PolynomialsABF< dim > Class Template Reference
[Polynomials and polynomial spaces]

List of all members.

Public Member Functions

 PolynomialsABF (const unsigned int k)
 ~PolynomialsABF ()
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

Static Public Member Functions

static unsigned int compute_n_pols (unsigned int degree)

Private Attributes

const unsigned int my_degree
AnisotropicPolynomials< dim > * polynomial_space
unsigned int n_pols
std::vector< doublep_values
std::vector< Tensor< 1, dim > > p_grads
std::vector< Tensor< 2, dim > > p_grad_grads

Detailed Description

template<int dim>
class PolynomialsABF< dim >

This class implements the Hdiv-conforming, vector-valued Arnold-Boffi-Falk polynomials as described in the article by Arnold-Boffi-Falk: Quadrilateral H(div) finite elements, SIAM J. Numer. Anal. Vol.42, No.6, pp.2429-2451

The ABF polynomials are constructed such that the divergence is in the tensor product polynomial space Qk. Therefore, the polynomial order of each component must be two orders higher in the corresponding direction, yielding the polynomial spaces (Qk+2,k, Qk,k+2) and (Qk+2,k,k, Qk,k+2,k, Qk,k,k+2) in 2D and 3D, resp.

Author:
Oliver Kayser-Herold, 2006 based on code from Guido Kanschat

Constructor & Destructor Documentation

template<int dim>
PolynomialsABF< dim >::PolynomialsABF ( const unsigned int  k  ) 

Constructor. Creates all basis functions for Raviart-Thomas polynomials of given degree.

  • k: the degree of the Raviart-Thomas-space, which is the degree of the largest tensor product polynomial space Qk contained.
template<int dim>
PolynomialsABF< dim >::~PolynomialsABF (  ) 

Destructor deleting the polynomials.


Member Function Documentation

template<int dim>
void PolynomialsABF< 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 Raviart-Thomas 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 PolynomialsABF< dim >::n (  )  const [inline]

Returns the number of ABF polynomials.

References PolynomialsABF< dim >::n_pols.

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

Returns the degree of the ABF space, which is two less than the highest polynomial degree.

References PolynomialsABF< dim >::my_degree.

template<int dim>
static unsigned int PolynomialsABF< dim >::compute_n_pols ( unsigned int  degree  )  [static]

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


Member Data Documentation

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

The degree of this object as given to the constructor.

Referenced by PolynomialsABF< dim >::degree().

template<int dim>
AnisotropicPolynomials<dim>* PolynomialsABF< 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.

template<int dim>
unsigned int PolynomialsABF< dim >::n_pols [private]

Number of Raviart-Thomas polynomials.

Referenced by PolynomialsABF< dim >::n().

template<int dim>
std::vector<double> PolynomialsABF< dim >::p_values [mutable, private]

Auxiliary memory.

template<int dim>
std::vector<Tensor<1,dim> > PolynomialsABF< dim >::p_grads [mutable, private]

Auxiliary memory.

template<int dim>
std::vector<Tensor<2,dim> > PolynomialsABF< dim >::p_grad_grads [mutable, private]

Auxiliary memory.


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

deal.II documentation generated on Mon Nov 23 22:57:59 2009 by doxygen 1.6.1