/usr/include/deal.II/base/polynomials_abf.h is in libdeal.ii-dev 8.4.2-2+b1.
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//
// Copyright (C) 2004 - 2015 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 dealii__polynomials_abf_h
#define dealii__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,
std::vector<Tensor<4,dim> > &third_derivatives,
std::vector<Tensor<5,dim> > &fourth_derivatives) 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;
/**
* Auxiliary memory.
*/
mutable std::vector<Tensor<3,dim> > p_third_derivatives;
/**
* Auxiliary memory.
*/
mutable std::vector<Tensor<4,dim> > p_fourth_derivatives;
};
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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