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

Inheritance diagram for PolynomialsP< dim >:
Inheritance graph
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List of all members.

Public Member Functions

 PolynomialsP (const unsigned int p)
unsigned int degree () const
void directional_degrees (unsigned int n, unsigned int(&degrees)[dim]) const

Private Member Functions

void create_polynomial_ordering (std::vector< unsigned int > &index_map) const

Private Attributes

const unsigned int p

Detailed Description

template<int dim>
class PolynomialsP< dim >

This class implements the polynomial space of degree p based on the monomials ${1,x,x^2,...}$. I.e. in d dimensions it constructs all polynomials of the form $\prod_{i=1}^d x_i^{n_i}$, where $\sum_i n_i\leq p$. The base polynomials are given a specific ordering, e.g. in 2 dimensions: ${1,x,y,xy,x^2,y^2,x^2y,xy^2,x^3,y^3,...}$. The ordering of the monomials in $P_k1$ matches the ordering of the monomials in $P_k2$ for $k2>k1$.

Author:
Ralf Hartmann, 2004

Constructor & Destructor Documentation

template<int dim>
PolynomialsP< dim >::PolynomialsP ( const unsigned int  p  ) 

Constructor. Creates all basis functions of $P_p$.

  • p: the degree of the polynomial space

Member Function Documentation

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

Returns the degree p of the polynomial space P_p.

Note, that this number is PolynomialSpace::degree()-1, compare definition in PolynomialSpace.

References PolynomialsP< dim >::p.

template<int dim>
void PolynomialsP< dim >::directional_degrees ( unsigned int  n,
unsigned int(&)  degrees[dim] 
) const [inline]

For the nth polynomial $p_n(x,y,z)=x^i y^j z^k$ this function gives the degrees i,j,k in the x,y,z directions.

template<int dim>
void PolynomialsP< dim >::create_polynomial_ordering ( std::vector< unsigned int > &  index_map  )  const [private]

Fills the index_map.

Member Data Documentation

template<int dim>
const unsigned int PolynomialsP< dim >::p [private]

Degree p of the polynomial space $P_p$, i.e. the number p which was given to the constructor.

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

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