Reference documentation for deal.II version 9.4.0
TensorPolynomialsBase< dim > Class Template Referenceabstract

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

Inheritance diagram for TensorPolynomialsBase< dim >:
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## Public Member Functions

TensorPolynomialsBase (const unsigned int deg, const unsigned int n_polynomials)

TensorPolynomialsBase (TensorPolynomialsBase< dim > &&)=default

TensorPolynomialsBase (const TensorPolynomialsBase< dim > &)=default

virtual ~TensorPolynomialsBase ()=default

virtual 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 =0

unsigned int n () const

unsigned int degree () const

virtual std::unique_ptr< TensorPolynomialsBase< dim > > clone () const =0

virtual std::string name () const =0

## Private Attributes

const unsigned int polynomial_degree

const unsigned int n_pols

## Detailed Description

template<int dim>
class TensorPolynomialsBase< dim >

This class provides a framework for the finite element polynomial classes for use with finite element classes that are derived from FE_PolyTensor. An object of this type (or rather of a type derived from this class) is stored as a member variable in each object of type FE_PolyTensor.

### Deriving classes

Any derived class must provide the most basic properties for shape functions evaluated on the reference cell. This includes, but is not limited to, implementing the evaluate(), name(), and clone() member functions. These functions are necessary to store the most basic information of how the polynomials in the derived class evaluate at a given point on the reference cell. More information on each function can be found in the corresponding function's documentation.

Some classes that derive from this class include

• PolynomialsABF
• PolynomialsBDM
• PolynomialsBernardiRaugel
• PolynomialsNedelec
• PolynomialsRaviartThomas
• PolynomialsRT_Bubbles

Definition at line 62 of file tensor_polynomials_base.h.

## ◆ TensorPolynomialsBase() [1/3]

template<int dim>
 TensorPolynomialsBase< dim >::TensorPolynomialsBase ( const unsigned int deg, const unsigned int n_polynomials )

Constructor. This takes the degree of the space, deg from the finite element class, and n, the number of polynomials for the space.

Definition at line 26 of file tensor_polynomials_base.cc.

## ◆ TensorPolynomialsBase() [2/3]

template<int dim>
 TensorPolynomialsBase< dim >::TensorPolynomialsBase ( TensorPolynomialsBase< dim > && )
default

Move constructor.

## ◆ TensorPolynomialsBase() [3/3]

template<int dim>
 TensorPolynomialsBase< dim >::TensorPolynomialsBase ( const TensorPolynomialsBase< dim > & )
default

Copy constructor.

## ◆ ~TensorPolynomialsBase()

template<int dim>
 virtual TensorPolynomialsBase< dim >::~TensorPolynomialsBase ( )
virtualdefault

Virtual destructor. Makes sure that pointers to this class are deleted properly.

## ◆ evaluate()

template<int dim>
 virtual void TensorPolynomialsBase< 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
pure virtual

Compute the value and the derivatives of the polynomials 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 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.

## ◆ n()

template<int dim>
 unsigned int TensorPolynomialsBase< dim >::n
inline

Return the number of polynomials.

Definition at line 157 of file tensor_polynomials_base.h.

## ◆ degree()

template<int dim>
 unsigned int TensorPolynomialsBase< dim >::degree
inline

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 166 of file tensor_polynomials_base.h.

## ◆ clone()

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

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.

## ◆ name()

template<int dim>
 virtual std::string TensorPolynomialsBase< dim >::name ( ) const
pure virtual

Return the name of the space.

## ◆ polynomial_degree

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

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

Definition at line 145 of file tensor_polynomials_base.h.

## ◆ n_pols

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

The number of polynomials represented by this object.

Definition at line 150 of file tensor_polynomials_base.h.

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