/usr/include/deal.II/base/polynomials_adini.h is in libdeal.ii-dev 8.1.0-4.
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// $Id: polynomials_adini.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2009 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__polynomials_adini_h
#define __deal2__polynomials_adini_h
#include <deal.II/base/point.h>
#include <deal.II/base/tensor.h>
#include <deal.II/base/table.h>
DEAL_II_NAMESPACE_OPEN
/**
* The cubic polynomial space for the Adini element
*
* This space consists of the cubic space <i>P<sub>3</sub></i>
* augmented by the functions <i>xy<sup>3</sup></i> and
* <i>x<sup>3</sup>y</i>.
*
* 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
*/
class PolynomialsAdini
{
public:
/**
* Constructor for
* the polynomials of
* the described space
*/
PolynomialsAdini ();
/**
* Computes the value and the
* first and second derivatives
* of each polynomial at
* <tt>unit_point</tt>.
*
* 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.
*/
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;
/**
* Computes the value of the
* <tt>i</tt>th polynomial at
* <tt>unit_point</tt>.
*
* Consider using compute() instead.
*/
double compute_value (const unsigned int i,
const Point<2> &p) const;
/**
* Computes the gradient of the
* <tt>i</tt>th polynomial at
* <tt>unit_point</tt>.
*
* Consider using compute() instead.
*/
Tensor<1,2> compute_grad (const unsigned int i,
const Point<2> &p) const;
/**
* Computes the second derivative
* (grad_grad) of the <tt>i</tt>th
* polynomial at
* <tt>unit_point</tt>.
*
* Consider using compute() instead.
*/
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:
/**
* Store the coefficients of the
* polynominals in the order
* $1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$
*/
Table<2, double> coef;
/**
* Store the coefficients of the x-derivative
* of the polynominals in the order
* $1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$
*/
Table<2, double> dx;
/**
* Store the coefficients of the y-derivative
* of the polynominals in the order
* $1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$
*/
Table<2, double> dy;
/**
* Store the coefficients of the second x-derivative
* of the polynominals in the order
* $1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$
*/
Table<2, double> dxx;
/**
* Store the coefficients of the second y-derivative
* of the polynominals in the order
* $1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$
*/
Table<2, double> dyy;
/**
* Store the coefficients of the second mixed derivative
* of the polynominals in the order
* $1,x,y,x^2,y^2,xy,x^3,y^3,xy^2,x^2y,x^3y,xy^3$
*/
Table<2, double> dxy;
};
DEAL_II_NAMESPACE_CLOSE
#endif
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