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Dune::DGFunction< GV, RT, o, SFSC > Class Template Reference
[Functions Hierarchy]

#include <dgfunction.hh>

Inheritance diagram for Dune::DGFunction< GV, RT, o, SFSC >:

List of all members.

---

Detailed Description

template<class GV, class RT, int o, template< class, class, int, int > class SFSC = MonomialShapeFunctionSetContainer>
class Dune::DGFunction< GV, RT, o, SFSC >

class for DG finite element functions on a grid

This class implements the interface of a DifferentiableGridFunction with piecewise discontinous elements using a orthonormal basis. It is assumed that all elements use the same shapefunction set.

In addition to the DifferentiableGridFunction interface. Dereferencing delivers the coefficient vector.

Parameters:

	GV	The GridView associating the values of the funciton with according entities
	RT	The type used for the component values of the function
	o	The order of the monomial shapefunctions
	SFSC	The type of the ShapeFunctionSetContainer

Public Types
typedef SFSC< DT, RT, G::dimension, o >	ShapeFunctionSetContainer
	type of ShapeFunctionSetContainer
typedef ShapeFunctionSetContainer::ShapeFunctionSet	ShapeFunctionSet
	type of ShapeFunctionSet
enum
	export dimension of domain and range
typedef DT	DomainFieldType
	export type for domain components
typedef RT	RangeFieldType
	export type for range components
enum
	export dimension of domain and range
typedef G::ctype	DomainFieldType
	export type for domain components
typedef RT	RangeFieldType
	export type for range components
Public Member Functions
	DGFunction (const GV &gv)
	allocate a vector with the data
	~DGFunction ()
	deallocate the vector
virtual RT	evallocal (int comp, const Entity &e, const Dune::FieldVector< DT, n > &xi) const
	evaluate single component comp in the entity e at local coordinates xi
void	interpolate (const C0Function< DT, RT, n, 1 > &u)
	interpolate nodal values from a grid function
const RepresentationType &	operator * () const
	return const reference to coefficient vector
RepresentationType &	operator * ()
	return reference to coefficient vector
void	preAdapt ()
void	postAdapt ()
	Initiate update process.
VTKWriter< GV >::VTKFunction *	vtkFunction (std::string s) const
	VTK output.
virtual RT	evallocal (int comp, const Entity &e, const Dune::FieldVector< DT, n > &xi) const =0
	evaluate single component comp in the entity e at local coordinates xi
virtual void	evalalllocal (const Entity &e, const Dune::FieldVector< DT, GV::Grid::dimension > &xi, Dune::FieldVector< RT, m > &y) const=0
	evaluate all components in the entity e at local coordinates xi
virtual RT	eval (int comp, const Dune::FieldVector< DT, n > &x) const=0
	evaluate single component comp at global point x
virtual void	evalall (const Dune::FieldVector< DT, n > &x, Dune::FieldVector< RT, m > &y) const=0
	evaluate all components at point x and store result in y
RT	evallocal (int comp, const Entity &e, const Dune::FieldVector< DT, n > &xi) const
	implement local evaluation with global evaluation
virtual RT	evallocal (int comp, const Entity &e, const Dune::FieldVector< DT, n > &xi) const =0
	evaluate single component comp in the entity e at local coordinates xi
void	evalalllocal (const Entity &e, const Dune::FieldVector< DT, GV::Grid::dimension > &xi, Dune::FieldVector< RT, m > &y) const
	does local evaluation via component-wise global evaluation
virtual void	evalalllocal (const Entity &e, const Dune::FieldVector< DT, G::dimension > &xi, Dune::FieldVector< RT, m > &y) const=0
	evaluate all components in the entity e at local coordinates xi
virtual RT	eval (int comp, const Dune::FieldVector< G::ctype, n > &x) const=0
	evaluate single component comp at global point x
virtual void	evalall (const Dune::FieldVector< G::ctype, n > &x, Dune::FieldVector< RT, m > &y) const=0
	evaluate all components at point x and store result in y
virtual RT	eval (int comp, const Dune::FieldVector< DT, n > &xi) const
	implement global evaluation with local evaluation
virtual void	evalall (const Dune::FieldVector< GV::Grid::ctype, n > &x, Dune::FieldVector< RT, m > &y) const
	default implemention for evaluation of all components
virtual int	order () const
	returns order 1
virtual RT	derivative (int comp, const Dune::FieldVector< int, n > &d, const Dune::FieldVector< DT, n > &x) const=0
	evaluate partial derivative
virtual RT	derivative (int comp, const Dune::FieldVector< int, n > &d, const Dune::FieldVector< DT, n > &x) const
virtual RT	derivativelocal (int comp, const Dune::FieldVector< int, n > &d, const Entity &e, const Dune::FieldVector< DT, n > &xi) const=0
	evaluate derivative in local coordinates
virtual RT	evallocal (int comp, const Entity &e, const Dune::FieldVector< DT, n > &xi) const =0
	evaluate single component comp in the entity e at local coordinates xi
virtual void	evalalllocal (const Entity &e, const Dune::FieldVector< DT, GV::Grid::dimension > &xi, Dune::FieldVector< RT, m > &y) const=0
	evaluate all components in the entity e at local coordinates xi
virtual RT	eval (int comp, const Dune::FieldVector< DT, n > &xi) const
	implement global evaluation with local evaluation
virtual int	order () const=0
	return number of partial derivatives that can be taken
Protected Types
enum
	get domain dimension from the grid
typedef G::ctype	DT
	get domain field type from the grid
typedef G::template Codim< 0 >::Entity	Entity
	get entity from the grid
Protected Member Functions
	DGFunction (const DGFunction &)
	make copy constructor private
Static Protected Attributes
static const int	BlockSize = ShapeFunctionSetContainer::maxsize
	size of local vector blocks

---

Member Function Documentation

template<class GV, class RT, int o, template< class, class, int, int > class SFSC = MonomialShapeFunctionSetContainer>

virtual RT Dune::DGFunction< GV, RT, o, SFSC >::evallocal	(	int	comp,
		const Entity &	e,
		const Dune::FieldVector< DT, n > &	xi
	)			const [inline, virtual]

evaluate single component comp in the entity e at local coordinates xi

Evaluate the function in an entity at local coordinates.

Parameters:

[in]	comp	number of component to be evaluated
[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e

Returns:

value of the component

template<class GV, class RT, int o, template< class, class, int, int > class SFSC = MonomialShapeFunctionSetContainer>

void Dune::DGFunction< GV, RT, o, SFSC >::interpolate

(

const C0Function< DT, RT, n, 1 > &

u

)

[inline]

interpolate nodal values from a grid function

L2 Projection of a C0 function

Parameters:

[in]

u

a continuous function

template<class GV, class RT, int o, template< class, class, int, int > class SFSC = MonomialShapeFunctionSetContainer>

const RepresentationType& Dune::DGFunction< GV, RT, o, SFSC >::operator *

(

)

const [inline]

return const reference to coefficient vector

Dereferencing a finite element function returns the coefficient representation of the finite element function. This is the const version.

template<class GV, class RT, int o, template< class, class, int, int > class SFSC = MonomialShapeFunctionSetContainer>

RepresentationType& Dune::DGFunction< GV, RT, o, SFSC >::operator *

(

)

[inline]

return reference to coefficient vector

Dereferencing a finite element function returns the coefficient representation of the finite element function. This is the non-const version.

template<class GV, class RT, int o, template< class, class, int, int > class SFSC = MonomialShapeFunctionSetContainer>

void Dune::DGFunction< GV, RT, o, SFSC >::preAdapt

(

)

[inline]

empty method to maintain symmetry For vertex data nothing is required in preAdapt but for other finite element functions this method is necessary.

template<class GV, class RT, int o, template< class, class, int, int > class SFSC = MonomialShapeFunctionSetContainer>

void Dune::DGFunction< GV, RT, o, SFSC >::postAdapt

(

)

[inline]

Initiate update process.

Call this method after the grid has been adapted. The representation is now updated to the new grid and the finite element function can be used on the new grid. However the data is not initialized. The old representation (with respect to the old grid) can still be accessed if it has been saved. It is deleted in endUpdate().

virtual RT Dune::GridFunction< GV::Grid , RT , m >::evallocal	(	int	comp,
		const Entity &	e,
		const Dune::FieldVector< DT, n > &	xi
	)			const [pure virtual, inherited]

evaluate single component comp in the entity e at local coordinates xi

Evaluate the function in an entity at local coordinates.

Parameters:

[in]	comp	number of component to be evaluated
[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e

Returns:

value of the component

virtual void Dune::GridFunction< GV::Grid , RT , m >::evalalllocal	(	const Entity &	e,
		const Dune::FieldVector< DT, GV::Grid ::dimension > &	xi,
		Dune::FieldVector< RT , m > &	y
	)			const [pure virtual, inherited]

evaluate all components in the entity e at local coordinates xi

Evaluates all components of a function at once.

Parameters:

[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e
[out]	y	vector with values to be filled

template<class DT, class RT, int n, int m>

virtual RT Dune::FunctionBase< DT, RT, n, m >::eval	(	int	comp,
		const Dune::FieldVector< DT, n > &	x
	)			const [pure virtual, inherited]

evaluate single component comp at global point x

Evaluate a single component of the vector-valued function.

Parameters:

[in]	comp	number of component to be evaluated
[in]	x	position to be evaluated

Returns:

value of the component

Implemented in Dune::GridFunctionAdapter< G, RT, m >, Dune::DifferentiableGridFunctionAdapter< G, RT, m >, Dune::GridLevelLeafFunctionAdapter< G, RT, m >, Dune::GridLeafFunctionAdapter< G, IS, RT, m >, Dune::GridFunctionGradient< G, RT >, Dune::GridFunctionMinus< G, RT, m >, Dune::GridFunctionGlobalEvalDefault< GV, RT, 1 >, Dune::GridFunctionGlobalEvalDefault< G::LevelGridView, RT, m >, Dune::GridFunctionGlobalEvalDefault< G::LeafGridView, RT, 1 >, Dune::GridFunctionGlobalEvalDefault< G::LeafGridView, RT, m >, and Dune::GridFunctionGlobalEvalDefault< G::LevelGridView, RT, 1 >.

template<class DT, class RT, int n, int m>

virtual void Dune::FunctionBase< DT, RT, n, m >::evalall	(	const Dune::FieldVector< DT, n > &	x,
		Dune::FieldVector< RT, m > &	y
	)			const [pure virtual, inherited]

evaluate all components at point x and store result in y

Evaluation function for all components at once.

Parameters:

[in]	x	position to be evaluated
[out]	y	result vector to be filled

Implemented in Dune::FunctionDefault< DT, RT, n, m >.

RT Dune::GridFunctionDefault< GV::Grid , RT , m >::evallocal	(	int	comp,
		const Entity &	e,
		const Dune::FieldVector< DT, n > &	xi
	)			const [inline, inherited]

implement local evaluation with global evaluation

Parameters:

[in]	comp	number of component to be evaluated
[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e

Returns:

value of the component

template<class G, class RT, int m>

virtual RT Dune::GridFunction< G, RT, m >::evallocal	(	int	comp,
		const Entity &	e,
		const Dune::FieldVector< DT, n > &	xi
	)			const [pure virtual, inherited]

evaluate single component comp in the entity e at local coordinates xi

Evaluate the function in an entity at local coordinates.

Parameters:

[in]	comp	number of component to be evaluated
[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e

Returns:

value of the component

Implemented in Dune::GridFunctionDefault< G, RT, m >, and Dune::GridFunctionDefault< G, RT, G::dimension >.

void Dune::GridFunctionDefault< GV::Grid , RT , m >::evalalllocal	(	const Entity &	e,
		const Dune::FieldVector< DT, GV::Grid ::dimension > &	xi,
		Dune::FieldVector< RT , m > &	y
	)			const [inline, inherited]

does local evaluation via component-wise global evaluation

Parameters:

[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e
[out]	y	vector with values to be filled

template<class G, class RT, int m>

virtual void Dune::GridFunction< G, RT, m >::evalalllocal	(	const Entity &	e,
		const Dune::FieldVector< DT, G::dimension > &	xi,
		Dune::FieldVector< RT, m > &	y
	)			const [pure virtual, inherited]

evaluate all components in the entity e at local coordinates xi

Evaluates all components of a function at once.

Parameters:

[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e
[out]	y	vector with values to be filled

Implemented in Dune::GridFunctionDefault< G, RT, m >, and Dune::GridFunctionDefault< G, RT, G::dimension >.

virtual RT Dune::FunctionBase< G::ctype , RT , n, m >::eval	(	int	comp,
		const Dune::FieldVector< G::ctype , n > &	x
	)			const [pure virtual, inherited]

evaluate single component comp at global point x

Evaluate a single component of the vector-valued function.

Parameters:

[in]	comp	number of component to be evaluated
[in]	x	position to be evaluated

Returns:

value of the component

Implemented in Dune::GridFunctionAdapter< G, RT, m >, Dune::DifferentiableGridFunctionAdapter< G, RT, m >, Dune::GridLevelLeafFunctionAdapter< G, RT, m >, Dune::GridLeafFunctionAdapter< G, IS, RT, m >, Dune::GridFunctionGradient< G, RT >, Dune::GridFunctionMinus< G, RT, m >, Dune::GridFunctionGlobalEvalDefault< GV, RT, 1 >, Dune::GridFunctionGlobalEvalDefault< G::LevelGridView, RT, m >, Dune::GridFunctionGlobalEvalDefault< G::LeafGridView, RT, 1 >, Dune::GridFunctionGlobalEvalDefault< G::LeafGridView, RT, m >, and Dune::GridFunctionGlobalEvalDefault< G::LevelGridView, RT, 1 >.

virtual void Dune::FunctionBase< G::ctype , RT , n, m >::evalall	(	const Dune::FieldVector< G::ctype , n > &	x,
		Dune::FieldVector< RT , m > &	y
	)			const [pure virtual, inherited]

evaluate all components at point x and store result in y

Evaluation function for all components at once.

Parameters:

[in]	x	position to be evaluated
[out]	y	result vector to be filled

virtual RT Dune::GridFunctionGlobalEvalDefault< GV , RT , m >::eval	(	int	comp,
		const Dune::FieldVector< DT, n > &	xi
	)			const [inline, virtual, inherited]

implement global evaluation with local evaluation

The local entity is searched via a hierarchic search

Parameters:

[in]	comp	number of component to be evaluated
[in]	xi	point in local coordinates of the reference element of e

Returns:

value of the component

Implements Dune::FunctionBase< G::ctype, RT, G::dimension, m >.

virtual void Dune::FunctionDefault< GV::Grid::ctype , RT , n, m >::evalall	(	const Dune::FieldVector< GV::Grid::ctype , n > &	x,
		Dune::FieldVector< RT , m > &	y
	)			const [inline, virtual, inherited]

default implemention for evaluation of all components

Evaluate all components at once using componentwise evaluation function

Parameters:

[in]	x	position to be evaluated
[out]	y	result vector to be filled

virtual int Dune::H1Function< GV::Grid::ctype , RT , n, m >::order

(

)

const [inline, virtual, inherited]

returns order 1

For H1 functions we can implement it here.

Implements Dune::DifferentiableFunction< DT, RT, n, m >.

template<class DT, class RT, int n, int m>

virtual RT Dune::DifferentiableFunction< DT, RT, n, m >::derivative	(	int	comp,
		const Dune::FieldVector< int, n > &	d,
		const Dune::FieldVector< DT, n > &	x
	)			const [pure virtual, inherited]

evaluate partial derivative

Evaluate partial derivative of a component of the vector-valued function.

Parameters:

[in]	comp	number of component that should be differentiated
[in]	d	vector giving order of derivative for each variable
[in]	x	position where derivative is to be evaluated

Returns:

value of the derivative

Implemented in Dune::DifferentiableGridFunctionAdapter< G, RT, m >, Dune::DifferentiableFunctionDefault< DT, RT, n, m >, Dune::P1Function< GV, RT, LC, m >, Dune::GridFunctionGlobalDifferentiationDefault< GV, RT, 1 >, Dune::GridFunctionGlobalDifferentiationDefault< G::LeafGridView, RT, 1 >, Dune::GridFunctionGlobalDifferentiationDefault< G::LevelGridView, RT, 1 >, Dune::P1Function< G::LevelGridView, RT, Dune::LevelCommunicate< G >, m >, and Dune::P1Function< G::LeafGridView, RT, Dune::LeafCommunicate< G >, m >.

virtual RT Dune::GridFunctionGlobalDifferentiationDefault< GV , RT , m >::derivative	(	int	comp,
		const Dune::FieldVector< int, n > &	d,
		const Dune::FieldVector< DT, n > &	x
	)			const [inline, virtual, inherited]

evaluate partial derivative

Evaluate partial derivative of a component of the vector-valued function.

Parameters:

[in]	comp	number of component that should be differentiated
[in]	d	vector giving order of derivative for each variable
[in]	x	position where derivative is to be evaluated

Returns:

value of the derivative

Implements Dune::DifferentiableFunction< G::ctype, RT, G::dimension, m >.

template<class G, class RT, int m>

virtual RT Dune::DifferentiableGridFunction< G, RT, m >::derivativelocal	(	int	comp,
		const Dune::FieldVector< int, n > &	d,
		const Entity &	e,
		const Dune::FieldVector< DT, n > &	xi
	)			const [pure virtual, inherited]

evaluate derivative in local coordinates

Evaluate the partial derivative a the given position in local coordinates in an entity.

Parameters:

[in]	comp	number of component that should be differentiated
[in]	d	vector giving order of derivative for each variable
[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e

Returns:

value of the derivative

Implemented in Dune::DifferentiableGridFunctionDefault< G, RT, m >.

virtual RT Dune::GridFunction< GV::Grid , RT , m >::evallocal	(	int	comp,
		const Entity &	e,
		const Dune::FieldVector< DT, n > &	xi
	)			const [pure virtual, inherited]

evaluate single component comp in the entity e at local coordinates xi

Evaluate the function in an entity at local coordinates.

Parameters:

[in]	comp	number of component to be evaluated
[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e

Returns:

value of the component

virtual void Dune::GridFunction< GV::Grid , RT , m >::evalalllocal	(	const Entity &	e,
		const Dune::FieldVector< DT, GV::Grid ::dimension > &	xi,
		Dune::FieldVector< RT , m > &	y
	)			const [pure virtual, inherited]

evaluate all components in the entity e at local coordinates xi

Evaluates all components of a function at once.

Parameters:

[in]	e	reference to grid entity of codimension 0
[in]	xi	point in local coordinates of the reference element of e
[out]	y	vector with values to be filled

template<class GV, class RT, int m>

virtual RT Dune::GridFunctionGlobalEvalDefault< GV, RT, m >::eval	(	int	comp,
		const Dune::FieldVector< DT, n > &	xi
	)			const [inline, virtual, inherited]

implement global evaluation with local evaluation

The local entity is searched via a hierarchic search

Parameters:

[in]	comp	number of component to be evaluated
[in]	xi	point in local coordinates of the reference element of e

Returns:

value of the component

virtual int Dune::DifferentiableFunction< G::ctype , RT , n, m >::order

(

)

const [pure virtual, inherited]

return number of partial derivatives that can be taken

A DifferentiableFunction can say how many derivatives exist and can be safely evaluated.

Implemented in Dune::DifferentiableGridFunctionAdapter< G, RT, m >, Dune::ElementwiseCInfinityFunction< G, RT, m >, Dune::P1Function< GV, RT, LC, m >, Dune::P2Function< GridType, RT, IS, m >, Dune::ElementwiseCInfinityFunction< G::LeafGridView::Grid, RT, m >, Dune::ElementwiseCInfinityFunction< G::LevelGridView::Grid, RT, m >, Dune::ElementwiseCInfinityFunction< GridType, RT, m >, Dune::ElementwiseCInfinityFunction< GV::Grid, RT, m >, Dune::P1Function< G::LevelGridView, RT, Dune::LevelCommunicate< G >, m >, Dune::P1Function< G::LeafGridView, RT, Dune::LeafCommunicate< G >, m >, Dune::P2Function< G, RT, G::template Codim< 0 >::LevelIndexSet, m >, and Dune::P2Function< G, RT, G::template Codim< 0 >::LeafIndexSet, m >.

---

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

• dgfunction.hh

Generated on 6 Jan 2009 with Doxygen (ver 1.5.1) [logfile].