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

List of all members.

Public Member Functions

 PolynomialsBDM (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

Static Public Member Functions

static unsigned int compute_n_pols (unsigned int degree)

Private Attributes

const PolynomialSpace< dim > polynomial_space
std::vector
< Polynomials::Polynomial
< double > > 
monomials
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 PolynomialsBDM< dim >

This class implements the Hdiv-conforming, vector-valued Brezzi-Douglas-Marini polynomials as described in the book by Brezzi and Fortin.

These polynomial spaces are based on the space Pk, realized by a PolynomialSpace constructed with Legendre polynomials. Since these shape functions are not sufficient, additional functions are added. These are the following vector valued polynomials:

In 2D:
The 2D-curl of the functions xk+1y and xyk+1.
In 3D:
For any i=0,...,k the curls of (0,0,xyi+1zk-i), (0,xk-iyzi+1,0) and (xi+1yk-iz,0,0)

Right now, they are implemented in two dimensions only.

Author:
Guido Kanschat, 2003, 2005

Constructor & Destructor Documentation

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

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

  • k: the degree of the BDM-space, which is the degree of the largest complete polynomial space Pk contained in the BDM-space.


Member Function Documentation

template<int dim>
void PolynomialsBDM< 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 BDM 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 PolynomialsBDM< dim >::n (  )  const [inline]

Returns the number of BDM polynomials.

References PolynomialsBDM< dim >::n_pols.

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

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

References PolynomialSpace< dim >::degree(), and PolynomialsBDM< dim >::polynomial_space.

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

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


Member Data Documentation

template<int dim>
const PolynomialSpace<dim> PolynomialsBDM< dim >::polynomial_space [private]

An object representing the polynomial space used here. The constructor fills this with the monomial basis.

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

template<int dim>
std::vector<Polynomials::Polynomial<double> > PolynomialsBDM< dim >::monomials [private]

Storage for monomials

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

Number of BDM polynomials.

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

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

Auxiliary memory.

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

Auxiliary memory.

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

Auxiliary memory.


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

deal.II documentation generated on Sat Aug 15 16:52:12 2009 by doxygen 1.5.9