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

Inheritance diagram for QGaussLobatto< dim >:

Public Types
using	SubQuadrature = Quadrature< dim==0 ? 0 :dim - 1 >

Public Member Functions
	QGaussLobatto (const unsigned int n)

	QGaussLobatto (const unsigned int)

bool	operator== (const Quadrature< dim > &p) const

void	initialize (const std::vector< Point< dim > > &points, const std::vector< double > &weights)

unsigned int	size () const

const Point< dim > &	point (const unsigned int i) const

const std::vector< Point< dim > > &	get_points () const

double	weight (const unsigned int i) const

const std::vector< double > &	get_weights () const

std::size_t	memory_consumption () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

bool	is_tensor_product () const

const std::array< Quadrature< 1 >, dim > &	get_tensor_basis () const

Protected Attributes
std::vector< Point< dim > >	quadrature_points

std::vector< double >	weights

bool	is_tensor_product_flag

std::unique_ptr< std::array< Quadrature< 1 >, dim > >	tensor_basis

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

std::atomic< unsigned int >	counter

std::map< std::string, unsigned int >	counter_map

std::vector< std::atomic< bool > * >	validity_pointers

const std::type_info *	object_info

static std::mutex	mutex

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

void	check_no_subscribers () const noexcept

Detailed Description

template<int dim>
class QGaussLobatto< dim >

The Gauss-Lobatto family of quadrature rules for numerical integration.

This modification of the Gauss quadrature uses the two interval end points as well. Being exact for polynomials of degree 2n-3, this formula is suboptimal by two degrees.

The quadrature points are interval end points plus the roots of the derivative of the Legendre polynomial P_n-1 of degree n-1. The quadrature weights are 2/(n(n-1)(P_n-1(x_i)²).

Note: This implementation has not been optimized concerning numerical stability and efficiency. It can be easily adapted to the general case of Gauss-Lobatto-Jacobi-Bouzitat quadrature with arbitrary parameters \(\alpha\), \(\beta\), of which the Gauss-Lobatto-Legendre quadrature ( \(\alpha = \beta = 0\)) is a special case.

See also: http://en.wikipedia.org/wiki/Handbook_of_Mathematical_Functions; Karniadakis, G.E. and Sherwin, S.J.: Spectral/hp element methods for computational fluid dynamics. Oxford: Oxford University Press, 2005

Definition at line 72 of file quadrature_lib.h.

Member Typedef Documentation

◆ SubQuadrature

template<int dim>

using Quadrature< dim >::SubQuadrature = Quadrature<dim == 0 ? 0 : dim - 1>

inherited

Define an alias for a quadrature that acts on an object of one dimension less. For cells, this would then be a face quadrature. A sub quadrature of a 0-dimensional quadrature is defined as still being 0-dimensional.

Definition at line 94 of file quadrature.h.

Constructor & Destructor Documentation

◆ QGaussLobatto() [1/2]

template<int dim>

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

Generate a formula with n quadrature points (in each space direction).

Definition at line 825 of file quadrature_lib.cc.

◆ QGaussLobatto() [2/2]

QGaussLobatto< 0 >::QGaussLobatto ( const unsigned int )

Definition at line 56 of file quadrature_lib.cc.

Member Function Documentation

◆ operator==()

template<int dim>

bool Quadrature< dim >::operator== ( const Quadrature< dim > & p ) const

inherited

Test for equality of two quadratures.

Definition at line 304 of file quadrature.cc.

◆ initialize()

template<int dim>

void Quadrature< dim >::initialize	(	const std::vector< Point< dim > > &	points,
		const std::vector< double > &	weights
	)

inherited

Set the quadrature points and weights to the values provided in the arguments.

Definition at line 52 of file quadrature.cc.

◆ size()

template<int dim>

unsigned int Quadrature< dim >::size ( ) const

inherited

Number of quadrature points.

◆ point()

template<int dim>

const Point< dim > & Quadrature< dim >::point ( const unsigned int i ) const

inherited

Return the ith quadrature point.

◆ get_points()

template<int dim>

const std::vector< Point< dim > > & Quadrature< dim >::get_points ( ) const

inherited

Return a reference to the whole array of quadrature points.

◆ weight()

template<int dim>

double Quadrature< dim >::weight ( const unsigned int i ) const

inherited

Return the weight of the ith quadrature point.

◆ get_weights()

template<int dim>

const std::vector< double > & Quadrature< dim >::get_weights ( ) const

inherited

Return a reference to the whole array of weights.

◆ memory_consumption()

template<int dim>

std::size_t Quadrature< dim >::memory_consumption

inherited

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

Definition at line 313 of file quadrature.cc.

◆ serialize()

template<int dim>

template<class Archive >

void Quadrature< dim >::serialize	(	Archive &	ar,
		const unsigned int	version
	)

inherited

Write or read the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

◆ is_tensor_product()

template<int dim>

bool Quadrature< dim >::is_tensor_product ( ) const

inherited

This function returns true if the quadrature object is a tensor product of one-dimensional formulas and the quadrature points are sorted lexicographically.

◆ get_tensor_basis()

template<int dim>

std::conditional< dim==1, std::array< Quadrature< 1 >, dim >, conststd::array< Quadrature< 1 >, dim > & >::type Quadrature< dim >::get_tensor_basis

inherited

In case the quadrature formula is a tensor product, this function returns the dim one-dimensional basis objects. Otherwise, calling this function is not allowed.

For dim equal to one, we can not return the std::array as a const reference and have to return it by value. In this case, the array will always contain a single element (this).

Note: The actual return type of this function is
std::conditional<dim == 1,

std::array<Quadrature<1>, dim>,

const std::array<Quadrature<1>, dim> &>::type

The type is abbreviated in the online documentation to improve readability of this page.

Definition at line 325 of file quadrature.cc.

Member Data Documentation

◆ quadrature_points

template<int dim>

std::vector<Point<dim> > Quadrature< dim >::quadrature_points

protectedinherited

List of quadrature points. To be filled by the constructors of derived classes.

Definition at line 290 of file quadrature.h.

◆ weights

template<int dim>

std::vector<double> Quadrature< dim >::weights

protectedinherited

List of weights of the quadrature points. To be filled by the constructors of derived classes.

Definition at line 296 of file quadrature.h.

◆ is_tensor_product_flag

template<int dim>

bool Quadrature< dim >::is_tensor_product_flag

protectedinherited

Indicates if this object represents quadrature formula that is a tensor product of one-dimensional formulas. This flag is set if dim==1 or the constructors taking a Quadrature<1> (and possibly a Quadrature<dim-1> object) is called. This implies that the quadrature points are sorted lexicographically.

Definition at line 305 of file quadrature.h.

◆ tensor_basis

template<int dim>

std::unique_ptr<std::array<Quadrature<1>, dim> > Quadrature< dim >::tensor_basis

protectedinherited

Stores the one-dimensional tensor basis objects in case this object can be represented by a tensor product.

Definition at line 311 of file quadrature.h.

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

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

Public Types

Public Member Functions

Protected Attributes

Subscriptor functionality

Detailed Description

Member Typedef Documentation

◆ SubQuadrature

Constructor & Destructor Documentation

◆ QGaussLobatto() [1/2]

◆ QGaussLobatto() [2/2]

Member Function Documentation

◆ operator==()

◆ initialize()

◆ size()

◆ point()

◆ get_points()

◆ weight()

◆ get_weights()

◆ memory_consumption()

◆ serialize()

◆ is_tensor_product()

◆ get_tensor_basis()

Member Data Documentation

◆ quadrature_points

◆ weights

◆ is_tensor_product_flag

◆ tensor_basis