Nedelec (or Whitney-1) base function set for triangles. More...

#include <nedelec.h>

Inheritance diagram for ug::NedelecLSFS< ReferenceTriangle >:

Public Types
typedef base_type::grad_type	grad_type
	Gradient type. More...

typedef ReferenceTriangle	reference_element_type
	Reference Element type. More...

typedef base_type::shape_type	shape_type
	Shape type. More...

Public Types inherited from ug::BaseLSFS< NedelecLSFS< ReferenceTriangle >, ReferenceTriangle::dim, MathVector< ReferenceTriangle::dim >, MathMatrix< ReferenceTriangle::dim, ReferenceTriangle::dim > >
typedef MathMatrix< ReferenceTriangle::dim, ReferenceTriangle::dim >	grad_type
	Gradient type. More...

typedef NedelecLSFS< ReferenceTriangle >	ImplType
	type of implementation More...

typedef MathVector< ReferenceTriangle::dim >	shape_type
	Shape type. More...

Public Member Functions
bool	continuous () const
	returns if space constructs continuous functions More...

void	grad (MathMatrix< dim, dim > &g, const size_t i, const MathVector< dim > &x) const
	evaluates the gradient of the shape function More...

	NedelecLSFS ()
	Constructor. More...

size_t	num_sh () const

bool	position (size_t i, MathVector< dim > &pos) const
	local position of DoF i More...

MathVector< dim >	shape (const size_t i, const MathVector< dim > &x) const
	evaluates the shape function More...

Public Member Functions inherited from ug::NedelecLDS< ReferenceTriangle >
bool	exact_position_available () const
	returns if the local dof position are exact More...

const LocalDoF &	local_dof (size_t dof) const
	returns the dof storage More...

	NedelecLDS ()
	constructor More...

size_t	num_dof () const
	returns the total number of DoFs on the finite element More...

size_t	num_dof (ReferenceObjectID type) const
	returns the number of DoFs on a sub-geometric object type More...

ReferenceObjectID	roid () const
	returns the type of reference element More...

Public Member Functions inherited from ug::BaseLSFS< NedelecLSFS< ReferenceTriangle >, ReferenceTriangle::dim, MathVector< ReferenceTriangle::dim >, MathMatrix< ReferenceTriangle::dim, ReferenceTriangle::dim > >
void	grad (grad_type &g, size_t i, const MathVector< dim > &x) const
	evaluates the gradient of the shape function More...

void	grads (grad_type *vGrad, const MathVector< dim > &x) const
	returns all gradients evaluated at a point More...

void	grads (std::vector< grad_type > &vGrad, const MathVector< dim > &x) const
	returns all gradients evaluated at a point More...

void	grads (std::vector< std::vector< grad_type > > &vvGrad, const std::vector< MathVector< dim > > &vLocPos) const
	returns all gradients evaluated at a point More...

void	shape (shape_type &sh, size_t i, const MathVector< dim > &x) const
	evaluates the shape function More...

shape_type	shape (size_t i, const MathVector< dim > &x) const
	evaluates the shape function More...

void	shapes (shape_type *vShape, const MathVector< dim > &x) const
	returns all shape functions evaluated at a point More...

void	shapes (std::vector< shape_type > &vShape, const MathVector< dim > &x) const
	returns all shape functions evaluated at a point More...

void	shapes (std::vector< std::vector< shape_type > > &vvShape, const std::vector< MathVector< dim > > &vLocPos) const
	returns all shape functions evaluated at a point More...

Static Public Attributes
static const int	dim = reference_element_type::dim
	Dimension, where shape functions are defined. More...

static const size_t	order = 1
	Order of Shape functions. More...

Static Public Attributes inherited from ug::BaseLSFS< NedelecLSFS< ReferenceTriangle >, ReferenceTriangle::dim, MathVector< ReferenceTriangle::dim >, MathMatrix< ReferenceTriangle::dim, ReferenceTriangle::dim > >
static const int	dim
	dimension of reference element More...

Static Protected Attributes
static const size_t	nsh = reference_element_type::numEdges
	number of shapes More...

Static Protected Attributes inherited from ug::NedelecLDS< ReferenceTriangle >
static const int	refDim
	dimension of reference element More...

Private Types
typedef BaseLSFS< NedelecLSFS< reference_element_type >, dim, MathVector< dim >, MathMatrix< dim, dim > >	base_type
	Base class. More...

Additional Inherited Members
Protected Member Functions inherited from ug::BaseLSFS< NedelecLSFS< ReferenceTriangle >, ReferenceTriangle::dim, MathVector< ReferenceTriangle::dim >, MathMatrix< ReferenceTriangle::dim, ReferenceTriangle::dim > >
ImplType &	getImpl ()
	access to implementation More...

const ImplType &	getImpl () const
	const access to implementation More...

Protected Attributes inherited from ug::NedelecLDS< ReferenceTriangle >
std::vector< LocalDoF >	m_vLocalDoF
	association to elements More...

size_t	nsh
	number of shapes (== number of edges) More...

Detailed Description

Nedelec (or Whitney-1) base function set for triangles.

Member Typedef Documentation

◆ base_type

typedef BaseLSFS<NedelecLSFS<reference_element_type>, dim, MathVector<dim>, MathMatrix<dim,dim> > ug::NedelecLSFS< ReferenceTriangle >::base_type

private

Base class.

◆ grad_type

typedef base_type::grad_type ug::NedelecLSFS< ReferenceTriangle >::grad_type

Gradient type.

◆ reference_element_type

typedef ReferenceTriangle ug::NedelecLSFS< ReferenceTriangle >::reference_element_type

Reference Element type.

◆ shape_type

typedef base_type::shape_type ug::NedelecLSFS< ReferenceTriangle >::shape_type

Shape type.

Constructor & Destructor Documentation

◆ NedelecLSFS()

ug::NedelecLSFS< ReferenceTriangle >::NedelecLSFS ( )

inline

Constructor.

Member Function Documentation

◆ continuous()

bool ug::NedelecLSFS< ReferenceTriangle >::continuous ( ) const

inline

returns if space constructs continuous functions

◆ grad()

void ug::NedelecLSFS< ReferenceTriangle >::grad	(	MathMatrix< dim, dim > &	g,
		const size_t	i,
		const MathVector< dim > &	x
	)		const

inline

evaluates the gradient of the shape function

This function returns the gradient of Shape Function i at an element-local evaluation point.

Parameters

[in]	i	number of DoF
[in]	x	Position on reference element (evaluation point)

Returns: gradient at point

References UG_THROW.

◆ num_sh()

size_t ug::NedelecLSFS< ReferenceTriangle >::num_sh ( ) const

inline

returns the total number of dofs on the finite element

◆ position()

bool ug::NedelecLSFS< ReferenceTriangle >::position	(	size_t	i,
		MathVector< dim > &	pos
	)		const

inline

local position of DoF i

This function returns the local position of a DoF if possible.

Parameters

[in]	i	number of DoF
[out]	pos	Position of DoF

Return values

true	if position exists
false	if no meaningful position available

References UG_THROW.

◆ shape()

MathVector<dim> ug::NedelecLSFS< ReferenceTriangle >::shape	(	const size_t	i,
		const MathVector< dim > &	x
	)		const

inline

evaluates the shape function

This function returns the value of Shape Function i at an element-local evaluation point.

Parameters

[in]	i	number of DoF
[in]	x	Position on reference element (evaluation point)

Returns: shape function value at point

References UG_THROW.

Member Data Documentation

◆ dim

const int ug::NedelecLSFS< ReferenceTriangle >::dim = reference_element_type::dim

static

Dimension, where shape functions are defined.

◆ nsh

const size_t ug::NedelecLSFS< ReferenceTriangle >::nsh = reference_element_type::numEdges

staticprotected

number of shapes

◆ order

const size_t ug::NedelecLSFS< ReferenceTriangle >::order = 1

static

Order of Shape functions.

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

ugbase/lib_disc/local_finite_element/nedelec/nedelec.h

Public Types

Public Member Functions

Static Public Attributes

Static Protected Attributes

Private Types

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ base_type

◆ grad_type

◆ reference_element_type

◆ shape_type

Constructor & Destructor Documentation

◆ NedelecLSFS()

Member Function Documentation

◆ continuous()

◆ grad()

◆ num_sh()

◆ position()

◆ shape()

Member Data Documentation

◆ dim

◆ nsh

◆ order