PolynomialsABF< dim > Class Template Reference

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

Public Member Functions
	PolynomialsABF (const unsigned int k)
void	compute (const Point< dim > &unit_point, std::vector< Tensor< 1, dim >> &values, std::vector< Tensor< 2, dim >> &grads, std::vector< Tensor< 3, dim >> &grad_grads, std::vector< Tensor< 4, dim >> &third_derivatives, std::vector< Tensor< 5, dim >> &fourth_derivatives) const
unsigned int	n () const
unsigned int	degree () const
std::string	name () const

Static Public Member Functions
static unsigned int	compute_n_pols (unsigned int degree)

Private Attributes
const unsigned int	my_degree
const AnisotropicPolynomials< dim >	polynomial_space
unsigned int	n_pols
Threads::Mutex	mutex
std::vector< double >	p_values
std::vector< Tensor< 1, dim > >	p_grads
std::vector< Tensor< 2, dim > >	p_grad_grads
std::vector< Tensor< 3, dim > >	p_third_derivatives
std::vector< Tensor< 4, dim > >	p_fourth_derivatives

Detailed Description

template<int dim>
class PolynomialsABF< dim >

This class implements the H^div-conforming, vector-valued Arnold-Boffi-Falk polynomials as described in the article by Arnold-Boffi- Falk: Quadrilateral H(div) finite elements, SIAM J. Numer. Anal. Vol.42, No.6, pp.2429-2451

The ABF polynomials are constructed such that the divergence is in the tensor product polynomial space Q_k. Therefore, the polynomial order of each component must be two orders higher in the corresponding direction, yielding the polynomial spaces (Q_k+2,k, Q_k,k+2) and (Q_k+2,k,k, Q_k,k+2,k, Q_k,k,k+2) in 2D and 3D, resp.

Author

Oliver Kayser-Herold, based on code from Guido Kanschat

Date

2006

Definition at line 54 of file polynomials_abf.h.

Constructor & Destructor Documentation

PolynomialsABF()

template<int dim>

PolynomialsABF< dim >::PolynomialsABF

(

const unsigned int

k

)

Constructor. Creates all basis functions for Raviart-Thomas polynomials of given degree.

• k: the degree of the Raviart-Thomas-space, which is the degree of the largest tensor product polynomial space Q_k contained.

Definition at line 49 of file polynomials_abf.cc.

Member Function Documentation

compute()

template<int dim>

void PolynomialsABF< dim >::compute	(	const Point< dim > &	unit_point,
		std::vector< Tensor< 1, dim >> &	values,
		std::vector< Tensor< 2, dim >> &	grads,
		std::vector< Tensor< 3, dim >> &	grad_grads,
		std::vector< Tensor< 4, dim >> &	third_derivatives,
		std::vector< Tensor< 5, dim >> &	fourth_derivatives
	)		const

Compute the value and the first and second derivatives of each Raviart- Thomas polynomial at unit_point.

The size of the vectors must either be zero or equal n(). In the first case, the function will not compute these values.

If you need values or derivatives of all tensor product polynomials then use this function, rather than using any of the compute_value, compute_grad or compute_grad_grad functions, see below, in a loop over all tensor product polynomials.

Definition at line 64 of file polynomials_abf.cc.

n()

template<int dim>

unsigned int PolynomialsABF< dim >::n ( ) const

inline

Return the number of ABF polynomials.

Definition at line 166 of file polynomials_abf.h.

degree()

template<int dim>

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

inline

Return the degree of the ABF space, which is two less than the highest polynomial degree.

Definition at line 174 of file polynomials_abf.h.

name()

template<int dim>

std::string PolynomialsABF< dim >::name ( ) const

inline

Return the name of the space, which is ABF.

Definition at line 182 of file polynomials_abf.h.

compute_n_pols()

template<int dim>

unsigned int PolynomialsABF< dim >::compute_n_pols ( unsigned int  degree )

static

Return the number of polynomials in the space RT(degree) without requiring to build an object of PolynomialsABF. This is required by the FiniteElement classes.

Definition at line 157 of file polynomials_abf.cc.

Member Data Documentation

my_degree

template<int dim>

const unsigned int PolynomialsABF< dim >::my_degree

private

The degree of this object as given to the constructor.

Definition at line 118 of file polynomials_abf.h.

polynomial_space

template<int dim>

const AnisotropicPolynomials<dim> PolynomialsABF< dim >::polynomial_space

private

An object representing the polynomial space for a single component. We can re-use it for the other vector components by rotating the coordinates of the evaluation point.

Definition at line 125 of file polynomials_abf.h.

n_pols

template<int dim>

unsigned int PolynomialsABF< dim >::n_pols

private

Number of Raviart-Thomas polynomials.

Definition at line 130 of file polynomials_abf.h.

mutex

template<int dim>

Threads::Mutex PolynomialsABF< dim >::mutex

mutableprivate

A mutex that guards the following scratch arrays.

Definition at line 135 of file polynomials_abf.h.

p_values

template<int dim>

std::vector<double> PolynomialsABF< dim >::p_values

mutableprivate

Auxiliary memory.

Definition at line 140 of file polynomials_abf.h.

p_grads

template<int dim>

std::vector<Tensor<1, dim> > PolynomialsABF< dim >::p_grads

mutableprivate

Auxiliary memory.

Definition at line 145 of file polynomials_abf.h.

p_grad_grads

template<int dim>

std::vector<Tensor<2, dim> > PolynomialsABF< dim >::p_grad_grads

mutableprivate

Auxiliary memory.

Definition at line 150 of file polynomials_abf.h.

p_third_derivatives

template<int dim>

std::vector<Tensor<3, dim> > PolynomialsABF< dim >::p_third_derivatives

mutableprivate

Auxiliary memory.

Definition at line 155 of file polynomials_abf.h.

p_fourth_derivatives

template<int dim>

std::vector<Tensor<4, dim> > PolynomialsABF< dim >::p_fourth_derivatives

mutableprivate

Auxiliary memory.

Definition at line 160 of file polynomials_abf.h.

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

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