A container of hierarchic shape functions (see HierarchicSimplexShapeFunction) up to a given nominal order on the unit simplex of grid dimension. More...

#include <hierarchicshapefunctions.hh>

Detailed Description

template<class ctype, int dimension, class Scalar>
class Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >

A container of hierarchic shape functions (see HierarchicSimplexShapeFunction) up to a given nominal order on the unit simplex of grid dimension.

For Ord<0, this set is empty.

Definition at line 398 of file hierarchicshapefunctions.hh.

Inheritance diagram for Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >:

Public Types
typedef HierarchicSimplexShapeFunction< ctype, dimension, Scalar >	value_type

typedef ShapeFunctionSet< ctype, dimension, Scalar >::Matrix	Matrix

typedef Scalar	Scalar
	Scalar field type. 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< Scalar, 1, 1 > >	SfValueArray

Public Member Functions
	HierarchicSimplexShapeFunctionSet (int ord)
	Constructs a hierarchic shape function set. More...

	HierarchicSimplexShapeFunctionSet (HierarchicSimplexShapeFunctionSet const &other)=default
	Copy constructor. More...

	HierarchicSimplexShapeFunctionSet (HierarchicSimplexShapeFunctionSet &&other)=default
	Move constructor. More...

virtual	~HierarchicSimplexShapeFunctionSet ()

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

virtual Dune::GeometryType	type () const

virtual void	interpolate (typename ShapeFunctionSet< ctype, dimension, Scalar >::SfValueArray const &A, Matrix &IA) const

void	removeShapeFunction (size_t index)

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

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

auto	referenceElement () const

void	initHierarchicalProjection (ShapeFunctionSet< ctype, dimension, Scalar, 1 > 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...

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

Protected Attributes
std::vector< value_type >	sf

DynamicMatrix< Dune::FieldMatrix< Scalar, 1, 1 > >	pinv

InterpolationNodes	iNodes

Matrix	projection

int	order_

int	size_

Member Typedef Documentation

◆ InterpolationNodes

typedef std::vector<Dune::FieldVector<ctype,dimension> > Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::InterpolationNodes

inherited

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 Scalar >

typedef ShapeFunctionSet<ctype,dimension,Scalar>::Matrix Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::Matrix

Definition at line 402 of file hierarchicshapefunctions.hh.

◆ Scalar

typedef Scalar Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::Scalar

inherited

Scalar field type.

Definition at line 112 of file pshapefunctions.hh.

◆ SfValueArray

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

inherited

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 Scalar >

typedef HierarchicSimplexShapeFunction<ctype,dimension,Scalar> Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::value_type

Definition at line 401 of file hierarchicshapefunctions.hh.

Constructor & Destructor Documentation

◆ HierarchicSimplexShapeFunctionSet() [1/3]

template<class ctype , int dimension, class Scalar >

Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::HierarchicSimplexShapeFunctionSet ( int ord )

inline

Constructs a hierarchic shape function set.

The shape functions span the set \( \bigcup_{p=0}^{\mathrm{ord}} \Phi_p^d \) (see * HierarchicSimplexShapeFunction).

Definition at line 410 of file hierarchicshapefunctions.hh.

◆ HierarchicSimplexShapeFunctionSet() [2/3]

template<class ctype , int dimension, class Scalar >

Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::HierarchicSimplexShapeFunctionSet ( HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar > const & other )

default

Copy constructor.

◆ HierarchicSimplexShapeFunctionSet() [3/3]

template<class ctype , int dimension, class Scalar >

Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::HierarchicSimplexShapeFunctionSet ( HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar > && other )

default

Move constructor.

◆ ~HierarchicSimplexShapeFunctionSet()

template<class ctype , int dimension, class Scalar >

virtual Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::~HierarchicSimplexShapeFunctionSet ( )

inlinevirtual

Definition at line 467 of file hierarchicshapefunctions.hh.

Member Function Documentation

◆ evaluate()

void Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::evaluate	(	InterpolationNodes const &	iNodes,
		SfValueArray &	phi
	)		const

inlineinherited

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.

◆ hierarchicProjection()

Matrix const & Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::hierarchicProjection ( ) const

inlineinherited

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()

void Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::initHierarchicalProjection ( ShapeFunctionSet< ctype, dimension, Scalar , 1 > const * sfl )

inlineinherited

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

Definition at line 174 of file pshapefunctions.hh.

◆ interpolate() [1/2]

virtual void Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::interpolate	(	SfValueArray const &	A,
		Matrix &	IA
	)		const

pure virtualinherited

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.

◆ interpolate() [2/2]

template<class ctype , int dimension, class Scalar >

virtual void Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::interpolate	(	typename ShapeFunctionSet< ctype, dimension, Scalar >::SfValueArray const &	A,
		Matrix &	IA
	)		const

inlinevirtual

Definition at line 473 of file hierarchicshapefunctions.hh.

◆ interpolationNodes()

InterpolationNodes const & Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::interpolationNodes ( ) const

inlineinherited

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.

◆ operator[]()

template<class ctype , int dimension, class Scalar >

virtual value_type const & Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::operator[] ( int i ) const

inlinevirtual

Random access to a shape function.

Implements Kaskade::ShapeFunctionSet< ctype, dimension, Scalar >.

Definition at line 469 of file hierarchicshapefunctions.hh.

◆ order()

int Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::order ( ) const

inlineinherited

Maximal polynomial order of shape functions.

Definition at line 149 of file pshapefunctions.hh.

◆ referenceElement()

auto Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::referenceElement ( ) const

inlineinherited

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 Scalar >

void Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::removeShapeFunction ( size_t index )

inlinevirtual

Reimplemented from Kaskade::ShapeFunctionSet< ctype, dimension, Scalar >.

Definition at line 480 of file hierarchicshapefunctions.hh.

◆ size()

virtual int Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::size ( ) const

inlinevirtualinherited

Number of shape functions in the set.

Definition at line 144 of file pshapefunctions.hh.

◆ type()

template<class ctype , int dimension, class Scalar >

virtual Dune::GeometryType Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::type ( ) const

inlinevirtual

Definition at line 471 of file hierarchicshapefunctions.hh.

Member Data Documentation

◆ comps

int const Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::comps

staticinherited

Number of components of the shape function values.

Definition at line 132 of file pshapefunctions.hh.

◆ iNodes

InterpolationNodes Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::iNodes

protectedinherited

Definition at line 287 of file pshapefunctions.hh.

◆ order_

int Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::order_

protectedinherited

Definition at line 289 of file pshapefunctions.hh.

◆ pinv

template<class ctype , int dimension, class Scalar >

DynamicMatrix<Dune::FieldMatrix<Scalar,1,1> > Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::pinv

protected

Definition at line 490 of file hierarchicshapefunctions.hh.

Referenced by Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::interpolate().

◆ projection

Matrix Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::projection

protectedinherited

Definition at line 288 of file pshapefunctions.hh.

◆ sf

template<class ctype , int dimension, class Scalar >

std::vector<value_type> Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::sf

protected

Definition at line 489 of file hierarchicshapefunctions.hh.

Referenced by Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::HierarchicSimplexShapeFunctionSet(), Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::operator[](), and Kaskade::HierarchicSimplexShapeFunctionSet< ctype, dimension, Scalar >::removeShapeFunction().

◆ size_

int Kaskade::ShapeFunctionSet< ctype, dimension, Scalar , 1 >::size_

protectedinherited

Definition at line 290 of file pshapefunctions.hh.

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

Detailed Description

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Member Typedef Documentation

◆ InterpolationNodes

◆ Matrix

◆ Scalar

◆ SfValueArray

◆ value_type

Constructor & Destructor Documentation

◆ HierarchicSimplexShapeFunctionSet() [1/3]

◆ HierarchicSimplexShapeFunctionSet() [2/3]

◆ HierarchicSimplexShapeFunctionSet() [3/3]

◆ ~HierarchicSimplexShapeFunctionSet()

Member Function Documentation

◆ evaluate()

◆ hierarchicProjection()

◆ initHierarchicalProjection()

◆ interpolate() [1/2]

◆ interpolate() [2/2]

◆ interpolationNodes()

◆ operator[]()

◆ order()

◆ referenceElement()

◆ removeShapeFunction()

◆ size()

◆ type()

Member Data Documentation

◆ comps

◆ iNodes

◆ order_

◆ pinv

◆ projection

◆ sf

◆ size_