A constant local function carrying values for one entity. More...

#include <dune/fem/function/localfunction/const.hh>

Public Types
typedef BaseType::SizeType	SizeType
	type of SizeType

typedef FunctionSpaceType::DomainFieldType	DomainFieldType
	field type of the domain

typedef FunctionSpaceType::RangeFieldType	RangeFieldType
	field type of the range

typedef EntityType::Geometry::LocalCoordinate	LocalCoordinateType
	type of local coordinates

typedef Traits::derived_type	derived_type
	type of derived vector class

typedef Traits::value_type	value_type
	export the type representing the field

typedef FieldTraits< value_type >::field_type	field_type
	export the type representing the field

typedef Traits::value_type	block_type
	export the type representing the components

typedef Traits::size_type	size_type
	The type used for the index access and size operation.

typedef DenseIterator< DenseVector, value_type >	Iterator
	Iterator class for sequential access.

typedef Iterator	iterator
	typedef for stl compliant access

typedef DenseIterator< const DenseVector, const value_type >	ConstIterator
	ConstIterator class for sequential access.

typedef ConstIterator	const_iterator
	typedef for stl compliant access

Public Member Functions
	ConstLocalDiscreteFunction (const DiscreteFunctionType &df)
	constructor creating a local function without binding it to an entity More...

	ConstLocalDiscreteFunction (const typename DiscreteFunctionType::LocalFunctionType &localFunction)
	cast a MutableLocalFunction into this one !!! expensive !!!

	ConstLocalDiscreteFunction (const DiscreteFunctionType &df, const EntityType &entity)
	constructor creating a local function and binding it to an entity More...

	ConstLocalDiscreteFunction (const ThisType &other)
	copy constructor

	ConstLocalDiscreteFunction (ThisType &&other)
	move constructor

template<class Point >
RangeType	evaluate (const Point &p) const
	evaluate the local function More...

template<class Point >
JacobianRangeType	jacobian (const Point &p) const
	evaluate Jacobian of the local function More...

template<class Point >
HessianRangeType	hessian (const Point &p) const
	evaluate Hessian of the local function More...

void	init (const EntityType &entity)
	interface for local functions :: init More...

const LocalDofVectorType &	localDofVector () const
	return const reference to local Dof Vector

LocalDofVectorType &	localDofVector ()
	return mutable reference to local Dof Vector

template<class PointType >
void	evaluate (const PointType &x, RangeType &ret) const
	evaluate the local function More...

template<class PointType >
void	jacobian (const PointType &x, JacobianRangeType &ret) const
	evaluate Jacobian of the local function More...

template<class PointType >
void	hessian (const PointType &x, HessianRangeType &ret) const
	evaluate Hessian of the local function More...

value_type &	operator[] (size_type i)
	random access

const LocalDofVectorType &	localDofVector () const
	return const reference to local Dof Vector

template<class T >
void	assign (const LocalFunction< BasisFunctionSet, T > &other)
	assign all DoFs of this local function More...

template<class PointType >
void	axpy (const PointType &x, const RangeType &factor)
	axpy operation for local function More...

template<class PointType >
void	axpy (const PointType &x, const JacobianRangeType &factor)
	axpy operation for local function More...

template<class PointType >
void	axpy (const PointType &x, const RangeType &factor1, const JacobianRangeType &factor2)
	axpy operation for local function More...

derived_type &	axpy (const field_type &a, const DenseVector< Other > &x)
	vector space axpy operation ( *this += a x )

int	order () const
	obtain the order of this local function More...

const BasisFunctionSetType &	basisFunctionSet () const
	obtain the basis function set for this local function More...

const EntityType &	entity () const
	obtain the entity, this local function lives on More...

template<class PointType >
void	evaluate (const PointType &x, RangeType &ret) const
	evaluate the local function More...

template<class PointType >
void	jacobian (const PointType &x, JacobianRangeType &ret) const
	evaluate Jacobian of the local function More...

template<class PointType >
void	hessian (const PointType &x, HessianRangeType &ret) const
	evaluate Hessian of the local function More...

int	numDofs () const
	obtain the number of local DoFs More...

SizeType	size () const
	obtain the number of local DoFs More...

template<class QuadratureType , class ... Vectors>
void	axpyQuadrature (const QuadratureType &quad, const Vectors &... values)
	evaluate all basisfunctions for all quadrature points, multiply with the given factor and add the result to the local coefficients

template<class QuadratureType , class RangeVectorType , class JacobianRangeVectorType >
void	axpyQuadrature (const QuadratureType &quad, const RangeVectorType &rangeVector, const JacobianRangeVectorType &jacobianVector)
	evaluate all basisfunctions for all quadrature points, multiply with the given factor and add the result to the local coefficients

template<class QuadratureType , class ... Vectors>
void	evaluateQuadrature (const QuadratureType &quad, Vectors &... vec) const
	evaluate all basisfunctions for all quadrature points and store the results in the result vector

template<class QuadratureType , class ... Vectors>
void	jacobianQuadrature (const QuadratureType &quad, Vectors &... vec) const
	evaluate all Jacobians for all basis functions for all quadrature points and store the results in the result vector

template<class QuadratureType , class ... Vectors>
void	hessianQuadrature (const QuadratureType &quad, Vectors &... vec) const
	evaluate all hessians of all basis functions for all quadrature points and store the results in the result vector

bool	valid () const
	Returns true if local function if bind or init was previously called.

value_type &	front ()
	return reference to first element

const value_type &	front () const
	return reference to first element

value_type &	back ()
	return reference to last element

const value_type &	back () const
	return reference to last element

bool	empty () const
	checks whether the container is empty

Iterator	begin ()
	begin iterator

ConstIterator	begin () const
	begin ConstIterator

Iterator	end ()
	end iterator

ConstIterator	end () const
	end ConstIterator

Iterator	beforeEnd ()

ConstIterator	beforeEnd () const

Iterator	beforeBegin ()

ConstIterator	beforeBegin () const

Iterator	find (size_type i)
	return iterator to given element or end()

ConstIterator	find (size_type i) const
	return iterator to given element or end()

derived_type &	operator+= (const DenseVector< Other > &x)
	vector space addition

std::enable_if< std::is_convertible< ValueType, value_type >::value, derived_type >::type &	operator+= (const ValueType &kk)
	vector space add scalar to all comps More...

derived_type &	operator-= (const DenseVector< Other > &x)
	vector space subtraction

std::enable_if< std::is_convertible< ValueType, value_type >::value, derived_type >::type &	operator-= (const ValueType &kk)
	vector space subtract scalar from all comps More...

derived_type	operator+ (const DenseVector< Other > &b) const
	Binary vector addition.

derived_type	operator- (const DenseVector< Other > &b) const
	Binary vector subtraction.

derived_type	operator- () const
	Vector negation.

std::enable_if< std::is_convertible< FieldType, field_type >::value, derived_type >::type &	operator*= (const FieldType &kk)
	vector space multiplication with scalar More...

std::enable_if< std::is_convertible< FieldType, field_type >::value, derived_type >::type &	operator/= (const FieldType &kk)
	vector space division by scalar More...

bool	operator== (const DenseVector< Other > &x) const
	Binary vector comparison.

bool	operator!= (const DenseVector< Other > &x) const
	Binary vector incomparison.

PromotionTraits< field_type, typename DenseVector< Other >::field_type >::PromotedType	operator* (const DenseVector< Other > &x) const
	indefinite vector dot product \(\left (x^T \cdot y \right)\) which corresponds to Petsc's VecTDot More...

PromotionTraits< field_type, typename DenseVector< Other >::field_type >::PromotedType	dot (const DenseVector< Other > &x) const
	vector dot product \(\left (x^H \cdot y \right)\) which corresponds to Petsc's VecDot More...

FieldTraits< value_type >::real_type	one_norm () const
	one norm (sum over absolute values of entries)

FieldTraits< value_type >::real_type	one_norm_real () const
	simplified one norm (uses Manhattan norm for complex values)

FieldTraits< value_type >::real_type	two_norm () const
	two norm sqrt(sum over squared values of entries)

FieldTraits< value_type >::real_type	two_norm2 () const
	square of two norm (sum over squared values of entries), need for block recursion

FieldTraits< vt >::real_type	infinity_norm () const
	infinity norm (maximum of absolute values of entries)

FieldTraits< vt >::real_type	infinity_norm () const
	infinity norm (maximum of absolute values of entries)

FieldTraits< vt >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)

FieldTraits< vt >::real_type	infinity_norm_real () const
	simplified infinity norm (uses Manhattan norm for complex values)

size_type	N () const
	number of blocks in the vector (are of size 1 here)

size_type	dim () const
	dimension of the vector space

Static Public Attributes
static const int	dimDomain = FunctionSpaceType::dimDomain
	dimension of the domain

static const int	dimRange = FunctionSpaceType::dimRange
	dimension of the range

constexpr static int	blocklevel
	The number of block levels we contain. This is the leaf, that is, 1.

Protected Member Functions
void	clear ()
	set all DoFs to zero

template<class T >
void	assign (const LocalFunction< BasisFunctionSet, T > &other)
	assign all DoFs of this local function More...

template<class PointType >
void	axpy (const PointType &x, const RangeType &factor)
	axpy operation for local function More...

template<class PointType >
void	axpy (const PointType &x, const JacobianRangeType &factor)
	axpy operation for local function More...

template<class PointType >
void	axpy (const PointType &x, const RangeType &factor1, const JacobianRangeType &factor2)
	axpy operation for local function More...

void	init (const EntityType &entity)
	initialize the local function for an entity More...

void	init (const BasisFunctionSetType &basisFunctionSet)
	initialize the local function for an basisFunctionSet More...

void	bind (const EntityType &entity)
	initialize the local function for an entity More...

Related Functions
(Note that these are not member functions.)
std::ostream &	operator<< (std::ostream &s, const DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > > &v)
	Write a DenseVector to an output stream. More...

Detailed Description

template<class DiscreteFunction>
class Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >

A constant local function carrying values for one entity.

A ConstLocalDiscreteFunction is a LocalFunction which is basically doing the same as the LocalFunction of a discrete function. The difference is that the local dofs are not kept as references but are copied to a local storage. Therefore, this is a const local function and any modification of dofs is not allowed.

Note: Local DoF numbers correspond directly to array indices. Hence it may be more cache efficient to generate a ConstLocalFunction when only a const access to the local function is needed.

Parameters

DiscreteFunction type of the discrete function, the local function shall belong to

Constructor & Destructor Documentation

◆ ConstLocalDiscreteFunction() [1/2]

template<class DiscreteFunction >

Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::ConstLocalDiscreteFunction ( const DiscreteFunctionType & df )

inlineexplicit

constructor creating a local function without binding it to an entity

Creates the local function without initializing the fields depending on the current entity.

Note: Before using the local function it must be initilized by
localFunction.init( entity );

Dune::Fem::LocalFunction::entity
const EntityType & entity() const
obtain the entity, this local function lives on
Definition: localfunction.hh:302

Parameters

[in] df discrete function the local function shall belong to

◆ ConstLocalDiscreteFunction() [2/2]

template<class DiscreteFunction >

Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::ConstLocalDiscreteFunction	(	const DiscreteFunctionType &	df,
		const EntityType &	entity
	)

inline

constructor creating a local function and binding it to an entity

Creates the local function and initilizes the fields depending on the current entity. It is not necessary, though allowed, to call init before using the discrete function.

Note: The degrees of freedom are not initialized by this function.

Parameters

[in]	df	discrete function the local function shall belong to
[in]	entity	entity for initialize the local function to

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::entity(), and Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::localDofVector().

Member Function Documentation

◆ assign() [1/2]

template<class BasisFunctionSet , class LocalDofVector >

template<class T >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::assign ( class T )

inlineprotectedinherited

assign all DoFs of this local function

Parameters

[in] lf local function to assign DoFs from

◆ assign() [2/2]

template<class BasisFunctionSet , class LocalDofVector >

template<class T >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::assign ( const LocalFunction< BasisFunctionSet, T > & other )

inlineinherited

assign all DoFs of this local function

Parameters

[in] lf local function to assign DoFs from

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

Referenced by Dune::Fem::ProlongFunction< LRP >::operator()(), Dune::Fem::RestrictFunction< LRP >::operator()(), and Dune::Fem::hpDG::DefaultDataProjection< DiscreteFunction >::operator()().

◆ axpy() [1/6]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::axpy ( class PointType )

inlineprotectedinherited

axpy operation for local function

Denoting the DoFs of the local function by \(u_i\) and the basis functions by \(\varphi_i\), this function performs the following operation:

\[ u_i = u_i + factor \cdot \nabla\varphi_i( x ) \]

Parameters

[in]	x	point to evaluate jacobian of basis functions in
[in]	factor	axpy factor

◆ axpy() [2/6]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::axpy	(	const PointType &	x,
		const JacobianRangeType &	factor
	)

inlineinherited

axpy operation for local function

Denoting the DoFs of the local function by \(u_i\) and the basis functions by \(\varphi_i\), this function performs the following operation:

\[ u_i = u_i + factor \cdot \nabla\varphi_i( x ) \]

Parameters

[in]	x	point to evaluate jacobian of basis functions in
[in]	factor	axpy factor

References Dune::Fem::BasisFunctionSet< Entity, Range >::axpy(), Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), and Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

◆ axpy() [3/6]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::axpy ( class PointType )

inlineprotectedinherited

axpy operation for local function

Denoting the DoFs of the local function by \(u_i\) and the basis functions by \(\varphi_i\), this function performs the following operation:

\[ u_i = u_i + factor \cdot \varphi_i( x ) \]

Parameters

[in]	x	point to evaluate basis functions in
[in]	factor	axpy factor

◆ axpy() [4/6]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::axpy	(	const PointType &	x,
		const RangeType &	factor
	)

inlineinherited

axpy operation for local function

Denoting the DoFs of the local function by \(u_i\) and the basis functions by \(\varphi_i\), this function performs the following operation:

\[ u_i = u_i + factor \cdot \varphi_i( x ) \]

Parameters

[in]	x	point to evaluate basis functions in
[in]	factor	axpy factor

References Dune::Fem::BasisFunctionSet< Entity, Range >::axpy(), Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), and Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

Referenced by Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::axpyQuadrature().

◆ axpy() [5/6]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::axpy ( class PointType )

inlineprotectedinherited

axpy operation for local function

Denoting the DoFs of the local function by \(u_i\) and the basis functions by \(\varphi_i\), this function performs the following operation:

\[ u_i = u_i + factor1 \cdot \varphi_i( x ) + factor2 \cdot \nabla\varphi_i( x ) \]

Parameters

[in]	x	point to evaluate basis functions in
[in]	factor1	axpy factor for \(\varphi( x )\)
[in]	factor2	axpy factor for \(\nabla\varphi( x )\)

◆ axpy() [6/6]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::axpy	(	const PointType &	x,
		const RangeType &	factor1,
		const JacobianRangeType &	factor2
	)

inlineinherited

axpy operation for local function

Denoting the DoFs of the local function by \(u_i\) and the basis functions by \(\varphi_i\), this function performs the following operation:

\[ u_i = u_i + factor1 \cdot \varphi_i( x ) + factor2 \cdot \nabla\varphi_i( x ) \]

Parameters

[in]	x	point to evaluate basis functions in
[in]	factor1	axpy factor for \(\varphi( x )\)
[in]	factor2	axpy factor for \(\nabla\varphi( x )\)

References Dune::Fem::BasisFunctionSet< Entity, Range >::axpy(), Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), and Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

◆ basisFunctionSet()

template<class BasisFunctionSet , class LocalDofVector >

const BasisFunctionSetType& Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet ( ) const

inlineinherited

obtain the basis function set for this local function

Returns: reference to the basis function set

◆ beforeBegin() [1/2]

Iterator Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::beforeBegin ( )

inlineinherited

Returns: an iterator that is positioned before the first entry of the vector.

◆ beforeBegin() [2/2]

ConstIterator Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::beforeBegin ( ) const

inlineinherited

Returns: an iterator that is positioned before the first entry of the vector.

◆ beforeEnd() [1/2]

Iterator Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::beforeEnd ( )

inlineinherited

Returns: an iterator that is positioned before the end iterator of the vector, i.e. at the last entry.

◆ beforeEnd() [2/2]

ConstIterator Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::beforeEnd ( ) const

inlineinherited

Returns: an iterator that is positioned before the end iterator of the vector. i.e. at the last element

◆ bind()

template<class BasisFunctionSet , class LocalDofVector >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::bind ( const EntityType & entity )

inlineprotectedinherited

initialize the local function for an entity

Binds the local function to an basisFunctionSet and entity.

Note: Must be overloaded on the derived implementation class.

Parameters

[in] entity to bind the local function to

References DUNE_THROW.

◆ dot()

PromotionTraits<field_type,typename DenseVector<Other>::field_type>::PromotedType Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::dot ( const DenseVector< Other > & x ) const

inlineinherited

vector dot product \(\left (x^H \cdot y \right)\) which corresponds to Petsc's VecDot

http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecDot.html

Parameters

x	other vector

Returns

◆ entity()

template<class BasisFunctionSet , class LocalDofVector >

const EntityType& Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::entity ( ) const

inlineinherited

obtain the entity, this local function lives on

Returns: reference to the entity

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), and Dune::Fem::BasisFunctionSet< Entity, Range >::entity().

Referenced by Dune::Fem::LocalOrthonormalL2Projection< GridPart, BasisFunctionSet, Quadrature >::apply(), Dune::Fem::LocalMassMatrixImplementation< DiscreteFunctionSpace, VolumeQuadrature, refElemScaling >::applyInverse(), Dune::Fem::LocalMassMatrixImplementationDgOrthoNormal< DiscreteFunctionSpace, VolumeQuadrature, refElemScaling >::applyInverse(), Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::ConstLocalDiscreteFunction(), Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::init(), Dune::Fem::RestrictProlongDefault< DiscreteFunction >::restrictFinalize(), and Dune::Fem::RestrictProlongDefault< DiscreteFunction >::restrictLocal().

◆ evaluate() [1/3]

template<class DiscreteFunction >

template<class Point >

RangeType Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::evaluate ( const Point & p ) const

inline

evaluate the local function

Parameters

[in] x evaluation point in local coordinates

Returns: value of the function in the given point

◆ evaluate() [2/3]

template<class DiscreteFunction >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::evaluate ( class PointType )

inline

evaluate the local function

Parameters

[in]	x	evaluation point in local coordinates
[out]	ret	value of the function in the given point

◆ evaluate() [3/3]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::evaluate	(	const PointType &	x,
		RangeType &	ret
	)		const

inlineinherited

evaluate the local function

Parameters

[in]	x	evaluation point in local coordinates
[out]	ret	value of the function in the given point

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), Dune::Fem::BasisFunctionSet< Entity, Range >::evaluateAll(), and Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

◆ hessian() [1/3]

template<class DiscreteFunction >

template<class Point >

HessianRangeType Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::hessian ( const Point & p ) const

inline

evaluate Hessian of the local function

Note: Though the Hessian is evaluated on the reference element, the return value is the Hessian with respect to the actual entity.

Parameters

[in] x evaluation point in local coordinates

Returns: Hessian of the function in the evaluation point

◆ hessian() [2/3]

template<class DiscreteFunction >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::hessian ( class PointType )

inline

evaluate Hessian of the local function

Note: Though the Hessian is evaluated on the reference element, the return value is the Hessian with respect to the actual entity.

Parameters

[in]	x	evaluation point in local coordinates
[out]	ret	Hessian of the function in the evaluation point

◆ hessian() [3/3]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::hessian	(	const PointType &	x,
		HessianRangeType &	ret
	)		const

inlineinherited

evaluate Hessian of the local function

Note: Though the Hessian is evaluated on the reference element, the return value is the Hessian with respect to the actual entity.

Parameters

[in]	x	evaluation point in local coordinates
[out]	ret	Hessian of the function in the evaluation point

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), Dune::Fem::BasisFunctionSet< Entity, Range >::hessianAll(), and Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

◆ init() [1/3]

template<class BasisFunctionSet , class LocalDofVector >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::init ( const BasisFunctionSetType & basisFunctionSet )

inlineprotectedinherited

initialize the local function for an basisFunctionSet

Binds the local function to an basisFunctionSet and entity.

Note: A local function must be initialized to an entity before it can be used.; This function can be called multiple times to use the local function for more than one entity.

Parameters

[in] basisFunctionSet to bind the local function to

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), and Dune::Fem::BasisFunctionSet< Entity, Range >::size().

◆ init() [2/3]

template<class DiscreteFunction >

void Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::init ( const EntityType & entity )

inline

interface for local functions :: init

Local functions are used to represend a discrete function on one entity. The LocalFunctionInterface defines the functionality that can be expected from such a local function. :: init

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::entity(), and Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::localDofVector().

◆ init() [3/3]

template<class BasisFunctionSet , class LocalDofVector >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::init ( const EntityType & entity )

inlineprotectedinherited

initialize the local function for an entity

Binds the local function to an basisFunctionSet and entity.

Note: Must be overloaded on the derived implementation class.

Parameters

[in] entity to bind the local function to

References DUNE_THROW.

Referenced by Dune::Fem::BasicTemporaryLocalFunction< DiscreteFunctionSpace, DofVector >::init().

◆ jacobian() [1/3]

template<class DiscreteFunction >

template<class Point >

JacobianRangeType Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >::jacobian ( const Point & p ) const

inline

evaluate Jacobian of the local function

Note: Though the Jacobian is evaluated on the reference element, the return value is the Jacobian with respect to the actual entity.

Parameters

[in] x evaluation point in local coordinates

Returns: Jacobian of the function in the evaluation point

◆ jacobian() [2/3]

template<class DiscreteFunction >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::jacobian ( class PointType )

inline

evaluate Jacobian of the local function

Note: Though the Jacobian is evaluated on the reference element, the return value is the Jacobian with respect to the actual entity.

Parameters

[in]	x	evaluation point in local coordinates
[out]	ret	Jacobian of the function in the evaluation point

◆ jacobian() [3/3]

template<class BasisFunctionSet , class LocalDofVector >

template<class PointType >

void Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::jacobian	(	const PointType &	x,
		JacobianRangeType &	ret
	)		const

inlineinherited

evaluate Jacobian of the local function

Note: Though the Jacobian is evaluated on the reference element, the return value is the Jacobian with respect to the actual entity.

Parameters

[in]	x	evaluation point in local coordinates
[out]	ret	Jacobian of the function in the evaluation point

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), Dune::Fem::BasisFunctionSet< Entity, Range >::jacobianAll(), and Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

◆ numDofs()

template<class BasisFunctionSet , class LocalDofVector >

int Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::numDofs ( ) const

inlineinherited

obtain the number of local DoFs

Obtain the number of local DoFs of this local function. The value is identical to the number of basis functons on the entity.

Returns: number of local DoFs

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

◆ operator*()

PromotionTraits<field_type,typename DenseVector<Other>::field_type>::PromotedType Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::operator* ( const DenseVector< Other > & x ) const

inlineinherited

indefinite vector dot product \(\left (x^T \cdot y \right)\) which corresponds to Petsc's VecTDot

http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecTDot.html

Parameters

x	other vector

Returns

◆ operator*=()

std::enable_if< std::is_convertible<FieldType, field_type>::value, derived_type >::type& Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::operator*= ( const FieldType & kk )

inlineinherited

vector space multiplication with scalar

we use enable_if to avoid an ambiguity, if the function parameter can be converted to field_type implicitly. (see FS#1457)

The function is only enabled, if the parameter is directly convertible to field_type.

◆ operator+=()

std::enable_if< std::is_convertible<ValueType, value_type>::value, derived_type >::type& Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::operator+= ( const ValueType & kk )

inlineinherited

vector space add scalar to all comps

we use enable_if to avoid an ambiguity, if the function parameter can be converted to value_type implicitly. (see FS#1457)

The function is only enabled, if the parameter is directly convertible to value_type.

◆ operator-=()

std::enable_if< std::is_convertible<ValueType, value_type>::value, derived_type >::type& Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::operator-= ( const ValueType & kk )

inlineinherited

vector space subtract scalar from all comps

we use enable_if to avoid an ambiguity, if the function parameter can be converted to value_type implicitly. (see FS#1457)

The function is only enabled, if the parameter is directly convertible to value_type.

◆ operator/=()

std::enable_if< std::is_convertible<FieldType, field_type>::value, derived_type >::type& Dune::DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > >::operator/= ( const FieldType & kk )

inlineinherited

vector space division by scalar

we use enable_if to avoid an ambiguity, if the function parameter can be converted to field_type implicitly. (see FS#1457)

The function is only enabled, if the parameter is directly convertible to field_type.

◆ order()

template<class BasisFunctionSet , class LocalDofVector >

int Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::order ( ) const

inlineinherited

obtain the order of this local function

The order of a local function refers to the polynomial order required to integrate it exactly.

Note: It is not completely clear what this value should be, e.g., for bilinear basis functions.

Returns: order of the local function

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::basisFunctionSet(), and Dune::Fem::BasisFunctionSet< Entity, Range >::order().

Referenced by Dune::Fem::LocalOrthonormalL2Projection< GridPart, BasisFunctionSet, Quadrature >::apply().

◆ size()

template<class BasisFunctionSet , class LocalDofVector >

SizeType Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::size ( ) const

inlineinherited

obtain the number of local DoFs

Obtain the number of local DoFs of this local function. The value is identical to the number of basis functons on the entity.

Returns: number of local DoFs

References Dune::Fem::LocalFunction< BasisFunctionSet, LocalDofVector >::localDofVector().

Referenced by Dune::Fem::LocalMassMatrixImplementation< DiscreteFunctionSpace, VolumeQuadrature, refElemScaling >::applyInverseDefault(), Dune::Fem::LocalMassMatrixImplementation< DiscreteFunctionSpace, VolumeQuadrature, refElemScaling >::applyInverseLocally(), and Dune::Fem::hpDG::DefaultDataProjection< DiscreteFunction >::operator()().

Friends And Related Function Documentation

◆ operator<<()

std::ostream & operator<<	(	std::ostream &	s,
		const DenseVector< LocalFunction< BasisFunctionSet, LocalDofVector > > &	v
	)

Parameters

[in]	s	std :: ostream to write to
[in]	v	DenseVector to write

Returns: the output stream (s)

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

dune/fem/function/localfunction/const.hh

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Related Functions

Detailed Description

template<class DiscreteFunction> class Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >

Constructor & Destructor Documentation

◆ ConstLocalDiscreteFunction() [1/2]

◆ ConstLocalDiscreteFunction() [2/2]

Member Function Documentation

◆ assign() [1/2]

◆ assign() [2/2]

◆ axpy() [1/6]

◆ axpy() [2/6]

◆ axpy() [3/6]

◆ axpy() [4/6]

◆ axpy() [5/6]

◆ axpy() [6/6]

◆ basisFunctionSet()

◆ beforeBegin() [1/2]

◆ beforeBegin() [2/2]

◆ beforeEnd() [1/2]

◆ beforeEnd() [2/2]

◆ bind()

◆ dot()

◆ entity()

◆ evaluate() [1/3]

◆ evaluate() [2/3]

◆ evaluate() [3/3]

◆ hessian() [1/3]

◆ hessian() [2/3]

◆ hessian() [3/3]

◆ init() [1/3]

◆ init() [2/3]

◆ init() [3/3]

◆ jacobian() [1/3]

◆ jacobian() [2/3]

◆ jacobian() [3/3]

◆ numDofs()

◆ operator*()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator/=()

◆ order()

◆ size()

Friends And Related Function Documentation

◆ operator<<()

template<class DiscreteFunction>
class Dune::Fem::ConstLocalDiscreteFunction< DiscreteFunction >