PolynomialsNedelec< dim > Class Template Reference

#include <deal.II/base/polynomials_nedelec.h>

Public Member Functions
	PolynomialsNedelec (const unsigned int k)
void	compute (const Point< dim > &unit_point, std::vector< Tensor< 1, dim >> &values, std::vector< Tensor< 2, dim >> &grads, std::vector< Tensor< 3, dim >> &grad_grads, std::vector< Tensor< 4, dim >> &third_derivatives, std::vector< Tensor< 5, dim >> &fourth_derivatives) const
unsigned int	n () const
unsigned int	degree () const
std::string	name () const

Static Public Member Functions
static unsigned int	compute_n_pols (unsigned int degree)

Static Private Member Functions
static std::vector< std::vector< Polynomials::Polynomial< double > > >	create_polynomials (const unsigned int k)

Private Attributes
const unsigned int	my_degree
const AnisotropicPolynomials< dim >	polynomial_space
const unsigned int	n_pols

Detailed Description

template<int dim>
class PolynomialsNedelec< dim >

This class implements the first family H^curl-conforming, vector-valued polynomials, proposed by J.-C. Nédélec in 1980 (Numer. Math. 35).

The Nédélec polynomials are constructed such that the curl is in the tensor product polynomial space Q_k. Therefore, the polynomial order of each component must be one order higher in the corresponding two directions, yielding the polynomial spaces (Q_k,k+1, Q_k+1,k) and (Q_k,k+1,k+1, Q_k+1,k,k+1, Q_k+1,k+1,k) in 2D and 3D, resp.

Author

Markus Bürg

Date

2009, 2010

Definition at line 52 of file polynomials_nedelec.h.

Constructor & Destructor Documentation

PolynomialsNedelec()

template<int dim>

PolynomialsNedelec< dim >::PolynomialsNedelec

(

const unsigned int

k

)

Constructor. Creates all basis functions for Nédélec polynomials of given degree.

• k: the degree of the Nédélec space, which is the degree of the largest tensor product polynomial space Q_k contained.

Definition at line 28 of file polynomials_nedelec.cc.

Member Function Documentation

compute()

template<int dim>

void PolynomialsNedelec< dim >::compute	(	const Point< dim > &	unit_point,
		std::vector< Tensor< 1, dim >> &	values,
		std::vector< Tensor< 2, dim >> &	grads,
		std::vector< Tensor< 3, dim >> &	grad_grads,
		std::vector< Tensor< 4, dim >> &	third_derivatives,
		std::vector< Tensor< 5, dim >> &	fourth_derivatives
	)		const

Compute the value and the first and second derivatives of each Nédélec polynomial at unit_point.

The size of the vectors must either be zero or equal n(). In the first case, the function will not compute these values.

If you need values or derivatives of all tensor product polynomials then use this function, rather than using any of the compute_value, compute_grad or compute_grad_grad functions, see below, in a loop over all tensor product polynomials.

Definition at line 54 of file polynomials_nedelec.cc.

n()

template<int dim>

unsigned int PolynomialsNedelec< dim >::n ( ) const

inline

Return the number of Nédélec polynomials.

Definition at line 139 of file polynomials_nedelec.h.

degree()

template<int dim>

unsigned int PolynomialsNedelec< dim >::degree ( ) const

inline

Return the degree of the Nédélec space, which is one less than the highest polynomial degree.

Definition at line 147 of file polynomials_nedelec.h.

name()

template<int dim>

std::string PolynomialsNedelec< dim >::name ( ) const

inline

Return the name of the space, which is Nedelec.

Definition at line 155 of file polynomials_nedelec.h.

compute_n_pols()

template<int dim>

unsigned int PolynomialsNedelec< dim >::compute_n_pols ( unsigned int  degree )

static

Return the number of polynomials in the space N(degree) without requiring to build an object of PolynomialsNedelec. This is required by the FiniteElement classes.

Definition at line 1487 of file polynomials_nedelec.cc.

create_polynomials()

template<int dim>

std::vector< std::vector< Polynomials::Polynomial< double > > > PolynomialsNedelec< dim >::create_polynomials ( const unsigned int  k )

staticprivate

A static member function that creates the polynomial space we use to initialize the polynomial_space member variable.

Definition at line 36 of file polynomials_nedelec.cc.

Member Data Documentation

my_degree

template<int dim>

const unsigned int PolynomialsNedelec< dim >::my_degree

private

The degree of this object as given to the constructor.

Definition at line 115 of file polynomials_nedelec.h.

polynomial_space

template<int dim>

const AnisotropicPolynomials<dim> PolynomialsNedelec< dim >::polynomial_space

private

An object representing the polynomial space for a single component. We can re-use it by rotating the coordinates of the evaluation point.

Definition at line 121 of file polynomials_nedelec.h.

n_pols

template<int dim>

const unsigned int PolynomialsNedelec< dim >::n_pols

private

Number of Nédélec polynomials.

Definition at line 126 of file polynomials_nedelec.h.

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

• deal.II/base/polynomials_nedelec.h
• source/base/polynomials_nedelec.cc