Reference documentation for deal.II version Git 1ab60d1 2017-10-16 22:02:15 +0200
Public Member Functions | Static Public Member Functions | Private Attributes | List of all members
PolynomialsABF< dim > Class Template Reference

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

Public Member Functions

 PolynomialsABF (const unsigned int k)
 
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
 
unsigned int n () const
 
unsigned int degree () const
 
std::string name () const
 

Static Public Member Functions

static unsigned int compute_n_pols (unsigned int degree)
 

Private Attributes

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

Detailed Description

template<int dim>
class PolynomialsABF< dim >

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

Author
Oliver Kayser-Herold, based on code from Guido Kanschat
Date
2006

Definition at line 54 of file polynomials_abf.h.

Constructor & Destructor Documentation

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 Qk contained.

Definition at line 48 of file polynomials_abf.cc.

Member Function Documentation

template<int dim>
void PolynomialsABF< dim >::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

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.

Definition at line 65 of file polynomials_abf.cc.

template<int dim>
unsigned int PolynomialsABF< dim >::n ( ) const
inline

Return the number of ABF polynomials.

Definition at line 161 of file polynomials_abf.h.

template<int dim>
unsigned int PolynomialsABF< dim >::degree ( ) const
inline

Return the degree of the ABF space, which is two less than the highest polynomial degree.

Definition at line 169 of file polynomials_abf.h.

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

Return the name of the space, which is ABF.

Definition at line 177 of file polynomials_abf.h.

template<int dim>
unsigned int PolynomialsABF< dim >::compute_n_pols ( 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 150 of file polynomials_abf.cc.

Member Data Documentation

template<int dim>
const unsigned int PolynomialsABF< dim >::my_degree
private

The degree of this object as given to the constructor.

Definition at line 113 of file polynomials_abf.h.

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 120 of file polynomials_abf.h.

template<int dim>
unsigned int PolynomialsABF< dim >::n_pols
private

Number of Raviart-Thomas polynomials.

Definition at line 125 of file polynomials_abf.h.

template<int dim>
Threads::Mutex PolynomialsABF< dim >::mutex
mutableprivate

A mutex that guards the following scratch arrays.

Definition at line 130 of file polynomials_abf.h.

template<int dim>
std::vector<double> PolynomialsABF< dim >::p_values
mutableprivate

Auxiliary memory.

Definition at line 135 of file polynomials_abf.h.

template<int dim>
std::vector<Tensor<1,dim> > PolynomialsABF< dim >::p_grads
mutableprivate

Auxiliary memory.

Definition at line 140 of file polynomials_abf.h.

template<int dim>
std::vector<Tensor<2,dim> > PolynomialsABF< dim >::p_grad_grads
mutableprivate

Auxiliary memory.

Definition at line 145 of file polynomials_abf.h.

template<int dim>
std::vector<Tensor<3,dim> > PolynomialsABF< dim >::p_third_derivatives
mutableprivate

Auxiliary memory.

Definition at line 150 of file polynomials_abf.h.

template<int dim>
std::vector<Tensor<4,dim> > PolynomialsABF< dim >::p_fourth_derivatives
mutableprivate

Auxiliary memory.

Definition at line 155 of file polynomials_abf.h.


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