PolynomialsAdini Class Reference

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

Public Member Functions
	PolynomialsAdini ()
void	compute (const Point< 2 > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, 2 >> &grads, std::vector< Tensor< 2, 2 >> &grad_grads) const
double	compute_value (const unsigned int i, const Point< 2 > &p) const
Tensor< 1, 2 >	compute_grad (const unsigned int i, const Point< 2 > &p) const
Tensor< 2, 2 >	compute_grad_grad (const unsigned int i, const Point< 2 > &p) const

Private Attributes
Table< 2, double >	coef
Table< 2, double >	dx
Table< 2, double >	dy
Table< 2, double >	dxx
Table< 2, double >	dyy
Table< 2, double >	dxy

Detailed Description

The cubic polynomial space for the Adini element

This space consists of the cubic space P₃ augmented by the functions xy³ and x³y.

The basis of the space is chosen to match the node functionals of the Adini element.

Todo:

This polynomial space is implemented in 2D only.

Author

Bärbel Janssen, 2007

Definition at line 40 of file polynomials_adini.h.

Constructor & Destructor Documentation

PolynomialsAdini()

PolynomialsAdini::PolynomialsAdini

(

)

Constructor for the polynomials of the described space

Definition at line 38 of file polynomials_adini.cc.

Member Function Documentation

compute()

void PolynomialsAdini::compute	(	const Point< 2 > &	unit_point,
		std::vector< double > &	values,
		std::vector< Tensor< 1, 2 >> &	grads,
		std::vector< Tensor< 2, 2 >> &	grad_grads
	)		const

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

The size of the vectors must either be equal 0 or equal n(). In the first case, the function will not compute these values, i.e. you indicate what you want to have computed by resizing those vectors which you want filled.

If you need values or derivatives of all 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 polynomials.

Definition at line 129 of file polynomials_adini.cc.

compute_value()

double PolynomialsAdini::compute_value	(	const unsigned int	i,
		const Point< 2 > &	p
	)		const

Compute the value of the ith polynomial at unit_point.

Consider using compute() instead.

Definition at line 161 of file polynomials_adini.cc.

compute_grad()

Tensor< 1, 2 > PolynomialsAdini::compute_grad	(	const unsigned int	i,
		const Point< 2 > &	p
	)		const

Compute the gradient of the ith polynomial at unit_point.

Consider using compute() instead.

Definition at line 173 of file polynomials_adini.cc.

compute_grad_grad()

Tensor< 2, 2 > PolynomialsAdini::compute_grad_grad	(	const unsigned int	i,
		const Point< 2 > &	p
	)		const

Compute the second derivative (grad_grad) of the ith polynomial at unit_point.

Consider using compute() instead.

Definition at line 193 of file polynomials_adini.cc.

Member Data Documentation

coef

Table<2, double> PolynomialsAdini::coef

private

Store the coefficients of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)

Definition at line 102 of file polynomials_adini.h.

dx

Table<2, double> PolynomialsAdini::dx

private

Store the coefficients of the x-derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)

Definition at line 109 of file polynomials_adini.h.

dy

Table<2, double> PolynomialsAdini::dy

private

Store the coefficients of the y-derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)

Definition at line 115 of file polynomials_adini.h.

dxx

Table<2, double> PolynomialsAdini::dxx

private

Store the coefficients of the second x-derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)

Definition at line 120 of file polynomials_adini.h.

dyy

Table<2, double> PolynomialsAdini::dyy

private

Store the coefficients of the second y-derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)

Definition at line 125 of file polynomials_adini.h.

dxy

Table<2, double> PolynomialsAdini::dxy

private

Store the coefficients of the second mixed derivative of the polynomials in the order \(1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3\)

Definition at line 130 of file polynomials_adini.h.

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

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