PolynomialsABF< dim > Class Template Reference

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

Inheritance diagram for PolynomialsABF< dim >:

Public Member Functions
	PolynomialsABF (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)

Private Attributes
const AnisotropicPolynomials< dim >	polynomial_space
Threads::Mutex	mutex
std::vector< double >	p_values
std::vector< Tensor< 1, dim > >	p_grads
std::vector< Tensor< 2, dim > >	p_grad_grads
std::vector< Tensor< 3, dim > >	p_third_derivatives
std::vector< Tensor< 4, dim > >	p_fourth_derivatives
const unsigned int	polynomial_degree
const unsigned int	n_pols

Detailed Description

template<int dim>
class PolynomialsABF< dim >

This class implements the H^div-conforming, vector-valued Arnold-Boffi-Falk polynomials as described in the article by Arnold, Boffi, and 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 Q_k. Therefore, the polynomial order of each component must be two orders higher in the corresponding direction, yielding the polynomial spaces (Q_k+2,k, Q_k,k+2) and (Q_k+2,k,k, Q_k,k+2,k, Q_k,k,k+2) in 2d and 3d, resp.

Definition at line 52 of file polynomials_abf.h.

Constructor & Destructor Documentation

PolynomialsABF()

template<int dim>

PolynomialsABF< dim >::PolynomialsABF

(

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 Q_k contained.

Definition at line 49 of file polynomials_abf.cc.

Member Function Documentation

evaluate()

template<int dim>

void PolynomialsABF< 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 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.

Implements TensorPolynomialsBase< dim >.

Definition at line 63 of file polynomials_abf.cc.

name()

template<int dim>

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

inlineoverridevirtual

Return the name of the space, which is ABF.

Implements TensorPolynomialsBase< dim >.

Definition at line 142 of file polynomials_abf.h.

n_polynomials()

template<int dim>

unsigned int PolynomialsABF< dim >::n_polynomials ( const unsigned int degree )

static

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

Definition at line 156 of file polynomials_abf.cc.

clone()

template<int dim>

std::unique_ptr< TensorPolynomialsBase< dim > > PolynomialsABF< 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 184 of file polynomials_abf.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> PolynomialsABF< dim >::polynomial_space

private

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

Definition at line 106 of file polynomials_abf.h.

mutex

template<int dim>

Threads::Mutex PolynomialsABF< dim >::mutex

mutableprivate

A mutex that guards the following scratch arrays.

Definition at line 111 of file polynomials_abf.h.

p_values

template<int dim>

std::vector<double> PolynomialsABF< dim >::p_values

mutableprivate

Auxiliary memory.

Definition at line 116 of file polynomials_abf.h.

p_grads

template<int dim>

std::vector<Tensor<1, dim> > PolynomialsABF< dim >::p_grads

mutableprivate

Auxiliary memory.

Definition at line 121 of file polynomials_abf.h.

p_grad_grads

template<int dim>

std::vector<Tensor<2, dim> > PolynomialsABF< dim >::p_grad_grads

mutableprivate

Auxiliary memory.

Definition at line 126 of file polynomials_abf.h.

p_third_derivatives

template<int dim>

std::vector<Tensor<3, dim> > PolynomialsABF< dim >::p_third_derivatives

mutableprivate

Auxiliary memory.

Definition at line 131 of file polynomials_abf.h.

p_fourth_derivatives

template<int dim>

std::vector<Tensor<4, dim> > PolynomialsABF< dim >::p_fourth_derivatives

mutableprivate

Auxiliary memory.

Definition at line 136 of file polynomials_abf.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:

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