Reference documentation for deal.II version 9.5.0
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Public Member Functions | Private Attributes | List of all members
PolynomialsAdini< dim > Class Template Reference

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

Inheritance diagram for PolynomialsAdini< dim >:
[legend]

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
 

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 44 of file polynomials_adini.h.

Constructor & Destructor Documentation

◆ PolynomialsAdini()

Constructor for the polynomials of the described space

Definition at line 42 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 138 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 193 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 181 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 192 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 203 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 214 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 209 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 233 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 225 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 262 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
orderThe order of the derivative.

Definition at line 259 of file scalar_polynomials_base.h.

◆ n()

template<int dim>
unsigned int ScalarPolynomialsBase< dim >::n
inlineinherited

Return the number of polynomials.

Definition at line 240 of file scalar_polynomials_base.h.

◆ degree()

template<int dim>
unsigned int ScalarPolynomialsBase< dim >::degree
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 249 of file scalar_polynomials_base.h.

◆ memory_consumption()

template<int dim>
std::size_t ScalarPolynomialsBase< dim >::memory_consumption
virtualinherited

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

Reimplemented in BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, TensorProductPolynomials< dim, PolynomialType >, and TensorProductPolynomials< dim - 1 >.

Definition at line 39 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 144 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 150 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 156 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 162 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 168 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 174 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 228 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 233 of file scalar_polynomials_base.h.


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