grads,
		std::vector< DerivativeForm< 1, spacedim, dim > > &	inverse_jacobians,
		std::vector< Point< spacedim > > &	cell_normal_vectors,
		CellSimilarity::Similarity &	cell_similarity
	)		const

virtual

Implementation of the interface in Mapping.

Reimplemented in MappingQ< dim, spacedim >, MappingQ1Eulerian< dim, VECTOR, spacedim >, and MappingQEulerian< dim, VECTOR, spacedim >.

template<int dim, int spacedim = dim>

virtual void MappingQ1< dim, spacedim >::fill_fe_face_values	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const Quadrature< dim-1 > &	quadrature,
		typename Mapping< dim, spacedim >::InternalDataBase &	mapping_data,
		typename std::vector< Point< spacedim > > &	quadrature_points,
		std::vector< double > &	JxW_values,
		typename std::vector< Tensor< 1, spacedim > > &	boundary_form,
		typename std::vector< Point< spacedim > > &	normal_vectors
	)		const

virtual

Implementation of the interface in Mapping.

Reimplemented in MappingQ< dim, spacedim >.

template<int dim, int spacedim = dim>

virtual void MappingQ1< dim, spacedim >::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,
		typename Mapping< dim, spacedim >::InternalDataBase &	mapping_data,
		typename std::vector< Point< spacedim > > &	quadrature_points,
		std::vector< double > &	JxW_values,
		typename std::vector< Tensor< 1, spacedim > > &	boundary_form,
		typename std::vector< Point< spacedim > > &	normal_vectors
	)		const

virtual

Implementation of the interface in Mapping.

Reimplemented in MappingQ< dim, spacedim >.

template<int dim, int spacedim = dim>

void MappingQ1< dim, spacedim >::compute_shapes	(	const std::vector< Point< dim > > &	unit_points,
		InternalData &	data
	)		const

Compute shape values and/or derivatives.

Calls either the compute_shapes_virtual of this class or that of the derived class, depending on whether data.is_mapping_q1_data equals true or false.

template<int dim, int spacedim = dim>

void MappingQ1< dim, spacedim >::compute_data	(	const UpdateFlags	flags,
		const Quadrature< dim > &	quadrature,
		const unsigned int	n_orig_q_points,
		InternalData &	data
	)		const

Do the computations for the get_data functions. Here, the data vectors of InternalData are reinitialized to proper size and shape values are computed.

template<int dim, int spacedim = dim>

void MappingQ1< dim, spacedim >::compute_face_data	(	const UpdateFlags	flags,
		const Quadrature< dim > &	quadrature,
		const unsigned int	n_orig_q_points,
		InternalData &	data
	)		const

Do the computations for the get_face_data functions. Here, the data vectors of InternalData are reinitialized to proper size and shape values and derivatives are computed. Furthermore unit_tangential vectors of the face are computed.

template<int dim, int spacedim = dim>

void MappingQ1< dim, spacedim >::compute_fill	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	npts,
		const DataSetDescriptor	data_set,
		const CellSimilarity::Similarity	cell_similarity,
		InternalData &	data,
		std::vector< Point< spacedim > > &	quadrature_points
	)		const

Do the computation for the fill_* functions.

template<int dim, int spacedim = dim>

void MappingQ1< dim, spacedim >::compute_fill_face	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const unsigned int	face_no,
		const unsigned int	subface_no,
		const unsigned int	npts,
		const DataSetDescriptor	data_set,
		const std::vector< double > &	weights,
		InternalData &	mapping_data,
		std::vector< Point< spacedim > > &	quadrature_points,
		std::vector< double > &	JxW_values,
		std::vector< Tensor< 1, spacedim > > &	boundary_form,
		std::vector< Point< spacedim > > &	normal_vectors
	)		const

Do the computation for the fill_* functions.

template<int dim, int spacedim = dim>

virtual void MappingQ1< dim, spacedim >::compute_shapes_virtual	(	const std::vector< Point< dim > > &	unit_points,
		InternalData &	data
	)		const

virtual

Compute shape values and/or derivatives.

template<int dim, int spacedim = dim>

Point<spacedim> MappingQ1< dim, spacedim >::transform_unit_to_real_cell_internal ( const InternalData & mdata ) const

Transforms a point p on the unit cell to the point p_real on the real cell cell and returns p_real.

This function is called by transform_unit_to_real_cell and multiple times (through the Newton iteration) by transform_real_to_unit_cell_internal.

Takes a reference to an InternalData that must already include the shape values at point p and the mapping support points of the cell.

This InternalData argument avoids multiple computations of the shape values at point p and especially multiple computations of the mapping support points.

template<int dim, int spacedim = dim>

Point<dim> MappingQ1< dim, spacedim >::transform_real_to_unit_cell_internal	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		const Point< spacedim > &	p,
		const Point< dim > &	initial_p_unit,
		InternalData &	mdata
	)		const

Transforms the point p on the real cell to the corresponding point on the unit cell cell by a Newton iteration.

Takes a reference to an InternalData that is assumed to be previously created by the get_data function with UpdateFlags including update_transformation_values and update_transformation_gradients and a one point Quadrature that includes the given initial guess for the transformation initial_p_unit. Hence this function assumes that mdata already includes the transformation shape values and gradients computed at initial_p_unit.

mdata will be changed by this function.

template<int dim, int spacedim = dim>

virtual bool MappingQ1< dim, spacedim >::preserves_vertex_locations ( ) const

virtual

Always returns true because MappingQ1 preserves vertex locations.

Implements Mapping< dim, spacedim >.

Reimplemented in MappingQ1Eulerian< dim, VECTOR, spacedim >, and MappingQEulerian< dim, VECTOR, spacedim >.

template<int dim, int spacedim = dim>

Point<dim> MappingQ1< dim, spacedim >::transform_real_to_unit_cell_initial_guess	(	const std::vector< Point< spacedim > > &	vertex,
		const Point< spacedim > &	p
	)		const

protected

Compute an initial guess to pass to the Newton method in transform_real_to_unit_cell.

For the initial guess we proceed in the following way:

find the least square dim-dimensional plane approximating the cell vertices, i.e. we find and affine map A x_hat + b from the reference cell to the real space.
Solve the equation A x_hat + b = p for x_hat
This x_hat is the initial solution used for the Newton Method.

Note: if dim<spacedim we first project p onto the plane.; if dim==1 (for any spacedim) the initial guess is the exact solution and no Newton iteration is needed.

Some details about how we compute the least square plane. We look for a spacedim x (dim + 1) matrix X such that

X * M = Y

where M is a (dim+1) x n_vertices matrix and Y a spacedim x n_vertices.

And: The i-th column of M is unit_vertex[i] and the last row all 1's. The i-th column of Y is real_vertex[i].

If we split X=[A|b], the least square approx is A x_hat+b

Classically X = Y * (M^t (M M^t)^{-1})

Let K = M^t * (M M^t)^{-1} = [KA Kb] this can be precomputed, and that is exactely what we do.

Finally A = Y*KA and b = Y*Kb.

template<int dim, int spacedim = dim>

virtual UpdateFlags MappingQ1< dim, spacedim >::update_once ( const UpdateFlags flags ) const

privatevirtual

Implementation of the interface in Mapping.

Description of effects:

if update_quadrature_points is required, the output will contain update_transformation_values. This computes the values of the transformation basis polynomials at the unit cell quadrature points.
if any of update_covariant_transformation, update_contravariant_transformation, update_JxW_values, update_boundary_forms, update_normal_vectors is required, the output will contain update_transformation_gradients to compute derivatives of the transformation basis polynomials.

Implements Mapping< dim, spacedim >.

template<int dim, int spacedim = dim>

virtual UpdateFlags MappingQ1< dim, spacedim >::update_each ( const UpdateFlags flags ) const

privatevirtual

Implementation of the interface in Mapping.

Description of effects if flags contains:

update_quadrature_points is copied to the output to compute the quadrature points on the real cell.
update_JxW_values is copied and requires update_boundary_forms on faces. The latter, because the surface element is just the norm of the boundary form.
update_normal_vectors is copied and requires update_boundary_forms. The latter, because the normal vector is the normalized boundary form.
update_covariant_transformation is copied and requires update_contravariant_transformation, since it is computed as the inverse of the latter.
update_JxW_values is copied and requires update_contravariant_transformation, since it is computed as one over determinant of the latter.
update_boundary_forms is copied and requires update_contravariant_transformation, since the boundary form is computed as the contravariant image of the normal vector to the unit cell.

Implements Mapping< dim, spacedim >.

template<int dim, int spacedim = dim>

virtual Mapping<dim,spacedim>::InternalDataBase* MappingQ1< dim, spacedim >::get_data	(	const UpdateFlags	,
		const Quadrature< dim > &	quadrature
	)		const

privatevirtual

Prepare internal data structures and fill in values independent of the cell.

Implements Mapping< dim, spacedim >.

Reimplemented in MappingQ< dim, spacedim >.

template<int dim, int spacedim = dim>

virtual Mapping<dim,spacedim>::InternalDataBase* MappingQ1< dim, spacedim >::get_face_data	(	const UpdateFlags	flags,
		const Quadrature< dim-1 > &	quadrature
	)		const

privatevirtual

Prepare internal data structure for transformation of faces and fill in values independent of the cell.

Implements Mapping< dim, spacedim >.

Reimplemented in MappingQ< dim, spacedim >.

template<int dim, int spacedim = dim>

virtual Mapping<dim,spacedim>::InternalDataBase* MappingQ1< dim, spacedim >::get_subface_data	(	const UpdateFlags	flags,
		const Quadrature< dim-1 > &	quadrature
	)		const

privatevirtual

Prepare internal data structure for transformation of children of faces and fill in values independent of the cell.

Implements Mapping< dim, spacedim >.

Reimplemented in MappingQ< dim, spacedim >.

template<int dim, int spacedim = dim>

virtual void MappingQ1< dim, spacedim >::compute_mapping_support_points	(	const typename Triangulation< dim, spacedim >::cell_iterator &	cell,
		std::vector< Point< spacedim > > &	a
	)		const

privatevirtual

Computes the support points of the mapping. For MappingQ1 these are the vertices. However, other classes may override this function. In particular, the MappingQ1Eulerian class does exactly this by not computing the support points from the geometry of the current cell but instead evaluating an externally given displacement field in addition to the geometry of the cell.

Reimplemented in MappingQ< dim, spacedim >, MappingQEulerian< dim, VECTOR, spacedim >, and MappingQ1Eulerian< dim, VECTOR, spacedim >.

Member Data Documentation

template<int dim, int spacedim = dim>

const unsigned int MappingQ1< dim, spacedim >::n_shape_functions = GeometryInfo<dim>::vertices_per_cell

staticprivate

Number of shape functions. Is simply the number of vertices per cell for the Q1 mapping.

Definition at line 760 of file mapping_q1.h.

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

include/deal.II/fe/mapping_q1.h

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Detailed Description

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

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