/usr/include/deal.II/base/polynomials_nedelec.h is in libdeal.ii-dev 8.4.2-2+b1.
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//
// Copyright (C) 2010 - 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_nedelec_h
#define dealii__polynomials_nedelec_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 <vector>
DEAL_II_NAMESPACE_OPEN
/**
* This class implements the first family <i>H<sup>curl</sup></i>-conforming,
* vector-valued polynomials, proposed by J.-C. Nédélec in 1980 (Numer.
* Math. 35).
*
* The Nédélec polynomials are constructed such that the curl is in the
* tensor product polynomial space <i>Q<sub>k</sub></i>. Therefore, the
* polynomial order of each component must be one order higher in the
* corresponding two directions, yielding the polynomial spaces
* <i>(Q<sub>k,k+1</sub>, Q<sub>k+1,k</sub>)</i> and
* <i>(Q<sub>k,k+1,k+1</sub>, Q<sub>k+1,k,k+1</sub>,
* Q<sub>k+1,k+1,k</sub>)</i> in 2D and 3D, resp.
*
* @ingroup Polynomials
* @author Markus Bürg
* @date 2009, 2010
*/
template <int dim>
class PolynomialsNedelec
{
public:
/**
* Constructor. Creates all basis functions for Nédélec polynomials of
* given degree.
*
* @arg k: the degree of the Nédélec space, which is the degree of the
* largest tensor product polynomial space <i>Q<sub>k</sub></i> contained.
*/
PolynomialsNedelec (const unsigned int k);
/**
* Computes the value and the first and second derivatives of each Nédélec
* 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 Nédélec polynomials.
*/
unsigned int n () const;
/**
* Returns the degree of the Nédélec space, which is one less than the
* highest polynomial degree.
*/
unsigned int degree () const;
/**
* Return the name of the space, which is <tt>Nedelec</tt>.
*/
std::string name () const;
/**
* Return the number of polynomials in the space <tt>N(degree)</tt> without
* requiring to build an object of PolynomialsNedelec. 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.
*/
const AnisotropicPolynomials<dim> polynomial_space;
/**
* Number of Nédélec polynomials.
*/
const unsigned int n_pols;
/**
* A static member function that creates the polynomial space we use to
* initialize the #polynomial_space member variable.
*/
static std::vector<std::vector< Polynomials::Polynomial< double > > > create_polynomials (const unsigned int k);
};
template <int dim>
inline unsigned int PolynomialsNedelec<dim>::n () const
{
return n_pols;
}
template <int dim>
inline unsigned int PolynomialsNedelec<dim>::degree () const
{
return my_degree;
}
template <int dim>
inline std::string
PolynomialsNedelec<dim>::name() const
{
return "Nedelec";
}
DEAL_II_NAMESPACE_CLOSE
#endif
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