PolynomialsAdini< dim > Class Template Reference

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

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.

Definition at line 41 of file 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 override
virtual Tensor< 1, dim >	compute_1st_derivative (const unsigned int i, const Point< dim > &p) const override
virtual Tensor< 2, dim >	compute_2nd_derivative (const unsigned int i, const Point< dim > &p) const override
virtual Tensor< 3, dim >	compute_3rd_derivative (const unsigned int i, const Point< dim > &p) const override
virtual Tensor< 4, dim >	compute_4th_derivative (const unsigned int i, const Point< dim > &p) const override
Tensor< 1, dim >	compute_grad (const unsigned int i, const Point< dim > &p) const override
Tensor< 2, dim >	compute_grad_grad (const unsigned int i, const Point< dim > &p) const override
std::string	name () const override
virtual std::unique_ptr< ScalarPolynomialsBase< dim > >	clone () const override
template<int order>
Tensor< order, dim >	compute_derivative (const unsigned int i, const Point< dim > &p) const
unsigned int	n () const
virtual 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
const unsigned int	polynomial_degree
const unsigned int	n_pols

Constructor & Destructor Documentation

PolynomialsAdini()

template<int dim>

PolynomialsAdini< dim >::PolynomialsAdini

(

)

Constructor for the polynomials of the described space

Definition at line 51 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 147 of file polynomials_adini.cc.

compute_value()

template<int dim>

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

overridevirtual

Compute the value of the ith polynomial at unit_point.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 202 of file polynomials_adini.cc.

compute_1st_derivative()

template<int dim>

Tensor< 1, dim > PolynomialsAdini< dim >::compute_1st_derivative ( const unsigned int  i, const Point< dim > &  p  ) const

inlineoverridevirtual

Compute the first derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 178 of file polynomials_adini.h.

compute_2nd_derivative()

template<int dim>

Tensor< 2, dim > PolynomialsAdini< dim >::compute_2nd_derivative ( const unsigned int  i, const Point< dim > &  p  ) const

inlineoverridevirtual

Compute the second derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 189 of file polynomials_adini.h.

compute_3rd_derivative()

template<int dim>

Tensor< 3, dim > PolynomialsAdini< dim >::compute_3rd_derivative ( const unsigned int  i, const Point< dim > &  p  ) const

inlineoverridevirtual

Compute the third derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 200 of file polynomials_adini.h.

compute_4th_derivative()

template<int dim>

Tensor< 4, dim > PolynomialsAdini< dim >::compute_4th_derivative ( const unsigned int  i, const Point< dim > &  p  ) const

inlineoverridevirtual

Compute the fourth derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 211 of file polynomials_adini.h.

compute_grad()

template<int dim>

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

overridevirtual

Compute the gradient of the ith polynomial at unit_point.

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 218 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

overridevirtual

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

Consider using evaluate() instead.

Implements ScalarPolynomialsBase< dim >.

Definition at line 242 of file polynomials_adini.cc.

name()

template<int dim>

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

inlineoverridevirtual

Return the name of the space, which is PolynomialsAdini.

Implements ScalarPolynomialsBase< dim >.

Definition at line 222 of file polynomials_adini.h.

clone()

template<int dim>

std::unique_ptr< ScalarPolynomialsBase< dim > > PolynomialsAdini< dim >::clone ( ) const

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 271 of file polynomials_adini.cc.

compute_derivative()

template<int dim>

template<int order>

Tensor< order, dim > ScalarPolynomialsBase< dim >::compute_derivative ( const unsigned int  i, const Point< dim > &  p  ) const

inlineinherited

Compute the orderth derivative of the ith polynomial at unit point p.

Consider using evaluate() instead.

Template Parameters

order

The order of the derivative.

Definition at line 273 of file scalar_polynomials_base.h.

n()

template<int dim>

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

inlineinherited

Return the number of polynomials.

Definition at line 254 of file scalar_polynomials_base.h.

degree()

template<int dim>

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

inlinevirtualinherited

Return the highest polynomial degree of polynomials represented by this class. A derived class may override this if its value is different from my_degree.

Reimplemented in PolynomialsP< dim >.

Definition at line 263 of file scalar_polynomials_base.h.

memory_consumption()

template<int dim>

std::size_t ScalarPolynomialsBase< dim >::memory_consumption ( ) const

virtualinherited

Return an estimate (in bytes) for the memory consumption of this object.

Reimplemented in BarycentricPolynomials< dim >, TensorProductPolynomials< dim, PolynomialType >, and TensorProductPolynomials< dim - 1 >.

Definition at line 36 of file scalar_polynomials_base.cc.

Member Data Documentation

coef

template<int dim>

Table<2, double> PolynomialsAdini< dim >::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 141 of file polynomials_adini.h.

dx

template<int dim>

Table<2, double> PolynomialsAdini< dim >::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 147 of file polynomials_adini.h.

dy

template<int dim>

Table<2, double> PolynomialsAdini< dim >::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 153 of file polynomials_adini.h.

dxx

template<int dim>

Table<2, double> PolynomialsAdini< dim >::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 159 of file polynomials_adini.h.

dyy

template<int dim>

Table<2, double> PolynomialsAdini< dim >::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 165 of file polynomials_adini.h.

dxy

template<int dim>

Table<2, double> PolynomialsAdini< dim >::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 171 of file polynomials_adini.h.

polynomial_degree

template<int dim>

const unsigned int ScalarPolynomialsBase< dim >::polynomial_degree

privateinherited

The highest polynomial degree of this functions represented by this object.

Definition at line 225 of file scalar_polynomials_base.h.

n_pols

template<int dim>

const unsigned int ScalarPolynomialsBase< dim >::n_pols

privateinherited

The number of polynomials represented by this object.

Definition at line 230 of file scalar_polynomials_base.h.

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

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