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

Inheritance diagram for PolynomialsAdini< dim >:

Public Member Functions
	PolynomialsAdini ()

void	evaluate (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 override

double	compute_value (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

std::string	name () const override

virtual std::unique_ptr< ScalarPolynomialsBase< dim > >	clone () const override

Public Member Functions inherited from ScalarPolynomialsBase< dim >
	ScalarPolynomialsBase (const unsigned int deg, const unsigned int n_polynomials)

	ScalarPolynomialsBase (ScalarPolynomialsBase< dim > &&)=default

	ScalarPolynomialsBase (const ScalarPolynomialsBase< dim > &)=default

virtual	~ScalarPolynomialsBase ()=default

unsigned int	n () const

unsigned int	degree () const

virtual std::size_t	memory_consumption () 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

template<int dim>
class PolynomialsAdini< dim >

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 and does not compute derivatives of order 3 or higher.

Author: Bärbel Janssen

Date: 2007

Definition at line 46 of file polynomials_adini.h.

Constructor & Destructor Documentation

◆ PolynomialsAdini()

template<int dim>

PolynomialsAdini< dim >::PolynomialsAdini

Constructor for the polynomials of the described space

Definition at line 41 of file polynomials_adini.cc.

Member Function Documentation

◆ evaluate()

template<int dim>

void PolynomialsAdini< dim >::evaluate	(	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

overridevirtual

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.

Implements ScalarPolynomialsBase< dim >.

Definition at line 137 of file polynomials_adini.cc.

◆ compute_value()

template<int dim>

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

Compute the value of the ith polynomial at unit_point.

Consider using evaluate() instead.

Definition at line 192 of file polynomials_adini.cc.

◆ compute_grad()

template<int dim>

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

Compute the gradient of the ith polynomial at unit_point.

Consider using evaluate() instead.

Definition at line 208 of file polynomials_adini.cc.

◆ compute_grad_grad()

template<int dim>

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

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

Consider using evaluate() instead.

Definition at line 232 of file polynomials_adini.cc.

◆ name()

template<int dim>

std::string PolynomialsAdini< dim >::name

inlineoverridevirtual

Return the name of the space, which is PolynomialsAdini.

Implements ScalarPolynomialsBase< dim >.

Definition at line 155 of file polynomials_adini.h.

◆ clone()

template<int dim>

std::unique_ptr< ScalarPolynomialsBase< dim > > PolynomialsAdini< dim >::clone

overridevirtual

A sort of virtual copy constructor, this function returns a copy of the polynomial space object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.

Some places in the library, for example the constructors of FE_Poly, need to make copies of polynomial spaces without knowing their exact type. They do so through this function.

Implements ScalarPolynomialsBase< dim >.

Definition at line 261 of file polynomials_adini.cc.