Kaskade::EquidistantLagrange< dim, Real > Class Template Reference

Lagrange shape functions on an equidistant grid over the simplex. These are polynomial basis functions \( p_i \) over the unit simplex, together with interpolation nodes \( \xi_j \), such that \( p_i(\xi_j) = \delta_{ij} \) holds. More...

#include <lagrangeshapefunctions.hh>

Detailed Description

template<int dim, class Real = double>
class Kaskade::EquidistantLagrange< dim, Real >

Lagrange shape functions on an equidistant grid over the simplex. These are polynomial basis functions \( p_i \) over the unit simplex, together with interpolation nodes \( \xi_j \), such that \( p_i(\xi_j) = \delta_{ij} \) holds.

Definition at line 313 of file lagrangeshapefunctions.hh.

Inheritance diagram for Kaskade::EquidistantLagrange< dim, Real >:

Public Types
using	Vector = Dune::FieldVector< Real, dim >

Public Member Functions
	EquidistantLagrange (int order)
	Constructor. More...
Vector	nodalPosition (int i) const
	The spatial location of the interpolation node \( \xi_i \) associated with the i-th basis function. More...
Real	value (int i, Vector const &xi) const
Real	derivative (int i, int dir, Vector const &xi) const
Real	derivative2 (int i, int dir1, int dir2, Vector const &xi) const
int	size () const
	The number of Lagrange polynomials. More...
int	order () const
	The polynomial ansatz order of this Lagrange basis. More...
std::array< int, dim+1 >	index (int i) const

Protected Attributes
int	myOrder
std::vector< std::array< int, dim+1 > >	ls

Member Typedef Documentation

Vector

template<int dim, class Real = double>

using Kaskade::EquidistantLagrange< dim, Real >::Vector = Dune::FieldVector<Real,dim>

Definition at line 316 of file lagrangeshapefunctions.hh.

Constructor & Destructor Documentation

EquidistantLagrange()

template<int dim, class Real = double>

Kaskade::EquidistantLagrange< dim, Real >::EquidistantLagrange

(

int

order

)

Constructor.

Parameters

l	the barycentric index of the shape function with nonnegative entries. The order of the shape function is \( p = \sum_{i=0}^d l_i \).

Member Function Documentation

derivative()

template<int dim, class Real = double>

Real Kaskade::EquidistantLagrange< dim, Real >::derivative	(	int	i,
		int	dir,
		Vector const &	xi
	)		const

derivative2()

template<int dim, class Real = double>

Real Kaskade::EquidistantLagrange< dim, Real >::derivative2	(	int	i,
		int	dir1,
		int	dir2,
		Vector const &	xi
	)		const

index()

template<int dim>

std::array< int, dim+1 > Kaskade::LagrangeBase< dim >::index ( int  i ) const

inlineinherited

Definition at line 293 of file lagrangeshapefunctions.hh.

nodalPosition()

template<int dim, class Real = double>

Vector Kaskade::EquidistantLagrange< dim, Real >::nodalPosition

(

int

i

)

const

The spatial location of the interpolation node \( \xi_i \) associated with the i-th basis function.

order()

template<int dim>

int Kaskade::LagrangeBase< dim >::order ( ) const

inlineinherited

The polynomial ansatz order of this Lagrange basis.

Definition at line 288 of file lagrangeshapefunctions.hh.

size()

template<int dim>

int Kaskade::LagrangeBase< dim >::size ( ) const

inlineinherited

The number of Lagrange polynomials.

Definition at line 280 of file lagrangeshapefunctions.hh.

value()

template<int dim, class Real = double>

Real Kaskade::EquidistantLagrange< dim, Real >::value	(	int	i,
		Vector const &	xi
	)		const

Member Data Documentation

ls

template<int dim>

std::vector<std::array<int,dim+1> > Kaskade::LagrangeBase< dim >::ls

protectedinherited

Definition at line 300 of file lagrangeshapefunctions.hh.

Referenced by Kaskade::LagrangeBase< dim >::index(), and Kaskade::LagrangeBase< dim >::size().

myOrder

template<int dim>

int Kaskade::LagrangeBase< dim >::myOrder

protectedinherited

Definition at line 299 of file lagrangeshapefunctions.hh.

Referenced by Kaskade::LagrangeBase< dim >::order().

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

• lagrangeshapefunctions.hh