Reference documentation for deal.II version Git c4822b6378 2021-05-16 08:02:52 +0200
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Public Member Functions | Static Public Member Functions | Static Private Member Functions | Private Attributes | List of all members
PolynomialsRaviartThomas< dim > Class Template Reference

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

Inheritance diagram for PolynomialsRaviartThomas< dim >:

Public Member Functions

 PolynomialsRaviartThomas (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

Detailed Description

template<int dim>
class PolynomialsRaviartThomas< dim >

This class implements the Hdiv-conforming, vector-valued Raviart-Thomas polynomials as described in the book by Brezzi and Fortin.

The Raviart-Thomas polynomials are constructed such that the divergence is in the tensor product polynomial space Qk. Therefore, the polynomial order of each component must be one order higher in the corresponding direction, yielding the polynomial spaces (Qk+1,k, Qk,k+1) and (Qk+1,k,k, Qk,k+1,k, Qk,k,k+1) in 2D and 3D, resp.

Definition at line 48 of file polynomials_raviart_thomas.h.

Constructor & Destructor Documentation

◆ PolynomialsRaviartThomas()

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

Constructor. Creates all basis functions for Raviart-Thomas polynomials of given degree.

  • k: the degree of the Raviart-Thomas-space, which is the degree of the largest tensor product polynomial space Qk contains.

Definition at line 38 of file

Member Function Documentation

◆ evaluate()

template<int dim>
void PolynomialsRaviartThomas< 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

Compute the value and the first and second derivatives of each Raviart- Thomas 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.

If you need values or derivatives of all tensor product 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 tensor product polynomials.

Implements TensorPolynomialsBase< dim >.

Definition at line 64 of file

◆ name()

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

Return the name of the space, which is RaviartThomas.

Implements TensorPolynomialsBase< dim >.

Definition at line 119 of file polynomials_raviart_thomas.h.

◆ n_polynomials()

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

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

Definition at line 173 of file

◆ clone()

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

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 189 of file

◆ create_polynomials()

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

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

Definition at line 47 of file

◆ n()

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

Return the number of polynomials.

Definition at line 155 of file tensor_polynomials_base.h.

◆ degree()

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

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 164 of file tensor_polynomials_base.h.

Member Data Documentation

◆ polynomial_space

template<int dim>
const AnisotropicPolynomials<dim> PolynomialsRaviartThomas< dim >::polynomial_space

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 106 of file polynomials_raviart_thomas.h.

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