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

Inheritance diagram for MappingQGeneric< dim, spacedim >::InternalData:

Public Member Functions
	InternalData (const unsigned int polynomial_degree)

void	initialize (const UpdateFlags update_flags, const Quadrature< dim > &quadrature, const unsigned int n_original_q_points)

void	initialize_face (const UpdateFlags update_flags, const Quadrature< dim > &quadrature, const unsigned int n_original_q_points)

void	compute_shape_function_values (const std::vector< Point< dim > > &unit_points)

const double &	shape (const unsigned int qpoint, const unsigned int shape_nr) const

double &	shape (const unsigned int qpoint, const unsigned int shape_nr)

const Tensor< 1, dim > &	derivative (const unsigned int qpoint, const unsigned int shape_nr) const

Tensor< 1, dim > &	derivative (const unsigned int qpoint, const unsigned int shape_nr)

const Tensor< 2, dim > &	second_derivative (const unsigned int qpoint, const unsigned int shape_nr) const

Tensor< 2, dim > &	second_derivative (const unsigned int qpoint, const unsigned int shape_nr)

const Tensor< 3, dim > &	third_derivative (const unsigned int qpoint, const unsigned int shape_nr) const

Tensor< 3, dim > &	third_derivative (const unsigned int qpoint, const unsigned int shape_nr)

const Tensor< 4, dim > &	fourth_derivative (const unsigned int qpoint, const unsigned int shape_nr) const

Tensor< 4, dim > &	fourth_derivative (const unsigned int qpoint, const unsigned int shape_nr)

virtual std::size_t	memory_consumption () const

Public Member Functions inherited from Mapping< dim, spacedim >::InternalDataBase
	InternalDataBase ()

virtual	~InternalDataBase ()

Public Attributes
std::vector< double >	shape_values

std::vector< Tensor< 1, dim > >	shape_derivatives

std::vector< Tensor< 2, dim > >	shape_second_derivatives

std::vector< Tensor< 3, dim > >	shape_third_derivatives

std::vector< Tensor< 4, dim > >	shape_fourth_derivatives

std_cxx11::array< std::vector< Tensor< 1, dim > >, GeometryInfo< dim >::faces_per_cell *(dim-1)>	unit_tangentials

const unsigned int	polynomial_degree

const unsigned int	n_shape_functions

std::vector< DerivativeForm< 1, dim, spacedim > >	covariant

std::vector< DerivativeForm< 1, dim, spacedim > >	contravariant

std::vector< std::vector< Tensor< 1, spacedim > > >	aux

std::vector< Point< spacedim > >	mapping_support_points

Triangulation< dim, spacedim >::cell_iterator	cell_of_current_support_points

std::vector< double >	volume_elements

Public Attributes inherited from Mapping< dim, spacedim >::InternalDataBase
UpdateFlags	update_each

Detailed Description

template<int dim, int spacedim = dim>
class MappingQGeneric< dim, spacedim >::InternalData

Storage for internal data of polynomial mappings. See Mapping::InternalDataBase for an extensive description.

For the current class, the InternalData class stores data that is computed once when the object is created (in get_data()) as well as data the class wants to store from between the call to fill_fe_values(), fill_fe_face_values(), or fill_fe_subface_values() until possible later calls from the finite element to functions such as transform(). The latter class of member variables are marked as 'mutable'.

Definition at line 256 of file mapping_q_generic.h.

Constructor & Destructor Documentation

◆ InternalData()

template<int dim, int spacedim>

MappingQGeneric< dim, spacedim >::InternalData::InternalData ( const unsigned int polynomial_degree )

Constructor. The argument denotes the polynomial degree of the mapping to which this object will correspond.

Definition at line 750 of file mapping_q_generic.cc.

Member Function Documentation

◆ initialize()

template<int dim, int spacedim>

void MappingQGeneric< dim, spacedim >::InternalData::initialize	(	const UpdateFlags	update_flags,
		const Quadrature< dim > &	quadrature,
		const unsigned int	n_original_q_points
	)

Initialize the object's member variables related to cell data based on the given arguments.

The function also calls compute_shape_function_values() to actually set the member variables related to the values and derivatives of the mapping shape functions.

Definition at line 781 of file mapping_q_generic.cc.

◆ initialize_face()

template<int dim, int spacedim>

void MappingQGeneric< dim, spacedim >::InternalData::initialize_face	(	const UpdateFlags	update_flags,
		const Quadrature< dim > &	quadrature,
		const unsigned int	n_original_q_points
	)

Initialize the object's member variables related to cell and face data based on the given arguments. In order to initialize cell data, this function calls initialize().

Definition at line 841 of file mapping_q_generic.cc.

◆ compute_shape_function_values()

template<int dim, int spacedim>

void MappingQGeneric< dim, spacedim >::InternalData::compute_shape_function_values ( const std::vector< Point< dim > > & unit_points )

Compute the values and/or derivatives of the shape functions used for the mapping.

Which values, derivatives, or higher order derivatives are computed is determined by which of the member arrays have nonzero sizes. They are typically set to their appropriate sizes by the initialize() and initialize_face() functions, which indeed call this function internally. However, it is possible (and at times useful) to do the resizing by hand and then call this function directly. An example is in a Newton iteration where we update the location of a quadrature point (e.g., in MappingQ::transform_real_to_uni_cell()) and need to re- compute the mapping and its derivatives at this location, but have already sized all internal arrays correctly.

Definition at line 980 of file mapping_q_generic.cc.

◆ shape() [1/2]

template<int dim, int spacedim = dim>

const double& MappingQGeneric< dim, spacedim >::InternalData::shape	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

Shape function at quadrature point. Shape functions are in tensor product order, so vertices must be reordered to obtain transformation.

◆ shape() [2/2]

template<int dim, int spacedim = dim>

double& MappingQGeneric< dim, spacedim >::InternalData::shape	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

Shape function at quadrature point. See above.

◆ derivative() [1/2]

template<int dim, int spacedim = dim>

const Tensor<1,dim>& MappingQGeneric< dim, spacedim >::InternalData::derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

Gradient of shape function in quadrature point. See above.

◆ derivative() [2/2]

template<int dim, int spacedim = dim>

Tensor<1,dim>& MappingQGeneric< dim, spacedim >::InternalData::derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

Gradient of shape function in quadrature point. See above.

◆ second_derivative() [1/2]

template<int dim, int spacedim = dim>

const Tensor<2,dim>& MappingQGeneric< dim, spacedim >::InternalData::second_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

Second derivative of shape function in quadrature point. See above.

◆ second_derivative() [2/2]

template<int dim, int spacedim = dim>

Tensor<2,dim>& MappingQGeneric< dim, spacedim >::InternalData::second_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

Second derivative of shape function in quadrature point. See above.

◆ third_derivative() [1/2]

template<int dim, int spacedim = dim>

const Tensor<3,dim>& MappingQGeneric< dim, spacedim >::InternalData::third_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

third derivative of shape function in quadrature point. See above.

◆ third_derivative() [2/2]

template<int dim, int spacedim = dim>

Tensor<3,dim>& MappingQGeneric< dim, spacedim >::InternalData::third_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

third derivative of shape function in quadrature point. See above.

◆ fourth_derivative() [1/2]

template<int dim, int spacedim = dim>

const Tensor<4,dim>& MappingQGeneric< dim, spacedim >::InternalData::fourth_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)		const

fourth derivative of shape function in quadrature point. See above.

◆ fourth_derivative() [2/2]

template<int dim, int spacedim = dim>

Tensor<4,dim>& MappingQGeneric< dim, spacedim >::InternalData::fourth_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr
	)

fourth derivative of shape function in quadrature point. See above.

◆ memory_consumption()

template<int dim, int spacedim>

std::size_t MappingQGeneric< dim, spacedim >::InternalData::memory_consumption ( ) const

virtual

Return an estimate (in bytes) or the memory consumption of this object.

Reimplemented from Mapping< dim, spacedim >::InternalDataBase.

Definition at line 761 of file mapping_q_generic.cc.

Member Data Documentation

◆ shape_values

template<int dim, int spacedim = dim>

std::vector<double> MappingQGeneric< dim, spacedim >::InternalData::shape_values

Values of shape functions. Access by function shape.

Computed once.

Definition at line 377 of file mapping_q_generic.h.

◆ shape_derivatives

template<int dim, int spacedim = dim>

std::vector<Tensor<1,dim> > MappingQGeneric< dim, spacedim >::InternalData::shape_derivatives

Values of shape function derivatives. Access by function derivative.

Computed once.

Definition at line 384 of file mapping_q_generic.h.

◆ shape_second_derivatives

template<int dim, int spacedim = dim>

std::vector<Tensor<2,dim> > MappingQGeneric< dim, spacedim >::InternalData::shape_second_derivatives

Values of shape function second derivatives. Access by function second_derivative.

Computed once.

Definition at line 392 of file mapping_q_generic.h.

◆ shape_third_derivatives

template<int dim, int spacedim = dim>

std::vector<Tensor<3,dim> > MappingQGeneric< dim, spacedim >::InternalData::shape_third_derivatives

Values of shape function third derivatives. Access by function second_derivative.

Computed once.

Definition at line 400 of file mapping_q_generic.h.

◆ shape_fourth_derivatives

template<int dim, int spacedim = dim>

std::vector<Tensor<4,dim> > MappingQGeneric< dim, spacedim >::InternalData::shape_fourth_derivatives

Values of shape function fourth derivatives. Access by function second_derivative.

Computed once.

Definition at line 408 of file mapping_q_generic.h.

◆ unit_tangentials

template<int dim, int spacedim = dim>

std_cxx11::array<std::vector<Tensor<1,dim> >, GeometryInfo<dim>::faces_per_cell *(dim-1)> MappingQGeneric< dim, spacedim >::InternalData::unit_tangentials

Unit tangential vectors. Used for the computation of boundary forms and normal vectors.

This array has (dim-1)*GeometryInfo::faces_per_cell entries. The first GeometryInfo::faces_per_cell contain the vectors in the first tangential direction for each face; the second set of GeometryInfo::faces_per_cell entries contain the vectors in the second tangential direction (only in 3d, since there we have 2 tangential directions per face), etc.

Filled once.

Definition at line 423 of file mapping_q_generic.h.

◆ polynomial_degree

template<int dim, int spacedim = dim>

const unsigned int MappingQGeneric< dim, spacedim >::InternalData::polynomial_degree

The polynomial degree of the mapping. Since the objects here are also used (with minor adjustments) by MappingQ, we need to store this.

Definition at line 429 of file mapping_q_generic.h.

◆ n_shape_functions

template<int dim, int spacedim = dim>

const unsigned int MappingQGeneric< dim, spacedim >::InternalData::n_shape_functions

Number of shape functions. If this is a Q1 mapping, then it is simply the number of vertices per cell. However, since also derived classes use this class (e.g. the Mapping_Q() class), the number of shape functions may also be different.

In general, it is \((p+1)^\text{dim}\), where \(p\) is the polynomial degree of the mapping.

Definition at line 440 of file mapping_q_generic.h.

◆ covariant

template<int dim, int spacedim = dim>

std::vector<DerivativeForm<1,dim, spacedim > > MappingQGeneric< dim, spacedim >::InternalData::covariant

mutable

Tensors of covariant transformation at each of the quadrature points. The matrix stored is the Jacobian * G^{-1}, where G = Jacobian^{t} * Jacobian, is the first fundamental form of the map; if dim=spacedim then it reduces to the transpose of the inverse of the Jacobian matrix, which itself is stored in the contravariant field of this structure.

Computed on each cell.

Definition at line 461 of file mapping_q_generic.h.

◆ contravariant

template<int dim, int spacedim = dim>

std::vector< DerivativeForm<1,dim,spacedim> > MappingQGeneric< dim, spacedim >::InternalData::contravariant

mutable

Tensors of contravariant transformation at each of the quadrature points. The contravariant matrix is the Jacobian of the transformation, i.e. \(J_{ij}=dx_i/d\hat x_j\).

Computed on each cell.

Definition at line 470 of file mapping_q_generic.h.

◆ aux

template<int dim, int spacedim = dim>

std::vector<std::vector<Tensor<1,spacedim> > > MappingQGeneric< dim, spacedim >::InternalData::aux

mutable

Auxiliary vectors for internal use.

Definition at line 475 of file mapping_q_generic.h.

◆ mapping_support_points

template<int dim, int spacedim = dim>

std::vector<Point<spacedim> > MappingQGeneric< dim, spacedim >::InternalData::mapping_support_points

mutable

Stores the support points of the mapping shape functions on the cell_of_current_support_points.

Definition at line 481 of file mapping_q_generic.h.

◆ cell_of_current_support_points

template<int dim, int spacedim = dim>

Triangulation<dim,spacedim>::cell_iterator MappingQGeneric< dim, spacedim >::InternalData::cell_of_current_support_points

mutable

Stores the cell of which the mapping_support_points are stored.

Definition at line 486 of file mapping_q_generic.h.

◆ volume_elements

template<int dim, int spacedim = dim>

std::vector<double> MappingQGeneric< dim, spacedim >::InternalData::volume_elements

mutable

The determinant of the Jacobian in each quadrature point. Filled if update_volume_elements.

Definition at line 492 of file mapping_q_generic.h.

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

deal.II/fe/mapping_q_generic.h
source/fe/mapping_q_generic.cc

Public Member Functions

Public Attributes

Detailed Description

template<int dim, int spacedim = dim> class MappingQGeneric< dim, spacedim >::InternalData

Constructor & Destructor Documentation

◆ InternalData()

Member Function Documentation

◆ initialize()

◆ initialize_face()

◆ compute_shape_function_values()

◆ shape() [1/2]

◆ shape() [2/2]

◆ derivative() [1/2]

◆ derivative() [2/2]

◆ second_derivative() [1/2]

◆ second_derivative() [2/2]

◆ third_derivative() [1/2]

◆ third_derivative() [2/2]

◆ fourth_derivative() [1/2]

◆ fourth_derivative() [2/2]

◆ memory_consumption()

Member Data Documentation

◆ shape_values

◆ shape_derivatives

◆ shape_second_derivatives

◆ shape_third_derivatives

◆ shape_fourth_derivatives

◆ unit_tangentials

◆ polynomial_degree

◆ n_shape_functions

◆ covariant

◆ contravariant

◆ aux

◆ mapping_support_points

◆ cell_of_current_support_points

◆ volume_elements

template<int dim, int spacedim = dim>
class MappingQGeneric< dim, spacedim >::InternalData