Public Member Functions | Static Public Member Functions | Static Private Member Functions | Private Attributes

PolynomialsNedelec< dim > Class Template Reference

List of all members.

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) 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 Hcurl-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 Qk. Therefore, the polynomial order of each component must be one order higher in the corresponding two directions, yielding the polynomial spaces (Qk,k+1, Qk+1,k) and (Qk,k+1,k+1, Qk+1,k,k+1, Qk+1,k+1,k) in 2D and 3D, resp.

Author:
Markus Bürg
Date:
2009, 2010

Definition at line 48 of file polynomials_nedelec.h.


Constructor & Destructor Documentation

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 Qk contained.

Member Function Documentation

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 
) const

Computes 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.

template<int dim>
unsigned int PolynomialsNedelec< dim >::n ( ) const [inline]

Returns the number of Nédélec polynomials.

Definition at line 153 of file polynomials_nedelec.h.

template<int dim>
unsigned int PolynomialsNedelec< dim >::degree ( ) const [inline]

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

Definition at line 160 of file polynomials_nedelec.h.

template<int dim>
std::string PolynomialsNedelec< dim >::name ( ) const [inline]

Return the name of the space , which is Nedelec.

Definition at line 168 of file polynomials_nedelec.h.

template<int dim>
static 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.

template<int dim>
static std::vector<std::vector< Polynomials::Polynomial< double > > > PolynomialsNedelec< dim >::create_polynomials ( const unsigned int  k) [static, private]

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


Member Data Documentation

template<int dim>
const unsigned int PolynomialsNedelec< dim >::my_degree [private]

The degree of this object as given to the constructor.

Definition at line 125 of file polynomials_nedelec.h.

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 134 of file polynomials_nedelec.h.

template<int dim>
const unsigned int PolynomialsNedelec< dim >::n_pols [private]

Number of Nédélec polynomials.

Definition at line 139 of file polynomials_nedelec.h.


The documentation for this class was generated from the following file:
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deal.II documentation generated on Mon May 21 2012 12:06:33 by doxygen 1.7.3