Reference documentation for deal.II version 8.1.0
Public Member Functions | Private Attributes | List of all members
PolynomialsAdini Class Reference

#include <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
 
Tensor< 2, 2 > compute_grad_grad_2 (const unsigned int i, const Point< 2 > &p) const
 

Private Attributes

Table< 2, doublecoef
 
Table< 2, doubledx
 
Table< 2, doubledy
 
Table< 2, doubledxx
 
Table< 2, doubledyy
 
Table< 2, doubledxy
 

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 42 of file polynomials_adini.h.

Constructor & Destructor Documentation

PolynomialsAdini::PolynomialsAdini ( )

Constructor for the polynomials of the described space

Member Function Documentation

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

Computes 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.

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

Computes the value of the ith polynomial at unit_point.

Consider using compute() instead.

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

Computes the gradient of the ith polynomial at unit_point.

Consider using compute() instead.

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

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

Consider using compute() instead.

Member Data Documentation

Table<2, double> PolynomialsAdini::coef
private

Store the coefficients of the polynominals 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 121 of file polynomials_adini.h.

Table<2, double> PolynomialsAdini::dx
private

Store the coefficients of the x-derivative of the polynominals 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 129 of file polynomials_adini.h.

Table<2, double> PolynomialsAdini::dy
private

Store the coefficients of the y-derivative of the polynominals 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 136 of file polynomials_adini.h.

Table<2, double> PolynomialsAdini::dxx
private

Store the coefficients of the second x-derivative of the polynominals 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 142 of file polynomials_adini.h.

Table<2, double> PolynomialsAdini::dyy
private

Store the coefficients of the second y-derivative of the polynominals 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 148 of file polynomials_adini.h.

Table<2, double> PolynomialsAdini::dxy
private

Store the coefficients of the second mixed derivative of the polynominals 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 154 of file polynomials_adini.h.


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