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

Inheritance diagram for QSimplex< dim >:

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

Public Member Functions
	QSimplex (const Quadrature< dim > &quad)

template<int spacedim = dim>
Quadrature< spacedim >	compute_affine_transformation (const std::array< Point< spacedim >, dim+1 > &vertices) const

template<int spacedim = dim>
Quadrature< spacedim >	mapped_quadrature (const std::vector< std::array< Point< spacedim >, dim+1 > > &simplices) const

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

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

Static Public Member Functions
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

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

Private Types
using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

Private Member Functions
void	check_no_subscribers () const noexcept

Private Attributes
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 Private Attributes
static std::mutex	mutex

Detailed Description

template<int dim>
class QSimplex< dim >

Given an arbitrary quadrature formula, return one that chops the quadrature points above the hyper-plane defined by \(\sum_i x_i = 1\). In other words, it extracts those quadrature points from the base formula that satisfy \(\sum_i (\mathbf x_q)_i \le 1+10^{-12}\)."

In general the resulting quadrature is not very useful, unless the quadrature you started from has been constructed specifically to integrate over triangles or tetrahedra. This class only ensures that the resulting quadrature formula only has quadrature points in the reference simplex or on its boundary.

No transformation is applied to the weights, and the weights referring to points that live outside the reference simplex are simply discarded. Because this leads to (or may lead to) a sum of quadrature weights that do not equal the area of the simplex, the resulting quadrature formula is not useful for actually computing integrals.

The main use of this quadrature formula is not to chop tensor product quadratures. Ideally you should pass to this class a quadrature formula constructed directly using points and weights in the reference simplex, capable of integrating on triangles or tetrahedra.

For finite elements based on quadrilaterals and hexahedra, a QSimplex quadrature formula is not very useful on its own. This class is typically used in conjunction with other classes, like QSplit, to patch the reference element using several QSimplex quadrature formulas.

Such quadrature formulas are useful to integrate functions with singularities at certain points, or functions that present jumps along a co-dimension one surface inside the reference element, like in the extended finite element method (XFEM).

Definition at line 602 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 130 of file quadrature.h.

◆ map_value_type

using Subscriptor::map_value_type = decltype(counter_map)::value_type

privateinherited

The data type used in counter_map.

Definition at line 230 of file subscriptor.h.

◆ map_iterator

using Subscriptor::map_iterator = decltype(counter_map)::iterator

privateinherited

The iterator type used in counter_map.

Definition at line 235 of file subscriptor.h.

Constructor & Destructor Documentation

◆ QSimplex()

template<int dim>

QSimplex< dim >::QSimplex ( const Quadrature< dim > & quad )

Construct a quadrature that only contains the points that are in the lower left reference simplex.

Parameters

[in] quad The input quadrature.

Definition at line 1204 of file quadrature_lib.cc.

Member Function Documentation

◆ compute_affine_transformation()

template<int dim>

template<int spacedim>

Quadrature< spacedim > QSimplex< dim >::compute_affine_transformation ( const std::array< Point< spacedim >, dim+1 > & vertices ) const

Return an affine transformation of this quadrature, that can be used to integrate on the simplex identified by vertices.

Both the quadrature point locations and the weights are transformed, so that you can effectively use the resulting quadrature to integrate on the simplex.

The transformation is defined as

\[ x = v_0 + B \hat x \]

where the matrix \(B\) is given by \(B_{ij} = v[j][i]-v[0][i]\).

The weights are scaled with the absolute value of the determinant of \(B\), that is \(J \dealcoloneq |\text{det}(B)|\). If \(J\) is zero, an empty quadrature is returned. This may happen, in two dimensions, if the three vertices are aligned, or in three dimensions if the four vertices are on the same plane. The present function works also in the codimension one and codimension two case. For instance, when dim=2 and spacedim=3, we can map the quadrature points so that they live on the physical triangle embedded in the three dimensional space. In such a case, the matrix \(B\) is not square anymore.

Parameters

[in] vertices The vertices of the simplex you wish to integrate on

Returns: A quadrature object that can be used to integrate on the simplex

Definition at line 1231 of file quadrature_lib.cc.

◆ mapped_quadrature()

template<int dim>

template<int spacedim>

Quadrature< spacedim > QSimplex< dim >::mapped_quadrature ( const std::vector< std::array< Point< spacedim >, dim+1 > > & simplices ) const

Given a collection of simplices, this function creates a global quadrature rule on the area covered by the simplices, by mapping the current quadrature on each simplex. A simplex is identified by its vertices, which are stored into an array of Points. Hence, this function can provide quadrature rules on polygons (or polyhedra), as they can be split into simplices.

Parameters

simplices A std::vector where each entry is an array of dim+1 points, which identifies the vertices of a simplex.

Returns: A Quadrature object on the cell.

Definition at line 1265 of file quadrature_lib.cc.

◆ operator==()

template<int dim>

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

inherited

Test for equality of two quadratures.

Definition at line 317 of file quadrature.cc.

◆ initialize()

template<int dim>

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

std::size_t Quadrature< dim >::memory_consumption

inherited

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

Definition at line 326 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 338 of file quadrature.cc.

◆ subscribe()

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

inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 136 of file subscriptor.cc.

◆ unsubscribe()

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

inherited

Unsubscribes a user from the object.

Note: The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 156 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const

inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

◆ list_subscribers() [1/2]

template<typename StreamType >

void Subscriptor::list_subscribers ( StreamType & stream ) const

inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 204 of file subscriptor.cc.

◆ check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

privatenoexceptinherited

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note: Since this function is just a consistency check it does nothing in release mode.; If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 219 of file subscriptor.h.

◆ counter_map

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

mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 225 of file subscriptor.h.

◆ validity_pointers

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

mutableprivateinherited

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 241 of file subscriptor.h.

◆ object_info

const std::type_info* Subscriptor::object_info

mutableprivateinherited

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 249 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex

staticprivateinherited

A mutex used to ensure data consistency when printing out the list of subscribers.

Definition at line 271 of file subscriptor.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

Static Public Member Functions

Protected Attributes

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ SubQuadrature

◆ map_value_type

◆ map_iterator

Constructor & Destructor Documentation

◆ QSimplex()

Member Function Documentation

◆ compute_affine_transformation()

◆ mapped_quadrature()

◆ operator==()

◆ initialize()

◆ size()

◆ point()

◆ get_points()

◆ weight()

◆ get_weights()

◆ memory_consumption()

◆ serialize()

◆ is_tensor_product()

◆ get_tensor_basis()

◆ subscribe()

◆ unsubscribe()

◆ n_subscriptions()

◆ list_subscribers() [1/2]

◆ list_subscribers() [2/2]

◆ check_no_subscribers()

Member Data Documentation

◆ quadrature_points

◆ weights

◆ is_tensor_product_flag

◆ tensor_basis

◆ counter

◆ counter_map

◆ validity_pointers

◆ object_info

◆ mutex