 Reference documentation for deal.II version Git 6d63218887 2020-10-30 17:17:53 -0400
ScalarPolynomialsBase< dim > Class Template Referenceabstract

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

## Public Member Functions

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

ScalarPolynomialsBase (ScalarPolynomialsBase< dim > &&)=default

ScalarPolynomialsBase (const ScalarPolynomialsBase< dim > &)=default

virtual ~ScalarPolynomialsBase ()=default

virtual void evaluate (const Point< dim > &unit_point, std::vector< double > &values, std::vector< Tensor< 1, dim >> &grads, std::vector< Tensor< 2, dim >> &grad_grads, std::vector< Tensor< 3, dim >> &third_derivatives, std::vector< Tensor< 4, dim >> &fourth_derivatives) const =0

virtual double compute_value (const unsigned int, const Point< dim > &) const =0

template<int order>
Tensor< order, dim > compute_derivative (const unsigned int i, const Point< dim > &p) const

virtual Tensor< 1, dim > compute_1st_derivative (const unsigned int i, const Point< dim > &p) const =0

virtual Tensor< 2, dim > compute_2nd_derivative (const unsigned int i, const Point< dim > &p) const =0

virtual Tensor< 3, dim > compute_3rd_derivative (const unsigned int i, const Point< dim > &p) const =0

virtual Tensor< 4, dim > compute_4th_derivative (const unsigned int i, const Point< dim > &p) const =0

virtual Tensor< 1, dim > compute_grad (const unsigned int, const Point< dim > &) const =0

virtual Tensor< 2, dim > compute_grad_grad (const unsigned int, const Point< dim > &) const =0

unsigned int n () const

virtual unsigned int degree () const

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

virtual std::string name () const =0

virtual std::size_t memory_consumption () const

## Private Attributes

const unsigned int polynomial_degree

const unsigned int n_pols

## Detailed Description

### template<int dim> class ScalarPolynomialsBase< dim >

This class provides a framework for the finite element polynomial classes for use with finite element classes that are derived from FE_Poly. 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_Poly.

### 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

• PolynomialsAdini
• PolynomialsRannacherTurek
• PolynomialsP
• PolynomialSpace
• TensorProductPolynomials
• TensorProductPolynomialsConst
• TensorProductPolynomialsBubbles

Definition at line 61 of file scalar_polynomials_base.h.

## ◆ ScalarPolynomialsBase() [1/3]

template<int dim>
 ScalarPolynomialsBase< dim >::ScalarPolynomialsBase ( 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 scalar_polynomials_base.cc.

## ◆ ScalarPolynomialsBase() [2/3]

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

Move constructor.

## ◆ ScalarPolynomialsBase() [3/3]

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

Copy constructor.

## ◆ ~ScalarPolynomialsBase()

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

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

## ◆ evaluate()

template<int dim>
 virtual void ScalarPolynomialsBase< dim >::evaluate ( const Point< dim > & unit_point, std::vector< double > & values, std::vector< Tensor< 1, dim >> & grads, std::vector< Tensor< 2, dim >> & grad_grads, std::vector< Tensor< 3, dim >> & third_derivatives, std::vector< Tensor< 4, 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.

## ◆ compute_value()

template<int dim>
 virtual double ScalarPolynomialsBase< dim >::compute_value ( const unsigned int, const Point< dim > & ) const
pure virtual

Compute the value of the ith polynomial at unit point p.

## ◆ compute_derivative()

template<int dim>
template<int order>
 Tensor< order, dim > ScalarPolynomialsBase< dim >::compute_derivative ( const unsigned int i, const Point< dim > & p ) const
inline

Compute the orderth derivative of the ith polynomial at unit point p.

Template Parameters
 order The order of the derivative.

Definition at line 257 of file scalar_polynomials_base.h.

## ◆ compute_1st_derivative()

template<int dim>
 virtual Tensor<1, dim> ScalarPolynomialsBase< dim >::compute_1st_derivative ( const unsigned int i, const Point< dim > & p ) const
pure virtual

Compute the first derivative of the ith polynomial at unit point p.

## ◆ compute_2nd_derivative()

template<int dim>
 virtual Tensor<2, dim> ScalarPolynomialsBase< dim >::compute_2nd_derivative ( const unsigned int i, const Point< dim > & p ) const
pure virtual

Compute the second derivative of the ith polynomial at unit point p.

## ◆ compute_3rd_derivative()

template<int dim>
 virtual Tensor<3, dim> ScalarPolynomialsBase< dim >::compute_3rd_derivative ( const unsigned int i, const Point< dim > & p ) const
pure virtual

Compute the third derivative of the ith polynomial at unit point p.

## ◆ compute_4th_derivative()

template<int dim>
 virtual Tensor<4, dim> ScalarPolynomialsBase< dim >::compute_4th_derivative ( const unsigned int i, const Point< dim > & p ) const
pure virtual

Compute the fourth derivative of the ith polynomial at unit point p.

template<int dim>
 virtual Tensor<1, dim> ScalarPolynomialsBase< dim >::compute_grad ( const unsigned int, const Point< dim > & ) const
pure virtual

Compute the gradient of the ith polynomial at unit point p.

template<int dim>
 virtual Tensor<2, dim> ScalarPolynomialsBase< dim >::compute_grad_grad ( const unsigned int, const Point< dim > & ) const
pure virtual

Compute the second derivative (grad_grad) of the ith polynomial at unit point p.

## ◆ n()

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

Return the number of polynomials.

Definition at line 238 of file scalar_polynomials_base.h.

## ◆ degree()

template<int dim>
 unsigned int ScalarPolynomialsBase< dim >::degree ( ) const
inlinevirtual

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 247 of file scalar_polynomials_base.h.

## ◆ clone()

template<int dim>
 virtual std::unique_ptr > ScalarPolynomialsBase< 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_Poly, 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 ScalarPolynomialsBase< dim >::name ( ) const
pure virtual

Return the name of the space.

## ◆ memory_consumption()

template<int dim>
 std::size_t ScalarPolynomialsBase< dim >::memory_consumption ( ) const
virtual

Return an estimate (in bytes) for the memory consumption of this object.

Definition at line 39 of file scalar_polynomials_base.cc.

## ◆ polynomial_degree

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

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

Definition at line 226 of file scalar_polynomials_base.h.

## ◆ n_pols

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

The number of polynomials represented by this object.

Definition at line 231 of file scalar_polynomials_base.h.

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