PolynomialsP< dim > Class Template Reference

#include <deal.II/base/polynomials_p.h>

Inheritance diagram for PolynomialsP< dim >:

Public Member Functions
	PolynomialsP (const unsigned int p)
unsigned int	degree () const
std::array< unsigned int, dim >	directional_degrees (unsigned int n) const
Public Member Functions inherited from PolynomialSpace< dim >
template<class Pol >
	PolynomialSpace (const std::vector< Pol > &pols)
template<class StreamType >
void	output_indices (StreamType &out) const
void	set_numbering (const std::vector< unsigned int > &renumber)
void	compute (const Point< dim > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, dim >> &grads, std::vector< Tensor< 2, dim >> &grad_grads, std::vector< Tensor< 3, dim >> &third_derivatives, std::vector< Tensor< 4, dim >> &fourth_derivatives) const
double	compute_value (const unsigned int i, const Point< dim > &p) const
template<int order>
Tensor< order, dim >	compute_derivative (const unsigned int i, const Point< dim > &p) const
Tensor< 1, dim >	compute_grad (const unsigned int i, const Point< dim > &p) const
Tensor< 2, dim >	compute_grad_grad (const unsigned int i, const Point< dim > &p) const
unsigned int	n () const
unsigned int	degree () const

Static Public Attributes
static const unsigned int	dimension = dim
Static Public Attributes inherited from PolynomialSpace< dim >
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

Additional Inherited Members
Static Public Member Functions inherited from PolynomialSpace< dim >
static unsigned int	compute_n_pols (const unsigned int n)
Protected Member Functions inherited from PolynomialSpace< dim >
std::array< unsigned int, dim >	compute_index (const unsigned int n) const

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 48 of file polynomials_p.h.

Constructor & Destructor Documentation

PolynomialsP()

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

Definition at line 23 of file polynomials_p.cc.

Member Function Documentation

degree()

template<int dim>

unsigned int PolynomialsP< dim >::degree ( ) const

inline

Return the degree p of the polynomial space P_p.

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

Definition at line 99 of file polynomials_p.h.

directional_degrees()

template<int dim>

std::array< unsigned int, dim > PolynomialsP< dim >::directional_degrees ( unsigned int  n ) 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.

In 1d and 2d, obviously only i and i,j are returned.

Definition at line 107 of file polynomials_p.h.

create_polynomial_ordering()

template<int dim>

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

private

Fills the index_map.

Member Data Documentation

dimension

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 55 of file polynomials_p.h.

p

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 92 of file polynomials_p.h.

---

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

• deal.II/base/polynomials_p.h
• source/base/polynomials_p.cc