Reference documentation for deal.II version 8.1.0
Public Member Functions | Static Public Attributes | Private Member Functions | Private Attributes | List of all members
PolynomialsP< dim > Class Template Reference

#include <polynomials_p.h>

Inheritance diagram for PolynomialsP< dim >:
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Public Member Functions

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

Static Public Attributes

static const unsigned int dimension = dim
 

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

Definition at line 50 of file polynomials_p.h.

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.

Definition at line 112 of file polynomials_p.h.

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.

Definition at line 120 of file polynomials_p.h.

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 >::dimension = dim
static

Access to the dimension of this object, for checking and automatic setting of dimension in other classes.

Definition at line 59 of file polynomials_p.h.

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.

Definition at line 105 of file polynomials_p.h.


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