#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 $k2>k1$ .