Public Member Functions | Private Attributes

PolynomialsAdini Class Reference

List of all members.

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 37 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.

Tensor<2,2> PolynomialsAdini::compute_grad_grad_2 ( const unsigned int  i,
const Point< 2 > &  p 
) const

Member Data Documentation

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 116 of file polynomials_adini.h.

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 124 of file polynomials_adini.h.

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 131 of file polynomials_adini.h.

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 137 of file polynomials_adini.h.

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 143 of file polynomials_adini.h.

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 149 of file polynomials_adini.h.


The documentation for this class was generated from the following file:
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Defines

deal.II documentation generated on Fri Feb 3 2012 06:04:10 by doxygen 1.7.2