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

Inheritance diagram for ScalarPolynomialsBase< dim >:

[legend]

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 i, const Point< dim > &p) 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

Definition at line 62 of file scalar_polynomials_base.h.

Constructor & Destructor Documentation

◆ 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 25 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.

Member Function Documentation

◆ 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.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ compute_value()

template<int dim>

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

pure virtual

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

Consider using evaluate() instead.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ 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.

Consider using evaluate() instead.

Template Parameters

order The order of the derivative.

Definition at line 258 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.

Consider using evaluate() instead.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ 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.

Consider using evaluate() instead.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ 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.

Consider using evaluate() instead.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ 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.

Consider using evaluate() instead.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ compute_grad()

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.

Consider using evaluate() instead.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ compute_grad_grad()

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.

Consider using evaluate() instead.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ n()

template<int dim>

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

inline

Return the number of polynomials.

Definition at line 239 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.

Reimplemented in PolynomialsP< dim >.

Definition at line 248 of file scalar_polynomials_base.h.

◆ clone()

template<int dim>

virtual std::unique_ptr< ScalarPolynomialsBase< dim > > 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.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, PolynomialsP< dim >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ name()

template<int dim>

virtual std::string ScalarPolynomialsBase< dim >::name ( ) const

pure virtual

Return the name of the space.

Implemented in PolynomialSpace< dim >, PolynomialSpace< dim - 1 >, PolynomialsAdini< dim >, BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, ScalarLagrangePolynomialPyramid< dim >, PolynomialsRannacherTurek< dim >, ScalarLagrangePolynomialWedge< dim >, TensorProductPolynomials< dim, PolynomialType >, TensorProductPolynomials< dim - 1 >, AnisotropicPolynomials< dim >, TensorProductPolynomialsBubbles< dim >, and TensorProductPolynomialsConst< dim >.

◆ 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.

Reimplemented in BarycentricPolynomials< dim >, BarycentricPolynomials< 1 >, BarycentricPolynomials< 2 >, TensorProductPolynomials< dim, PolynomialType >, and TensorProductPolynomials< dim - 1 >.

Definition at line 38 of file scalar_polynomials_base.cc.

Member Data Documentation

◆ 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 227 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 232 of file scalar_polynomials_base.h.

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

include/deal.II/base/scalar_polynomials_base.h
source/base/scalar_polynomials_base.cc

Public Member Functions

Private Attributes

Detailed Description

Deriving classes

Constructor & Destructor Documentation

◆ ScalarPolynomialsBase() [1/3]

◆ ScalarPolynomialsBase() [2/3]

◆ ScalarPolynomialsBase() [3/3]

◆ ~ScalarPolynomialsBase()

Member Function Documentation

◆ evaluate()

◆ compute_value()

◆ compute_derivative()

◆ compute_1st_derivative()

◆ compute_2nd_derivative()

◆ compute_3rd_derivative()

◆ compute_4th_derivative()

◆ compute_grad()

◆ compute_grad_grad()

◆ n()

◆ degree()

◆ clone()

◆ name()

◆ memory_consumption()

Member Data Documentation

◆ polynomial_degree

◆ n_pols