/usr/include/deal.II/base/polynomials_abf.h is in libdeal.ii-dev 8.1.0-4.
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// $Id: polynomials_abf.h 30036 2013-07-18 16:55:32Z maier $
//
// Copyright (C) 2004 - 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_abf_h
#define __deal2__polynomials_abf_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/tensor.h>
#include <deal.II/base/point.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/polynomial_space.h>
#include <deal.II/base/tensor_product_polynomials.h>
#include <deal.II/base/table.h>
#include <deal.II/base/thread_management.h>
#include <vector>
DEAL_II_NAMESPACE_OPEN
/**
* This class implements the <i>H<sup>div</sup></i>-conforming,
* vector-valued Arnold-Boffi-Falk polynomials as described in the
* article by Arnold-Boffi-Falk:
* Quadrilateral H(div) finite elements, SIAM J. Numer. Anal.
* Vol.42, No.6, pp.2429-2451
*
*
* The ABF polynomials are constructed such that the
* divergence is in the tensor product polynomial space
* <i>Q<sub>k</sub></i>. Therefore, the polynomial order of each
* component must be two orders higher in the corresponding direction,
* yielding the polynomial spaces <i>(Q<sub>k+2,k</sub>,
* Q<sub>k,k+2</sub>)</i> and <i>(Q<sub>k+2,k,k</sub>,
* Q<sub>k,k+2,k</sub>, Q<sub>k,k,k+2</sub>)</i> in 2D and 3D, resp.
*
* @ingroup Polynomials
* @author Oliver Kayser-Herold, based on code from Guido Kanschat
* @date 2006
*/
template <int dim>
class PolynomialsABF
{
public:
/**
* Constructor. Creates all basis
* functions for Raviart-Thomas polynomials
* of given degree.
*
* @arg k: the degree of the
* Raviart-Thomas-space, which is the degree
* of the largest tensor product
* polynomial space
* <i>Q<sub>k</sub></i> contained.
*/
PolynomialsABF (const unsigned int k);
/**
* Destructor deleting the polynomials.
*/
~PolynomialsABF ();
/**
* Computes the value and the
* first and second derivatives
* of each Raviart-Thomas
* polynomial at @p unit_point.
*
* The size of the vectors must
* either be zero or equal
* <tt>n()</tt>. In the
* first case, the function will
* not compute these values.
*
* If you need values or
* derivatives of all tensor
* product polynomials then use
* this function, rather than
* using any of the
* <tt>compute_value</tt>,
* <tt>compute_grad</tt> or
* <tt>compute_grad_grad</tt>
* functions, see below, in a
* loop over all tensor product
* polynomials.
*/
void compute (const Point<dim> &unit_point,
std::vector<Tensor<1,dim> > &values,
std::vector<Tensor<2,dim> > &grads,
std::vector<Tensor<3,dim> > &grad_grads) const;
/**
* Returns the number of ABF polynomials.
*/
unsigned int n () const;
/**
* Returns the degree of the ABF
* space, which is two less than
* the highest polynomial degree.
*/
unsigned int degree () const;
/**
* Return the name of the space,
* which is <tt>ABF</tt>.
*/
std::string name () const;
/**
* Return the number of
* polynomials in the space
* <TT>RT(degree)</tt> without
* requiring to build an object
* of PolynomialsABF. This is
* required by the FiniteElement
* classes.
*/
static unsigned int compute_n_pols(unsigned int degree);
private:
/**
* The degree of this object as
* given to the constructor.
*/
const unsigned int my_degree;
/**
* An object representing the
* polynomial space for a single
* component. We can re-use it by
* rotating the coordinates of
* the evaluation point.
*/
AnisotropicPolynomials<dim> *polynomial_space;
/**
* Number of Raviart-Thomas
* polynomials.
*/
unsigned int n_pols;
/**
* A mutex that guards the
* following scratch arrays.
*/
mutable Threads::Mutex mutex;
/**
* Auxiliary memory.
*/
mutable std::vector<double> p_values;
/**
* Auxiliary memory.
*/
mutable std::vector<Tensor<1,dim> > p_grads;
/**
* Auxiliary memory.
*/
mutable std::vector<Tensor<2,dim> > p_grad_grads;
};
template <int dim>
inline unsigned int
PolynomialsABF<dim>::n() const
{
return n_pols;
}
template <int dim>
inline unsigned int
PolynomialsABF<dim>::degree() const
{
return my_degree;
}
template <int dim>
inline std::string
PolynomialsABF<dim>::name() const
{
return "ABF";
}
DEAL_II_NAMESPACE_CLOSE
#endif
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