Calculates finite element data on the actual cell. More...

#include <fe_values.hh>

Collaboration diagram for FEValues< spacedim >:

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Classes
class	FEInternalData
	Structure for storing the precomputed finite element data. More...

struct	ViewsCache

Public Member Functions
	FEValues ()
	Default constructor with postponed initialization. More...

template<unsigned int DIM>
	FEValues (Quadrature &_quadrature, FiniteElement< DIM > &_fe, UpdateFlags _flags)

	~FEValues ()
	Correct deallocation of objects created by 'initialize' methods. More...

template<unsigned int DIM>
void	allocate (unsigned int n_points, FiniteElement< DIM > &_fe, UpdateFlags flags)
	Allocates space for computed data. More...

template<unsigned int DIM>
void	initialize (Quadrature &_quadrature, FiniteElement< DIM > &_fe, UpdateFlags _flags)
	Initialize structures and calculates cell-independent data. More...

void	reinit (const ElementAccessor< spacedim > &cell)
	Update cell-dependent data (gradients, Jacobians etc.) More...

void	reinit (const Side &cell_side)
	Update cell side-dependent FE data (values, gradients). More...

double	shape_value (const unsigned int function_no, const unsigned int point_no)
	Return the value of the `function_no-th` shape function at the `point_no-th` quadrature point. More...

arma::vec::fixed< spacedim >	shape_grad (const unsigned int function_no, const unsigned int point_no)
	Return the gradient of the `function_no-th` shape function at the `point_no-th` quadrature point. More...

double	shape_value_component (const unsigned int function_no, const unsigned int point_no, const unsigned int comp) const
	Return the value of the `function_no-th` shape function at the `point_no-th` quadrature point. More...

arma::vec::fixed< spacedim >	shape_grad_component (const unsigned int function_no, const unsigned int point_no, const unsigned int comp) const
	Return the gradient of the `function_no-th` shape function at the `point_no-th` quadrature point. More...

double	determinant (const unsigned int point_no)
	Return the relative volume change of the cell (Jacobian determinant). More...

double	JxW (const unsigned int point_no)
	Return the product of Jacobian determinant and the quadrature weight at given quadrature point. More...

arma::vec::fixed< spacedim >	point (const unsigned int point_no)
	Return coordinates of the quadrature point in the actual cell system. More...

const Armor::array &	point_list () const
	Return coordinates of all quadrature points in the actual cell system. More...

arma::vec::fixed< spacedim >	normal_vector (unsigned int point_no)
	Returns the normal vector to a side at given quadrature point. More...

const FEValuesViews::Scalar< spacedim > &	scalar_view (unsigned int i) const
	Accessor to scalar values of multicomponent FE. More...

const FEValuesViews::Vector< spacedim > &	vector_view (unsigned int i) const
	Accessor to vector values of multicomponent FE. More...

const FEValuesViews::Tensor< spacedim > &	tensor_view (unsigned int i) const
	Accessor to tensor values of multicomponent FE. More...

unsigned int	n_points () const
	Returns the number of quadrature points. More...

unsigned int	n_dofs () const
	Returns the number of shape functions. More...

unsigned int	dim () const
	Return dimension of reference space. More...

template<unsigned int DIM>
std::shared_ptr< typename FEValues< spacedim >::FEInternalData >	init_fe_data (const FiniteElement< DIM > &fe, const Quadrature &q)

Protected Member Functions
template<unsigned int DIM>
std::shared_ptr< FEInternalData >	init_fe_data (const FiniteElement< DIM > &fe, const Quadrature &q)
	Precompute finite element data on reference element. More...

void	fill_data (const ElementValues< spacedim > &elm_values, const FEInternalData &fe_data)
	Computes the shape function values and gradients on the actual cell and fills the FEValues structure. More...

void	fill_scalar_data (const ElementValues< spacedim > &elm_values, const FEInternalData &fe_data)
	Compute shape functions and gradients on the actual cell for scalar FE. More...

void	fill_vec_data (const ElementValues< spacedim > &elm_values, const FEInternalData &fe_data)
	Compute shape functions and gradients on the actual cell for vectorial FE. More...

void	fill_vec_contravariant_data (const ElementValues< spacedim > &elm_values, const FEInternalData &fe_data)
	Compute shape functions and gradients on the actual cell for vectorial FE. More...

void	fill_vec_piola_data (const ElementValues< spacedim > &elm_values, const FEInternalData &fe_data)
	Compute shape functions and gradients on the actual cell for Raviart-Thomas FE. More...

void	fill_tensor_data (const ElementValues< spacedim > &elm_values, const FEInternalData &fe_data)
	Compute shape functions and gradients on the actual cell for tensorial FE. More...

void	fill_system_data (const ElementValues< spacedim > &elm_values, const FEInternalData &fe_data)
	Compute shape functions and gradients on the actual cell for mixed system of FE. More...

Protected Attributes
unsigned int	dim_
	Dimension of reference space. More...

unsigned int	n_points_
	Number of integration points. More...

unsigned int	n_dofs_
	Number of finite element dofs. More...

FEType	fe_type_
	Type of finite element (scalar, vector, tensor). More...

std::vector< std::vector< unsigned int > >	fe_sys_dofs_
	Dof indices of FESystem sub-elements. More...

std::vector< unsigned int >	fe_sys_n_components_
	Numbers of components of FESystem sub-elements in reference space. More...

std::vector< unsigned int >	fe_sys_n_space_components_
	Numbers of components of FESystem sub-elements in real space. More...

std::vector< std::vector< double > >	shape_values
	Shape functions evaluated at the quadrature points. More...

std::vector< std::vector< arma::vec::fixed< spacedim > > >	shape_gradients

UpdateFlags	update_flags
	Flags that indicate which finite element quantities are to be computed. More...

std::shared_ptr< ElementValues< spacedim > >	elm_values
	Auxiliary object for calculation of element-dependent data. More...

std::vector< FEValues< spacedim > >	fe_values_vec
	Vector of FEValues for sub-elements of FESystem. More...

unsigned int	n_components_
	Number of components of the FE. More...

ViewsCache	views_cache_
	Auxiliary storage of FEValuesViews accessors. More...

std::shared_ptr< FEInternalData >	fe_data
	Precomputed finite element data. More...

std::vector< std::vector< shared_ptr< FEInternalData > > >	side_fe_data
	Precomputed FE data (shape functions on reference element) for all sides and permuted quadrature points. More...

Detailed Description

template<unsigned int spacedim = 3>
class FEValues< spacedim >

Calculates finite element data on the actual cell.

FEValues takes care of the calculation of finite element data on the actual cell or on its side, (values of shape functions at quadrature points, gradients of shape functions, Jacobians of the mapping from the reference cell etc.).

Parameters

spacedim Dimension of the Euclidean space where the actual cell lives.

Definition at line 59 of file fe_values.hh.

Constructor & Destructor Documentation

template<unsigned int spacedim>

FEValues< spacedim >::FEValues ( )

Default constructor with postponed initialization.

Definition at line 122 of file fe_values.cc.

template<unsigned int spacedim = 3>

template<unsigned int DIM>

FEValues< spacedim >::FEValues	(	Quadrature &	_quadrature,
		FiniteElement< DIM > &	_fe,
		UpdateFlags	_flags
	)

inline

Constructor with initialization of data structures (see initialize() for description of parameters).

Definition at line 83 of file fe_values.hh.

template<unsigned int spacedim>

FEValues< spacedim >::~FEValues ( )

Correct deallocation of objects created by 'initialize' methods.

Definition at line 130 of file fe_values.cc.

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Member Function Documentation

template<unsigned int spacedim>

template<unsigned int DIM>

void FEValues< spacedim >::allocate	(	unsigned int	n_points,
		FiniteElement< DIM > &	_fe,
		UpdateFlags	flags
	)

Allocates space for computed data.

Parameters

n_points	Number of quadrature points.
_fe	The finite element.
flags	The update flags.

Definition at line 183 of file fe_values.cc.

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template<unsigned int spacedim = 3>

double FEValues< spacedim >::determinant ( const unsigned int point_no )

inline

Return the relative volume change of the cell (Jacobian determinant).

If dim_==spacedim then the sign may be negative, otherwise the result is a positive number.

Parameters

point_no Number of the quadrature point.

Definition at line 188 of file fe_values.hh.

template<unsigned int spacedim = 3>

unsigned int FEValues< spacedim >::dim ( ) const

inline

Return dimension of reference space.

Definition at line 285 of file fe_values.hh.

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template<unsigned int spacedim>

void FEValues< spacedim >::fill_data	(	const ElementValues< spacedim > &	elm_values,
		const FEInternalData &	fe_data
	)

protected

Computes the shape function values and gradients on the actual cell and fills the FEValues structure.

Parameters

fe_data Precomputed finite element data.

Definition at line 515 of file fe_values.cc.

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template<unsigned int spacedim>

void FEValues< spacedim >::fill_scalar_data	(	const ElementValues< spacedim > &	elm_values,
		const FEInternalData &	fe_data
	)

protected

Compute shape functions and gradients on the actual cell for scalar FE.

Definition at line 310 of file fe_values.cc.

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template<unsigned int spacedim>

void FEValues< spacedim >::fill_system_data	(	const ElementValues< spacedim > &	elm_values,
		const FEInternalData &	fe_data
	)

protected

Compute shape functions and gradients on the actual cell for mixed system of FE.

Definition at line 458 of file fe_values.cc.

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template<unsigned int spacedim>

void FEValues< spacedim >::fill_tensor_data	(	const ElementValues< spacedim > &	elm_values,
		const FEInternalData &	fe_data
	)

protected

Compute shape functions and gradients on the actual cell for tensorial FE.

Definition at line 426 of file fe_values.cc.

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template<unsigned int spacedim>

void FEValues< spacedim >::fill_vec_contravariant_data	(	const ElementValues< spacedim > &	elm_values,
		const FEInternalData &	fe_data
	)

protected

Compute shape functions and gradients on the actual cell for vectorial FE.

Definition at line 361 of file fe_values.cc.

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template<unsigned int spacedim>

void FEValues< spacedim >::fill_vec_data	(	const ElementValues< spacedim > &	elm_values,
		const FEInternalData &	fe_data
	)

protected

Compute shape functions and gradients on the actual cell for vectorial FE.

Definition at line 329 of file fe_values.cc.

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template<unsigned int spacedim>

void FEValues< spacedim >::fill_vec_piola_data	(	const ElementValues< spacedim > &	elm_values,
		const FEInternalData &	fe_data
	)

protected

Compute shape functions and gradients on the actual cell for Raviart-Thomas FE.

Definition at line 393 of file fe_values.cc.

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template<unsigned int spacedim = 3>

template<unsigned int DIM>

std::shared_ptr<typename FEValues<spacedim>::FEInternalData> FEValues< spacedim >::init_fe_data	(	const FiniteElement< DIM > &	fe,
		const Quadrature &	q
	)

Definition at line 232 of file fe_values.cc.

template<unsigned int spacedim = 3>

template<unsigned int DIM>

std::shared_ptr<FEInternalData> FEValues< spacedim >::init_fe_data	(	const FiniteElement< DIM > &	fe,
		const Quadrature &	q
	)

protected

Precompute finite element data on reference element.

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template<unsigned int spacedim>

template<unsigned int DIM>

void FEValues< spacedim >::initialize	(	Quadrature &	_quadrature,
		FiniteElement< DIM > &	_fe,
		UpdateFlags	_flags
	)

Initialize structures and calculates cell-independent data.

Parameters

_quadrature	The quadrature rule for the cell associated to given finite element or for the cell side.
_fe	The finite element.
_flags	The update flags.

Definition at line 136 of file fe_values.cc.

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template<unsigned int spacedim = 3>

double FEValues< spacedim >::JxW ( const unsigned int point_no )

inline

Return the product of Jacobian determinant and the quadrature weight at given quadrature point.

Parameters

point_no Number of the quadrature point.

Definition at line 200 of file fe_values.hh.

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template<unsigned int spacedim = 3>

unsigned int FEValues< spacedim >::n_dofs ( ) const

inline

Returns the number of shape functions.

Definition at line 279 of file fe_values.hh.

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template<unsigned int spacedim = 3>

unsigned int FEValues< spacedim >::n_points ( ) const

inline

Returns the number of quadrature points.

Definition at line 273 of file fe_values.hh.

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template<unsigned int spacedim = 3>

arma::vec::fixed<spacedim> FEValues< spacedim >::normal_vector ( unsigned int point_no )

inline

Returns the normal vector to a side at given quadrature point.

Parameters

point_no Number of the quadrature point.

Definition at line 234 of file fe_values.hh.

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template<unsigned int spacedim = 3>

arma::vec::fixed<spacedim> FEValues< spacedim >::point ( const unsigned int point_no )

inline

Return coordinates of the quadrature point in the actual cell system.

Parameters

point_no Number of the quadrature point.

Definition at line 213 of file fe_values.hh.

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template<unsigned int spacedim = 3>

const Armor::array& FEValues< spacedim >::point_list ( ) const

inline

Return coordinates of all quadrature points in the actual cell system.

Definition at line 223 of file fe_values.hh.

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template<unsigned int spacedim>

void FEValues< spacedim >::reinit ( const ElementAccessor< spacedim > & cell )

Update cell-dependent data (gradients, Jacobians etc.)

Parameters

cell	The actual cell.

Definition at line 548 of file fe_values.cc.

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template<unsigned int spacedim>

void FEValues< spacedim >::reinit ( const Side & cell_side )

Update cell side-dependent FE data (values, gradients).

Parameters

cell_side Accessor to cell side.

Definition at line 563 of file fe_values.cc.

template<unsigned int spacedim = 3>

const FEValuesViews::Scalar<spacedim>& FEValues< spacedim >::scalar_view ( unsigned int i ) const

inline

Accessor to scalar values of multicomponent FE.

Parameters

i	Index of scalar component.

Definition at line 244 of file fe_values.hh.

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template<unsigned int spacedim>

arma::vec::fixed< spacedim > FEValues< spacedim >::shape_grad	(	const unsigned int	function_no,
		const unsigned int	point_no
	)

Return the gradient of the function_no-th shape function at the point_no-th quadrature point.

Parameters

function_no	Number of the shape function.
point_no	Number of the quadrature point.

Definition at line 277 of file fe_values.cc.

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template<unsigned int spacedim>

arma::vec::fixed< spacedim > FEValues< spacedim >::shape_grad_component	(	const unsigned int	function_no,
		const unsigned int	point_no,
		const unsigned int	comp
	)		const

Return the gradient of the function_no-th shape function at the point_no-th quadrature point.

For vectorial finite elements.

Parameters

function_no	Number of the shape function.
point_no	Number of the quadrature point.

Definition at line 298 of file fe_values.cc.

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template<unsigned int spacedim>

double FEValues< spacedim >::shape_value	(	const unsigned int	function_no,
		const unsigned int	point_no
	)

Return the value of the function_no-th shape function at the point_no-th quadrature point.

Parameters

function_no	Number of the shape function.
point_no	Number of the quadrature point.

Definition at line 268 of file fe_values.cc.

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template<unsigned int spacedim>

double FEValues< spacedim >::shape_value_component	(	const unsigned int	function_no,
		const unsigned int	point_no,
		const unsigned int	comp
	)		const

Return the value of the function_no-th shape function at the point_no-th quadrature point.

For vectorial finite elements.

Parameters

function_no	Number of the shape function.
point_no	Number of the quadrature point.

Definition at line 286 of file fe_values.cc.

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template<unsigned int spacedim = 3>

const FEValuesViews::Tensor<spacedim>& FEValues< spacedim >::tensor_view ( unsigned int i ) const

inline

Accessor to tensor values of multicomponent FE.

Parameters

i	Index of first tensor component.

Definition at line 264 of file fe_values.hh.

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template<unsigned int spacedim = 3>

const FEValuesViews::Vector<spacedim>& FEValues< spacedim >::vector_view ( unsigned int i ) const

inline

Accessor to vector values of multicomponent FE.

Parameters

i	Index of first vector component.

Definition at line 254 of file fe_values.hh.

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Member Data Documentation

template<unsigned int spacedim = 3>

unsigned int FEValues< spacedim >::dim_

protected

Dimension of reference space.

Definition at line 365 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::shared_ptr<ElementValues<spacedim> > FEValues< spacedim >::elm_values

protected

Auxiliary object for calculation of element-dependent data.

Definition at line 396 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::shared_ptr<FEInternalData> FEValues< spacedim >::fe_data

protected

Precomputed finite element data.

Definition at line 408 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::vector<std::vector<unsigned int> > FEValues< spacedim >::fe_sys_dofs_

protected

Dof indices of FESystem sub-elements.

Definition at line 377 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::vector<unsigned int> FEValues< spacedim >::fe_sys_n_components_

protected

Numbers of components of FESystem sub-elements in reference space.

Definition at line 380 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::vector<unsigned int> FEValues< spacedim >::fe_sys_n_space_components_

protected

Numbers of components of FESystem sub-elements in real space.

Definition at line 383 of file fe_values.hh.

template<unsigned int spacedim = 3>

FEType FEValues< spacedim >::fe_type_

protected

Type of finite element (scalar, vector, tensor).

Definition at line 374 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::vector<FEValues<spacedim> > FEValues< spacedim >::fe_values_vec

protected

Vector of FEValues for sub-elements of FESystem.

Definition at line 399 of file fe_values.hh.

template<unsigned int spacedim = 3>

unsigned int FEValues< spacedim >::n_components_

protected

Number of components of the FE.

Definition at line 402 of file fe_values.hh.

template<unsigned int spacedim = 3>

unsigned int FEValues< spacedim >::n_dofs_

protected

Number of finite element dofs.

Definition at line 371 of file fe_values.hh.

template<unsigned int spacedim = 3>

unsigned int FEValues< spacedim >::n_points_

protected

Number of integration points.

Definition at line 368 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::vector<std::vector<arma::vec::fixed<spacedim> > > FEValues< spacedim >::shape_gradients

protected

Gradients of shape functions evaluated at the quadrature points. Each row of the matrix contains the gradient of one shape function.

Definition at line 390 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::vector<std::vector<double> > FEValues< spacedim >::shape_values

protected

Shape functions evaluated at the quadrature points.

Definition at line 386 of file fe_values.hh.

template<unsigned int spacedim = 3>

std::vector<std::vector<shared_ptr<FEInternalData> > > FEValues< spacedim >::side_fe_data

protected

Precomputed FE data (shape functions on reference element) for all sides and permuted quadrature points.

Definition at line 411 of file fe_values.hh.

template<unsigned int spacedim = 3>

UpdateFlags FEValues< spacedim >::update_flags

protected

Flags that indicate which finite element quantities are to be computed.

Definition at line 393 of file fe_values.hh.

template<unsigned int spacedim = 3>

ViewsCache FEValues< spacedim >::views_cache_

protected

Auxiliary storage of FEValuesViews accessors.

Definition at line 405 of file fe_values.hh.

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

/opt/flow123d/flow123d/src/fem/fe_values.hh
/opt/flow123d/flow123d/src/fem/fe_values.cc

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<unsigned int spacedim = 3> class FEValues< spacedim >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<unsigned int spacedim = 3>
class FEValues< spacedim >