A set of shape functions. More...

#include <pshapefunctions.hh>

Detailed Description

template<class ctype, int dimension, class T, int comp = 1>
class Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >

A set of shape functions.

Template Parameters

ctype	scalar type for coordinates
dimension	spatial dimension
T	scalar type
comp	number of components

Definition at line 108 of file pshapefunctions.hh.

Public Types
typedef T	Scalar
	Scalar field type. More...

typedef ShapeFunction< ctype, dimension, T, comp >	value_type
	type of one shape function More...

typedef DynamicMatrix< Dune::FieldMatrix< T, 1, 1 > >	Matrix
	A matrix type mapping one-component coefficient vectors. More...

typedef std::vector< Dune::FieldVector< ctype, dimension > >	InterpolationNodes
	A container type for holding interpolation points in the reference elements. More...

typedef DynamicMatrix< Dune::FieldMatrix< T, comp, 1 > >	SfValueArray

Public Member Functions
	ShapeFunctionSet (Dune::GeometryType gt)
	Constructor. More...

	ShapeFunctionSet (ShapeFunctionSet const &other)=default

virtual	~ShapeFunctionSet ()

virtual value_type const &	operator[] (int i) const =0
	Random access to a shape function. More...

virtual int	size () const
	Number of shape functions in the set. More...

int	order () const
	Maximal polynomial order of shape functions. More...

Dune::GeometryType	type () const
	Type of geometry on which the shape functions are defined. More...

auto	referenceElement () const

void	initHierarchicalProjection (ShapeFunctionSet< ctype, dimension, T, comp > const *sfl)
	Initialize the hierarchical projection matrix based on the given lower order shape function set. More...

InterpolationNodes const &	interpolationNodes () const
	Interpolation points. More...

virtual void	interpolate (SfValueArray const &A, Matrix &IA) const =0
	Left-multiplies the provided matrix with the interpolation matrix of the shape function set. More...

void	evaluate (InterpolationNodes const &iNodes, SfValueArray &phi) const
	Evaluate shape function set at a set of points. In notation of the LocalToGlobalMapperConcept, this gives the matrix \( \Phi \): the entry Phi[i][j] is the value of shape function j evaluated at iNodes[i]. More...

Matrix const &	hierarchicProjection () const
	Returns a square matrix that projects shape function coefficients to a subspace spanned by shape functions of lower order. This is intended to be used to implement embedded error estimators. The actual definition of this subspace depends on the shape function set specified in the call to initHierarchicalProjection(). More...

virtual void	removeShapeFunction (size_t index)

Static Public Attributes
static int const	comps = comp
	Number of components of the shape function values. More...

Protected Attributes
InterpolationNodes	iNodes

Matrix	projection

int	order_

int	size_

Member Typedef Documentation

◆ InterpolationNodes

template<class ctype , int dimension, class T , int comp = 1>

typedef std::vector<Dune::FieldVector<ctype,dimension> > Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::InterpolationNodes

A container type for holding interpolation points in the reference elements.

Definition at line 164 of file pshapefunctions.hh.

◆ Matrix

template<class ctype , int dimension, class T , int comp = 1>

typedef DynamicMatrix<Dune::FieldMatrix<T,1,1> > Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::Matrix

A matrix type mapping one-component coefficient vectors.

Definition at line 119 of file pshapefunctions.hh.

◆ Scalar

template<class ctype , int dimension, class T , int comp = 1>

typedef T Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::Scalar

Scalar field type.

Definition at line 112 of file pshapefunctions.hh.

◆ SfValueArray

template<class ctype , int dimension, class T , int comp = 1>

typedef DynamicMatrix<Dune::FieldMatrix<T,comp,1> > Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::SfValueArray

A twodimensional array type for holding shape function values evaluated at a set of nodes.

Definition at line 168 of file pshapefunctions.hh.

◆ value_type

template<class ctype , int dimension, class T , int comp = 1>

typedef ShapeFunction<ctype,dimension,T,comp> Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::value_type

type of one shape function

Definition at line 114 of file pshapefunctions.hh.

Constructor & Destructor Documentation

◆ ShapeFunctionSet() [1/2]

template<class ctype , int dimension, class T , int comp = 1>

Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::ShapeFunctionSet ( Dune::GeometryType gt )

inline

Constructor.

Definition at line 122 of file pshapefunctions.hh.

◆ ShapeFunctionSet() [2/2]

template<class ctype , int dimension, class T , int comp = 1>

Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::ShapeFunctionSet ( ShapeFunctionSet< ctype, dimension, T, comp > const & other )

default

◆ ~ShapeFunctionSet()

template<class ctype , int dimension, class T , int comp = 1>

virtual Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::~ShapeFunctionSet ( )

inlinevirtual

Definition at line 135 of file pshapefunctions.hh.

Member Function Documentation

◆ evaluate()

template<class ctype , int dimension, class T , int comp = 1>

void Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::evaluate	(	InterpolationNodes const &	iNodes,
		SfValueArray &	phi
	)		const

inline

Evaluate shape function set at a set of points. In notation of the LocalToGlobalMapperConcept, this gives the matrix \( \Phi \): the entry Phi[i][j] is the value of shape function j evaluated at iNodes[i].

Parameters

iNodes	the points at which the shape functions are to be evaluated.
phi	the array that is filled with shape function values. The array will be resized if needed.

Definition at line 253 of file pshapefunctions.hh.

Referenced by Kaskade::computeSimplexSfPermutation(), Kaskade::evaluateGlobalShapeFunctions(), and Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::initHierarchicalProjection().

◆ hierarchicProjection()

template<class ctype , int dimension, class T , int comp = 1>

Matrix const & Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::hierarchicProjection ( ) const

inline

Returns a square matrix that projects shape function coefficients to a subspace spanned by shape functions of lower order. This is intended to be used to implement embedded error estimators. The actual definition of this subspace depends on the shape function set specified in the call to initHierarchicalProjection().

Definition at line 276 of file pshapefunctions.hh.

◆ initHierarchicalProjection()

template<class ctype , int dimension, class T , int comp = 1>

void Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::initHierarchicalProjection ( ShapeFunctionSet< ctype, dimension, T, comp > const * sfl )

inline

Initialize the hierarchical projection matrix based on the given lower order shape function set.

Definition at line 174 of file pshapefunctions.hh.

Referenced by Kaskade::HierarchicExtensionShapeFunctionSetContainer< ctype, dimension, Scalar, restricted >::HierarchicExtensionShapeFunctionSetContainer(), and Kaskade::HierarchicShapeFunctionSetContainer< ctype, dimension, Scalar, restricted >::HierarchicShapeFunctionSetContainer().

◆ interpolate()

template<class ctype , int dimension, class T , int comp = 1>

virtual void Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::interpolate	(	SfValueArray const &	A,
		Matrix &	IA
	)		const

pure virtual

Left-multiplies the provided matrix with the interpolation matrix of the shape function set.

Each column of A is interpreted as values of some function evaluated at this shape function set's interpolation points (see below). The columns of the output array IA then contain the shape function coefficients such that the corresponding linearcombination of shape functions "interpolates" that function in the interpolation points. What "interpolation" means is up to the actual implementation.

IA is automatically resized if needed.

Storage order: A[i][j] contains the value of function j at interpolation node i.

Referenced by Kaskade::approximateGlobalValues(), Kaskade::computeSimplexSfPermutation(), and Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::initHierarchicalProjection().

◆ interpolationNodes()

template<class ctype , int dimension, class T , int comp = 1>

InterpolationNodes const & Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::interpolationNodes ( ) const

inline

Interpolation points.

Provides interpolation points such that the shape function coefficients can be computed from function values at interpolation nodes by multiplication by this matrix. The interpolation points are guaranteed to be inside the reference element associated to this shape function set.

Definition at line 218 of file pshapefunctions.hh.

Referenced by Kaskade::approximateGlobalValues(), Kaskade::computeSimplexSfPermutation(), and Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::initHierarchicalProjection().

◆ operator[]()

template<class ctype , int dimension, class T , int comp = 1>

virtual value_type const & Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::operator[] ( int i ) const

pure virtual

Random access to a shape function.

Implemented in Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >, Kaskade::HierarchicExtensionSimplexShapeFunctionSet< ctype, dimension, Scalar >, Kaskade::LagrangeSimplexShapeFunctionSet< ctype, dimension, Scalar >, Kaskade::LagrangeCubeShapeFunctionSet< ctype, dimension, Scalar, Ord >, Kaskade::NedelecSimplexShapeFunctionSet< ctype, dimension, T >, Kaskade::HdivSimplexShapeFunctionSet< ctype, dimension, T >, and Kaskade::EmptyShapeFunctionSet< ctype, dimension, T, comp >.

◆ order()

template<class ctype , int dimension, class T , int comp = 1>

int Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::order ( ) const

inline

Maximal polynomial order of shape functions.

Definition at line 149 of file pshapefunctions.hh.

◆ referenceElement()

template<class ctype , int dimension, class T , int comp = 1>

auto Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::referenceElement ( ) const

inline

Returns a reference to the reference element on which this shape function set is defined.

Definition at line 158 of file pshapefunctions.hh.

◆ removeShapeFunction()

template<class ctype , int dimension, class T , int comp = 1>

virtual void Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::removeShapeFunction ( size_t index )

inlinevirtual

Reimplemented in Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >, Kaskade::HierarchicExtensionSimplexShapeFunctionSet< ctype, dimension, Scalar >, and Kaskade::LagrangeSimplexShapeFunctionSet< ctype, dimension, Scalar >.

Definition at line 284 of file pshapefunctions.hh.

◆ size()

template<class ctype , int dimension, class T , int comp = 1>

virtual int Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::size ( ) const

inlinevirtual

Number of shape functions in the set.

Definition at line 144 of file pshapefunctions.hh.

Referenced by Kaskade::MorleyMapper< ScalarType, GV >::Combiner::Combiner(), Kaskade::computeSimplexSfPermutation(), Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::evaluate(), Kaskade::ShapeFunctionCache< G, T, ComponentsEnd >::evaluate(), Kaskade::ShapeFunctionCache< G, T, ComponentsEnd >::evaluateDerivative(), Kaskade::ShapeFunctionCache< G, T, ComponentsEnd >::evaluateFunction(), Kaskade::evaluateGlobalShapeFunctions(), Kaskade::HdivSimplexShapeFunction< ctype, dimension, T >::HdivSimplexShapeFunction(), Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::hierarchicProjection(), Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::initHierarchicalProjection(), Kaskade::HdivMapper< ScalarType, GV >::update(), and Kaskade::NedelecMapper< ScalarType, GV >::update().

◆ type()

template<class ctype , int dimension, class T , int comp = 1>

Dune::GeometryType Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::type ( ) const

inline

Type of geometry on which the shape functions are defined.

Definition at line 152 of file pshapefunctions.hh.

Member Data Documentation

◆ comps

template<class ctype , int dimension, class T , int comp = 1>

int const Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::comps = comp

static

Number of components of the shape function values.

Definition at line 132 of file pshapefunctions.hh.

◆ iNodes

template<class ctype , int dimension, class T , int comp = 1>

InterpolationNodes Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::iNodes

protected

Definition at line 287 of file pshapefunctions.hh.

Referenced by Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::evaluate(), Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::interpolationNodes(), and Kaskade::LagrangeSimplexShapeFunctionSet< ctype, dimension, Scalar >::LagrangeSimplexShapeFunctionSet().

◆ order_

template<class ctype , int dimension, class T , int comp = 1>

int Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::order_

protected

Definition at line 289 of file pshapefunctions.hh.

Referenced by Kaskade::LagrangeSimplexShapeFunctionSet< ctype, dimension, Scalar >::LagrangeSimplexShapeFunctionSet(), and Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::order().

◆ projection

template<class ctype , int dimension, class T , int comp = 1>

Matrix Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::projection

protected

Definition at line 288 of file pshapefunctions.hh.

Referenced by Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::hierarchicProjection(), and Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::initHierarchicalProjection().

◆ size_

template<class ctype , int dimension, class T , int comp = 1>

int Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::size_

protected

Definition at line 290 of file pshapefunctions.hh.

Referenced by Kaskade::LagrangeSimplexShapeFunctionSet< ctype, dimension, Scalar >::LagrangeSimplexShapeFunctionSet(), and Kaskade::ShapeFunctionSet< ctype, dimension, T, comp >::size().

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

pshapefunctions.hh

Detailed Description

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Member Typedef Documentation

◆ InterpolationNodes

◆ Matrix

◆ Scalar

◆ SfValueArray

◆ value_type

Constructor & Destructor Documentation

◆ ShapeFunctionSet() [1/2]

◆ ShapeFunctionSet() [2/2]

◆ ~ShapeFunctionSet()

Member Function Documentation

◆ evaluate()

◆ hierarchicProjection()

◆ initHierarchicalProjection()

◆ interpolate()

◆ interpolationNodes()

◆ operator[]()

◆ order()

◆ referenceElement()

◆ removeShapeFunction()

◆ size()

◆ type()

Member Data Documentation

◆ comps

◆ iNodes

◆ order_

◆ projection

◆ size_