Reference documentation for deal.II version Git d9b14c2d54 2019-09-14 18:13:29 -0600
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Public Member Functions | Private Attributes | List of all members
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.


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