Reference documentation for deal.II version GIT relicensing-43-g3fc2fae7c3 2024-03-03 21:10:02+00:00
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Public Member Functions | Static Public Member Functions | Static Private Member Functions | Private Attributes | List of all members
PolynomialsNedelec< dim > Class Template Reference

#include <deal.II/base/polynomials_nedelec.h>

Inheritance diagram for PolynomialsNedelec< dim >:
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Public Member Functions

 PolynomialsNedelec (const unsigned int k)
 
void evaluate (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 override
 
std::string name () const override
 
virtual std::unique_ptr< TensorPolynomialsBase< dim > > clone () const override
 
unsigned int n () const
 
unsigned int degree () const
 

Static Public Member Functions

static unsigned int n_polynomials (const unsigned int degree)
 

Static Private Member Functions

static std::vector< std::vector< Polynomials::Polynomial< double > > > create_polynomials (const unsigned int k)
 

Private Attributes

const AnisotropicPolynomials< dim > polynomial_space
 
const unsigned int polynomial_degree
 
const unsigned int n_pols
 

Detailed Description

template<int dim>
class PolynomialsNedelec< dim >

This class implements the first family Hcurl-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 Qk. Therefore, the polynomial order of each component must be one order higher in the corresponding two directions, yielding the polynomial spaces (Qk,k+1, Qk+1,k) and (Qk,k+1,k+1, Qk+1,k,k+1, Qk+1,k+1,k) in 2d and 3d, resp.

Definition at line 50 of file polynomials_nedelec.h.

Constructor & Destructor Documentation

◆ PolynomialsNedelec()

template<int dim>
PolynomialsNedelec< dim >::PolynomialsNedelec ( const unsigned int  k)

Constructor. Creates all basis functions for Nédélec polynomials of given degree.

  • k: the degree of the Nédélec space, which is the degree of the largest tensor product polynomial space Qk contained.

Definition at line 28 of file polynomials_nedelec.cc.

Member Function Documentation

◆ evaluate()

template<int dim>
void PolynomialsNedelec< dim >::evaluate ( 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
overridevirtual

Compute the value and the first and second derivatives of each Nédélec polynomial at unit_point.

The size of the vectors must either be zero or equal n(). In the first case, the function will not compute these values.

Implements TensorPolynomialsBase< dim >.

Definition at line 53 of file polynomials_nedelec.cc.

◆ name()

template<int dim>
std::string PolynomialsNedelec< dim >::name ( ) const
inlineoverridevirtual

Return the name of the space, which is Nedelec.

Implements TensorPolynomialsBase< dim >.

Definition at line 115 of file polynomials_nedelec.h.

◆ n_polynomials()

template<int dim>
unsigned int PolynomialsNedelec< dim >::n_polynomials ( const unsigned int  degree)
static

Return the number of polynomials in the space N(degree) without requiring to build an object of PolynomialsNedelec. This is required by the FiniteElement classes.

Definition at line 1483 of file polynomials_nedelec.cc.

◆ clone()

template<int dim>
std::unique_ptr< TensorPolynomialsBase< dim > > PolynomialsNedelec< dim >::clone ( ) const
overridevirtual

A sort of virtual copy constructor, this function returns a copy of the polynomial space object. Derived classes need to override the function here in this base class and return an object of the same type as the derived class.

Some places in the library, for example the constructors of FE_PolyTensor, need to make copies of polynomial spaces without knowing their exact type. They do so through this function.

Implements TensorPolynomialsBase< dim >.

Definition at line 1507 of file polynomials_nedelec.cc.

◆ create_polynomials()

template<int dim>
std::vector< std::vector< Polynomials::Polynomial< double > > > PolynomialsNedelec< dim >::create_polynomials ( const unsigned int  k)
staticprivate

A static member function that creates the polynomial space we use to initialize the polynomial_space member variable.

Definition at line 35 of file polynomials_nedelec.cc.

◆ n()

template<int dim>
unsigned int TensorPolynomialsBase< dim >::n ( ) const
inlineinherited

Return the number of polynomials.

Definition at line 151 of file tensor_polynomials_base.h.

◆ degree()

template<int dim>
unsigned int TensorPolynomialsBase< dim >::degree ( ) const
inlineinherited

Return the highest polynomial degree of polynomials represented by this class. A derived class may override this if its value is different from my_degree.

Definition at line 160 of file tensor_polynomials_base.h.

Member Data Documentation

◆ polynomial_space

template<int dim>
const AnisotropicPolynomials<dim> PolynomialsNedelec< dim >::polynomial_space
private

An object representing the polynomial space for a single component. We can re-use it by rotating the coordinates of the evaluation point.

Definition at line 102 of file polynomials_nedelec.h.

◆ polynomial_degree

template<int dim>
const unsigned int TensorPolynomialsBase< dim >::polynomial_degree
privateinherited

The highest polynomial degree of this functions represented by this object.

Definition at line 139 of file tensor_polynomials_base.h.

◆ n_pols

template<int dim>
const unsigned int TensorPolynomialsBase< dim >::n_pols
privateinherited

The number of polynomials represented by this object.

Definition at line 144 of file tensor_polynomials_base.h.


The documentation for this class was generated from the following files: