The deal.II Library: PolynomialsP< dim > Class Template Reference

Reference documentation for deal.II version 8.1.0

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#include <polynomials_p.h>

Inheritance diagram for PolynomialsP< dim >:

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:

include/deal.II/base/polynomials_p.h