#include <lagrange.h>

Inheritance diagram for ug::LagrangeLSFS< ReferenceTriangle, TOrder >:

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

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

Public Types inherited from ug::BaseLSFS< LagrangeLSFS< ReferenceTriangle, TOrder >, 2 >
typedef MathVector< TDim >	grad_type
	Gradient type. More...

typedef LagrangeLSFS< ReferenceTriangle, TOrder >	ImplType
	type of implementation More...

typedef number	shape_type
	Shape type. More...

Public Member Functions
void	check_index (size_t i) const
	checks in debug mode that index is valid More...

void	check_multi_index (const MathVector< dim, int > &ind) const
	checks in debug mode that multi-index is valid More...

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

void	grad (grad_type &g, const MathVector< dim, int > ind, const MathVector< dim > &x) const
	evaluates the gradient More...

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

size_t	index (const MathVector< dim, int > &ind) const
	return the index for a multi_index More...

	LagrangeLSFS ()
	Constructor. More...

size_t	mapped_index (const MathVector< dim, int > &ind) const
	return the index for a multi_index More...

MathVector< dim, int >	mapped_multi_index (size_t i) const
	return the multi_index for an index More...

const MathVector< dim, int > &	multi_index (size_t i) const
	return Multi index for index i More...

size_t	num_sh () const

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

number	shape (const MathVector< dim, int > &ind, const MathVector< dim > &x) const
	shape value for a Multi Index More...

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

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

	LagrangeLDS (size_t order=1)
	constructor More...

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

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

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

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

void	set_order (size_t order)
	sets the order More...

Public Member Functions inherited from ug::LocalDoFSet
int	dim () const
	returns the reference dimension More...

size_t	num_dof (int d, size_t id) const
	returns the number of DoFs on a sub-geometric object of dim and id More...

bool	operator!= (const LocalDoFSet &v) const
	inequality check More...

bool	operator== (const LocalDoFSet &v) const
	equality check More...

virtual	~LocalDoFSet ()
	virtual destructor More...

size_t	num_dof () const

Public Member Functions inherited from ug::BaseLSFS< LagrangeLSFS< ReferenceTriangle, TOrder >, 2 >
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 = ReferenceTriangle::dim
	Dimension, where shape functions are defined. More...

static const size_t	nsh = BinomialCoefficient<dim + p, p>::value
	Number of shape functions. More...

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

Static Public Attributes inherited from ug::BaseLSFS< LagrangeLSFS< ReferenceTriangle, TOrder >, 2 >
static const int	dim
	dimension of reference element More...

Private Types
typedef BaseLSFS< LagrangeLSFS< ReferenceTriangle, TOrder >, 2 >	base_type
	base class More...

Private Attributes
Polynomial1D	m_vDPolynom [p+1]

MathVector< dim, int >	m_vMultiIndex [nsh]

Polynomial1D	m_vPolynom [p+1]

Static Private Attributes
static const size_t	p = TOrder
	abbreviation for order More...

Additional Inherited Members
Protected Member Functions inherited from ug::BaseLSFS< LagrangeLSFS< ReferenceTriangle, TOrder >, 2 >
ImplType &	getImpl ()
	access to implementation More...

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

Protected Attributes inherited from ug::LagrangeLDS< ReferenceTriangle >
std::vector< LocalDoF >	m_vLocalDoF
	association to geom obj More...

size_t	p
	order More...

Member Typedef Documentation

◆ base_type

template<int TOrder>

typedef BaseLSFS<LagrangeLSFS<ReferenceTriangle, TOrder>, 2> ug::LagrangeLSFS< ReferenceTriangle, TOrder >::base_type

private

base class

◆ grad_type

template<int TOrder>

typedef base_type::grad_type ug::LagrangeLSFS< ReferenceTriangle, TOrder >::grad_type

Gradient type.

◆ shape_type

template<int TOrder>

typedef base_type::shape_type ug::LagrangeLSFS< ReferenceTriangle, TOrder >::shape_type

Shape type.

Constructor & Destructor Documentation

◆ LagrangeLSFS()

template<int TOrder>

ug::LagrangeLSFS< ReferenceTriangle, TOrder >::LagrangeLSFS

Constructor.

References ug::Provider< TClass >::get(), p, and ug::SetLagrangeMultiIndex().

Member Function Documentation

◆ check_index()

template<int TOrder>

void ug::LagrangeLSFS< ReferenceTriangle, TOrder >::check_index ( size_t i ) const

inline

checks in debug mode that index is valid

References UG_ASSERT.

◆ check_multi_index()

template<int TOrder>

void ug::LagrangeLSFS< ReferenceTriangle, TOrder >::check_multi_index ( const MathVector< dim, int > & ind ) const

inline

checks in debug mode that multi-index is valid

References p, and UG_ASSERT.

◆ continuous()

template<int TOrder>

bool ug::LagrangeLSFS< ReferenceTriangle, TOrder >::continuous ( ) const

inline

returns if space constructs continuous functions

◆ grad() [1/2]

template<int TOrder>

void ug::LagrangeLSFS< ReferenceTriangle, TOrder >::grad	(	grad_type &	g,
		const MathVector< dim, int >	ind,
		const MathVector< dim > &	x
	)		const

inline

evaluates the gradient

References dim, p, ug::SMALL, and UG_ASSERT.

◆ grad() [2/2]

template<int TOrder>

void ug::LagrangeLSFS< ReferenceTriangle, TOrder >::grad	(	grad_type &	g,
		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

◆ index()

template<int TOrder>

size_t ug::LagrangeLSFS< ReferenceTriangle, TOrder >::index ( const MathVector< dim, int > & ind ) const

inline

return the index for a multi_index

References UG_THROW.

◆ mapped_index()

template<int TOrder>

size_t ug::LagrangeLSFS< ReferenceTriangle, TOrder >::mapped_index ( const MathVector< dim, int > & ind ) const

inline

return the index for a multi_index

References p.

◆ mapped_multi_index()

template<int TOrder>

MathVector<dim,int> ug::LagrangeLSFS< ReferenceTriangle, TOrder >::mapped_multi_index ( size_t i ) const

inline

return the multi_index for an index

References p, and UG_ASSERT.

◆ multi_index()

template<int TOrder>

const MathVector<dim,int>& ug::LagrangeLSFS< ReferenceTriangle, TOrder >::multi_index ( size_t i ) const

inline

return Multi index for index i

◆ num_sh()

template<int TOrder>

size_t ug::LagrangeLSFS< ReferenceTriangle, TOrder >::num_sh ( ) const

inlinevirtual

returns the total number of dofs on the finite element

Reimplemented from ug::LocalDoFSet.

◆ position()

template<int TOrder>

bool ug::LagrangeLSFS< ReferenceTriangle, TOrder >::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 dim, p, and ug::TruncatedEquidistantLagrange1D::position().

◆ shape() [1/2]

template<int TOrder>

number ug::LagrangeLSFS< ReferenceTriangle, TOrder >::shape	(	const MathVector< dim, int > &	ind,
		const MathVector< dim > &	x
	)		const

inline

shape value for a Multi Index

References p.

◆ shape() [2/2]

template<int TOrder>

number ug::LagrangeLSFS< ReferenceTriangle, TOrder >::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

Member Data Documentation

◆ dim

template<int TOrder>

const int ug::LagrangeLSFS< ReferenceTriangle, TOrder >::dim = ReferenceTriangle::dim

static

Dimension, where shape functions are defined.

◆ m_vDPolynom

template<int TOrder>

Polynomial1D ug::LagrangeLSFS< ReferenceTriangle, TOrder >::m_vDPolynom[p+1]

private

◆ m_vMultiIndex

template<int TOrder>

MathVector<dim,int> ug::LagrangeLSFS< ReferenceTriangle, TOrder >::m_vMultiIndex[nsh]

private

◆ m_vPolynom

template<int TOrder>

Polynomial1D ug::LagrangeLSFS< ReferenceTriangle, TOrder >::m_vPolynom[p+1]

private

◆ nsh

template<int TOrder>

const size_t ug::LagrangeLSFS< ReferenceTriangle, TOrder >::nsh = BinomialCoefficient<dim + p, p>::value

static

Number of shape functions.

◆ order

template<int TOrder>

const size_t ug::LagrangeLSFS< ReferenceTriangle, TOrder >::order = TOrder

static

Order of Shape functions.

◆ p

template<int TOrder>

const size_t ug::LagrangeLSFS< ReferenceTriangle, TOrder >::p = TOrder

staticprivate

abbreviation for order

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

ugbase/lib_disc/local_finite_element/lagrange/lagrange.h
ugbase/lib_disc/local_finite_element/lagrange/lagrange.cpp

Public Types

Public Member Functions

Static Public Attributes

Private Types

Private Attributes

Static Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ base_type

◆ grad_type

◆ shape_type

Constructor & Destructor Documentation

◆ LagrangeLSFS()

Member Function Documentation

◆ check_index()

◆ check_multi_index()

◆ continuous()

◆ grad() [1/2]

◆ grad() [2/2]

◆ index()

◆ mapped_index()

◆ mapped_multi_index()

◆ multi_index()

◆ num_sh()

◆ position()

◆ shape() [1/2]

◆ shape() [2/2]

Member Data Documentation

◆ dim

◆ m_vDPolynom

◆ m_vMultiIndex

◆ m_vPolynom

◆ nsh

◆ order

◆ p