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

Inheritance diagram for MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData:

Public Member Functions
	InternalData (const FiniteElement< dim, spacedim > &fe, const ComponentMask &mask)

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 override

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

	InternalDataBase (const InternalDataBase &)=delete

virtual	~InternalDataBase ()=default

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

unsigned int	n_shape_functions

ComponentMask	mask

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

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

std::vector< double >	volume_elements

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

std::vector< types::global_dof_index >	local_dof_indices

std::vector< double >	local_dof_values

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

Detailed Description

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>
class MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData

Storage for internal data of this mapping. See Mapping::InternalDataBase for an extensive description.

This includes 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', along with scratch arrays.

Definition at line 259 of file mapping_fe_field.h.

Constructor & Destructor Documentation

◆ InternalData()

template<int dim, int spacedim, typename VectorType , typename DoFHandlerType >

MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::InternalData	(	const FiniteElement< dim, spacedim > &	fe,
		const ComponentMask &	mask
	)

Constructor.

Definition at line 64 of file mapping_fe_field.cc.

Member Function Documentation

◆ shape() [1/2]

template<int dim, int spacedim, typename VectorType , typename DoFHandlerType >

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

inline

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

Definition at line 280 of file mapping_fe_field.cc.

◆ shape() [2/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

Shape function at quadrature point. See above.

Definition at line 88 of file mapping_fe_field.cc.

◆ derivative() [1/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

Gradient of shape function in quadrature point. See above.

Definition at line 103 of file mapping_fe_field.cc.

◆ derivative() [2/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

Gradient of shape function in quadrature point. See above.

Definition at line 117 of file mapping_fe_field.cc.

◆ second_derivative() [1/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

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

Definition at line 130 of file mapping_fe_field.cc.

◆ second_derivative() [2/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

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

Definition at line 146 of file mapping_fe_field.cc.

◆ third_derivative() [1/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

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

Definition at line 160 of file mapping_fe_field.cc.

◆ third_derivative() [2/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

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

Definition at line 174 of file mapping_fe_field.cc.

◆ fourth_derivative() [1/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

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

Definition at line 187 of file mapping_fe_field.cc.

◆ fourth_derivative() [2/2]

template<int dim, int spacedim, typename DoFHandlerType , typename VectorType >

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

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

Definition at line 203 of file mapping_fe_field.cc.

◆ memory_consumption()

template<int dim, int spacedim, typename VectorType , typename DoFHandlerType >

std::size_t MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::memory_consumption ( ) const

overridevirtual

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

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

Definition at line 78 of file mapping_fe_field.cc.

Member Data Documentation

◆ shape_values

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<double> MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::shape_values

Values of shape functions. Access by function shape.

Computed once.

Definition at line 343 of file mapping_fe_field.h.

◆ shape_derivatives

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<Tensor<1, dim> > MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::shape_derivatives

Values of shape function derivatives. Access by function derivative.

Computed once.

Definition at line 350 of file mapping_fe_field.h.

◆ shape_second_derivatives

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<Tensor<2, dim> > MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::shape_second_derivatives

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

Computed once.

Definition at line 358 of file mapping_fe_field.h.

◆ shape_third_derivatives

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<Tensor<3, dim> > MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::shape_third_derivatives

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

Computed once.

Definition at line 366 of file mapping_fe_field.h.

◆ shape_fourth_derivatives

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<Tensor<4, dim> > MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::shape_fourth_derivatives

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

Computed once.

Definition at line 374 of file mapping_fe_field.h.

◆ unit_tangentials

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::array<std::vector<Tensor<1, dim> >, GeometryInfo<dim>::faces_per_cell *(dim - 1)> MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::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 391 of file mapping_fe_field.h.

◆ n_shape_functions

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

unsigned int MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::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.

Definition at line 399 of file mapping_fe_field.h.

◆ mask

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

ComponentMask MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::mask

Stores the mask given at construction time. If no mask was specified at construction time, then a default one is used, which makes this class works in the same way of MappingQEulerian(), i.e., the first spacedim components of the FiniteElement are used for the euler_vector and the euler_dh.

If a mask is specified, then it has to match the underlying FiniteElement, and it has to have exactly spacedim non-zero elements, indicating the components (in order) of the FiniteElement which will be used for the euler vector and the euler dof handler.

Definition at line 413 of file mapping_fe_field.h.

◆ covariant

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<DerivativeForm<1, dim, spacedim> > MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::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 424 of file mapping_fe_field.h.

◆ contravariant

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<DerivativeForm<1, dim, spacedim> > MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::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 433 of file mapping_fe_field.h.

◆ volume_elements

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<double> MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::volume_elements

mutable

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

Definition at line 439 of file mapping_fe_field.h.

◆ aux

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<std::vector<Tensor<1, spacedim> > > MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::aux

mutable

Auxiliary vectors for internal use.

Definition at line 444 of file mapping_fe_field.h.

◆ local_dof_indices

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<types::global_dof_index> MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::local_dof_indices

mutable

Storage for the indices of the local degrees of freedom.

Definition at line 449 of file mapping_fe_field.h.

◆ local_dof_values

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>

std::vector<double> MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData::local_dof_values

mutable

Storage for local degrees of freedom.

Definition at line 454 of file mapping_fe_field.h.

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

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

Public Member Functions

Public Attributes

Detailed Description

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>> class MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData

Constructor & Destructor Documentation

◆ InternalData()

Member Function Documentation

◆ 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

◆ n_shape_functions

◆ mask

◆ covariant

◆ contravariant

◆ volume_elements

◆ aux

◆ local_dof_indices

◆ local_dof_values

template<int dim, int spacedim = dim, typename VectorType = Vector<double>, typename DoFHandlerType = DoFHandler<dim, spacedim>>
class MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData