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Dune::ElementwiseCInfinityFunction< G, RT, m > Class Template Reference
[Functions Hierarchy]

#include <functions.hh>

Inheritance diagram for Dune::ElementwiseCInfinityFunction< G, RT, m >:

List of all members.

---

Detailed Description

template<class G, class RT, int m>
class Dune::ElementwiseCInfinityFunction< G, RT, m >

Base class for elementwise infinitely differentiable functions.

This class is the base class for typical finite element functions which are elementwise polynomials. Using multiple inheritance functions can be given several properties.

Template parameters are:

• G a grid class, ctype and dimension are used for DT and n in the base class
• RT type for return values
  • m number of components of the vector-valued function

Public Types
enum
	export dimension of domain and range
enum
	export dimension of domain and range
typedef G::ctype	DomainFieldType
	export type for domain components
typedef DT	DomainFieldType
	export type for domain components
typedef RT	RangeFieldType
	export type for range components
typedef RT	RangeFieldType
	export type for range components
Public Member Functions
virtual int	order () const
	returns order InfinitelyDifferentiable
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, 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 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< G::ctype, n > &x, Dune::FieldVector< RT, m > &y) const=0
	evaluate all components at point x and store result in y
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
virtual RT	derivative (int comp, const Dune::FieldVector< int, n > &d, const Dune::FieldVector< G::ctype, n > &x) const=0
	evaluate partial derivative

---

Member Function Documentation

template<class G, class RT, int m>

virtual int Dune::ElementwiseCInfinityFunction< G, RT, m >::order

(

)

const [inline, virtual]

returns order InfinitelyDifferentiable

Can be implemented already here for this class of functions

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

Reimplemented in Dune::P1Function< GV, RT, LC, m >, Dune::P2Function< GridType, RT, IS, 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 >.

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 >.

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 >.

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 >.

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 >.

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

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 >.

virtual RT Dune::DifferentiableFunction< G::ctype , RT , n, m >::derivative	(	int	comp,
		const Dune::FieldVector< int, n > &	d,
		const Dune::FieldVector< G::ctype , 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::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 >.

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

• functions.hh

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