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Dune::P0Function< GV, RT, m > Class Template Reference
[Functions Hierarchy]

#include <p0function.hh>

Inheritance diagram for Dune::P0Function< GV, RT, m >:

List of all members.

---

Detailed Description

template<class GV, class RT, int m = 1>
class Dune::P0Function< GV, RT, m >

class for P0 finite element functions on a grid

This class implements the interface of a DifferentiableGridFunction with piecewise linear elements using a Lagrange basis. It is implemented using the general shape functions, thus it should work for all element types and dimensions.

In addition to the DifferentiableGridFunction interface P0 functions can be initialized from a C0GridFunction via Lagrange interpolation. Dereferencing delivers the coefficient vector.

Public Types
enum
	export dimension of domain and range
typedef DT	DomainFieldType
	export type for domain components
typedef RT	RangeFieldType
	export type for range components
Public Member Functions
	P0Function (const GV &gv_)
	create function with undefined degrees of freedom
	~P0Function ()
	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
virtual void	evalalllocal (const Entity &e, const Dune::FieldVector< DT, G::dimension > &xi, Dune::FieldVector< RT, m > &y) const
	evaluate all components in the entity e at local coordinates xi
void	interpolate (const C0GridFunction< G, RT, m > &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.
const MultipleCodimMultipleGeomTypeMapper< G, typename GV::IndexSet, P0Layout > &	mapper () const
	export the mapper for external use
void	vtkout (VTKWriter< GV > &vtkwriter, 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
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

---

Member Function Documentation

template<class GV, class RT, int m = 1>

virtual RT Dune::P0Function< GV, RT, m >::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 m = 1>

virtual void Dune::P0Function< GV, RT, m >::evalalllocal	(	const Entity &	e,
		const Dune::FieldVector< DT, G::dimension > &	xi,
		Dune::FieldVector< RT, m > &	y
	)			const [inline, virtual]

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 = 1>

void Dune::P0Function< GV, RT, m >::interpolate

(

const C0GridFunction< G, RT, m > &

u

)

[inline]

interpolate nodal values from a grid function

Lagrange interpolation of a P0 finite element function from given continuous grid function. Evaluation is done by visiting the vertices of each element and storing a bitvector of visited vertices.

Parameters:

[in]

u

a continuous grid function

template<class GV, class RT, int m = 1>

const RepresentationType& Dune::P0Function< GV, RT, m >::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 m = 1>

RepresentationType& Dune::P0Function< GV, RT, m >::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 m = 1>

void Dune::P0Function< GV, RT, m >::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 m = 1>

void Dune::P0Function< GV, RT, m >::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 >.

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 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

---

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

• p0function.hh

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