PolynomialsVectorAnisotropic< dim > Class Template Reference

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

Detailed Description

template<int dim>
class PolynomialsVectorAnisotropic< dim >

This class implements vector-valued anisotropic polynomials and can be used further for the generation of vector-valued polynomials with degrees being different in the dim - 1 tangential directions and the normal direction, respectively. The known examples include Raviart-Thomas and Nédélec polynomials. The polynomial space can be renumbered as required by specific elements. In fact, Raviart-Thomas and Nédélec elements will choose a different ordering to ensure continuity in normal or tangential direction, respectively

Definition at line 45 of file polynomials_vector_anisotropic.h.

Inheritance diagram for PolynomialsVectorAnisotropic< dim >:

Public Member Functions
	PolynomialsVectorAnisotropic (const unsigned int degree_normal, const unsigned int degree_tangential, const std::vector< unsigned int > &polynomial_ordering)
	PolynomialsVectorAnisotropic (const PolynomialsVectorAnisotropic &other)=default
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
unsigned int	get_tangential_degree () const
unsigned int	get_normal_degree () const
virtual std::unique_ptr< TensorPolynomialsBase< dim > >	clone () const override
std::vector< Point< dim > >	get_polynomial_support_points () const
unsigned int	n () const
unsigned int	degree () const

Static Public Member Functions
static unsigned int	n_polynomials (const unsigned int normal_degree, const unsigned int tangential_degree)

Private Attributes
const unsigned int	normal_degree
const unsigned int	tangential_degree
const AnisotropicPolynomials< dim >	polynomial_space
std::vector< unsigned int >	lexicographic_to_hierarchic
std::vector< unsigned int >	hierarchic_to_lexicographic
std::array< std::vector< unsigned int >, dim >	renumber_aniso
const unsigned int	polynomial_degree
const unsigned int	n_pols

Constructor & Destructor Documentation

PolynomialsVectorAnisotropic() [1/2]

template<int dim>

PolynomialsVectorAnisotropic< dim >::PolynomialsVectorAnisotropic	(	const unsigned int	degree_normal,
		const unsigned int	degree_tangential,
		const std::vector< unsigned int > &	polynomial_ordering
	)

Constructor. Creates all basis functions for anisotropic vector-valued polynomials of given degrees in normal and tangential directions, respectively.

Definition at line 80 of file polynomials_vector_anisotropic.cc.

PolynomialsVectorAnisotropic() [2/2]

template<int dim>

PolynomialsVectorAnisotropic< dim >::PolynomialsVectorAnisotropic ( const PolynomialsVectorAnisotropic< dim > &  other )

default

Copy constructor.

Member Function Documentation

evaluate()

template<int dim>

void PolynomialsVectorAnisotropic< 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 certain derivatives of each anisotropic 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 142 of file polynomials_vector_anisotropic.cc.

name()

template<int dim>

std::string PolynomialsVectorAnisotropic< dim >::name ( ) const

overridevirtual

Return the name of the space, which is PolynomialsVectorAnisotropic.

Implements TensorPolynomialsBase< dim >.

Definition at line 248 of file polynomials_vector_anisotropic.cc.

n_polynomials()

template<int dim>

unsigned int PolynomialsVectorAnisotropic< dim >::n_polynomials ( const unsigned int  normal_degree, const unsigned int  tangential_degree  )

static

Return the number of polynomials in the space without requiring to build an object of PolynomialsVectorAnisotropic. This is required by the FiniteElement classes.

Definition at line 257 of file polynomials_vector_anisotropic.cc.

get_tangential_degree()

template<int dim>

unsigned int PolynomialsVectorAnisotropic< dim >::get_tangential_degree

(

)

const

Return degree of polynomials in tangential direction.

Definition at line 269 of file polynomials_vector_anisotropic.cc.

get_normal_degree()

template<int dim>

unsigned int PolynomialsVectorAnisotropic< dim >::get_normal_degree

(

)

const

Return degree of polynomials in normal direction.

Definition at line 278 of file polynomials_vector_anisotropic.cc.

clone()

template<int dim>

std::unique_ptr< TensorPolynomialsBase< dim > > PolynomialsVectorAnisotropic< 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 >.

Reimplemented in PolynomialsRaviartThomas< dim >.

Definition at line 287 of file polynomials_vector_anisotropic.cc.

get_polynomial_support_points()

template<int dim>

std::vector< Point< dim > > PolynomialsVectorAnisotropic< dim >::get_polynomial_support_points

(

)

const

Compute the generalized support points in the ordering used by the polynomial shape functions. Note that these points are not support points in the classical sense as the Lagrange polynomials of the different components have different points, which need to be combined in terms of Piola transformations.

Definition at line 296 of file polynomials_vector_anisotropic.cc.

n()

template<int dim>

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

inlineinherited

Return the number of polynomials.

Definition at line 160 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 169 of file tensor_polynomials_base.h.

Member Data Documentation

normal_degree

template<int dim>

const unsigned int PolynomialsVectorAnisotropic< dim >::normal_degree

private

The given degree in the normal direction.

Definition at line 128 of file polynomials_vector_anisotropic.h.

tangential_degree

template<int dim>

const unsigned int PolynomialsVectorAnisotropic< dim >::tangential_degree

private

The given degree in the tangential direction.

Definition at line 133 of file polynomials_vector_anisotropic.h.

polynomial_space

template<int dim>

const AnisotropicPolynomials<dim> PolynomialsVectorAnisotropic< dim >::polynomial_space

private

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

Definition at line 140 of file polynomials_vector_anisotropic.h.

lexicographic_to_hierarchic

template<int dim>

std::vector<unsigned int> PolynomialsVectorAnisotropic< dim >::lexicographic_to_hierarchic

private

Renumbering from lexicographic order that is used in the underlying scalar anisotropic tensor-product polynomial space to the numbering used by the finite element.

Definition at line 147 of file polynomials_vector_anisotropic.h.

hierarchic_to_lexicographic

template<int dim>

std::vector<unsigned int> PolynomialsVectorAnisotropic< dim >::hierarchic_to_lexicographic

private

Renumbering from hierarchic to lexicographic order. Inverse of lexicographic_to_hierarchic.

Definition at line 153 of file polynomials_vector_anisotropic.h.

renumber_aniso

template<int dim>

std::array<std::vector<unsigned int>, dim> PolynomialsVectorAnisotropic< dim >::renumber_aniso

private

Renumbering from shifted polynomial spaces to lexicographic one.

Definition at line 158 of file polynomials_vector_anisotropic.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 137 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 142 of file tensor_polynomials_base.h.

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

• include/deal.II/base/polynomials_vector_anisotropic.h
• source/base/polynomials_vector_anisotropic.cc