Reference documentation for deal.II version GIT relicensing-437-g81ec864850 2024-04-19 07:30:02+00:00
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Public Types | Public Member Functions | Static Public Member Functions | Protected Attributes | Private Types | Private Member Functions | Private Attributes | Static Private Attributes | List of all members
Quadrature< dim > Class Template Reference

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

Inheritance diagram for Quadrature< dim >:
Inheritance graph
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Public Types

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

Public Member Functions

 Quadrature (const unsigned int n_quadrature_points=0)
 
 Quadrature (const SubQuadrature &, const Quadrature< 1 > &)
 
 Quadrature (const Quadrature< dim !=1 ? 1 :0 > &quadrature_1d)
 
 Quadrature (const Quadrature< dim > &q)
 
 Quadrature (Quadrature< dim > &&) noexcept=default
 
 Quadrature (const std::vector< Point< dim > > &points, const std::vector< double > &weights)
 
 Quadrature (std::vector< Point< dim > > &&points, std::vector< double > &&weights)
 
 Quadrature (const std::vector< Point< dim > > &points)
 
 Quadrature (const Point< dim > &point)
 
virtual ~Quadrature () override=default
 
Quadratureoperator= (const Quadrature< dim > &)
 
Quadratureoperator= (Quadrature< dim > &&)=default
 
bool operator== (const Quadrature< dim > &p) const
 
void initialize (const ArrayView< const Point< dim > > &points, const ArrayView< const double > &weights={})
 
unsigned int size () const
 
bool empty () 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 ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (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 intcounter
 
std::map< std::string, unsigned intcounter_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 Quadrature< dim >

Base class for quadrature formulae in arbitrary dimensions. Quadrature is a means to approximate an integral by evaluating the integrand at specific points \(\mathbf x_q\) and summing the point values with specific weights \(w_q\); that is, quadrature computes

\begin{align*} \int_K f(\mathbf x) \; dx \approx \sum_{q=0,\ldots,Q-1} f(\mathbf x_q) w_q. \end{align*}

This class stores quadrature points \(\mathbf x_q\) and weights \(w_q\) for concrete "quadrature formulas" when \(K\) (the domain we integrate over) is a reference cell. That is, points and weights are expressed in the coordinate system of a reference cell (see the ReferenceCell class) and as such serves to represent quadrature points and weights on the unit line segment \([0,1]\) in 1d, on the unit square or unit triangle in 2d, as well as the unit tetrahedron, cube, pyramid, and wedge reference cells in 3d. Integration over concrete cells is done by coordinate transformation to the reference cell represented by the current class.

There are a number of derived classes, denoting concrete integration formulae. Their names are prefixed by Q. Refer to the list of derived classes for more details.

At least for quadrilaterals and hexahedra (or, more precisely, since we work on reference cells: for the unit square and the unit cube), quadrature formulas are typically tensor products of one-dimensional formulas (see also the section on implementation detail below).

In order to allow for dimension independent programming, a quadrature formula of dimension zero exists. Since an integral over zero dimensions is the evaluation at a single point, any constructor of such a formula initializes to a single quadrature point with weight one. Access to the weight is possible, while access to the quadrature point is not permitted, since a Point of dimension zero contains no information. The main purpose of these formulae is their use in QProjector, which will create a useful formula of dimension one out of them.

Mathematical background

For each quadrature formula we denote by m, the maximal degree of polynomials integrated exactly on the reference cell the quadrature formula corresponds to. This number is given in the documentation of each formula. The order of the integration error is m+1, that is, the error is the size of the cell to the m+1 by the Bramble-Hilbert Lemma. The number m is to be found in the documentation of each concrete formula. For the optimal formulae QGauss we have \(m = 2N-1\), where \(N\) is the constructor parameter to QGauss. The tensor product formulae are exact on tensor product polynomials of degree m in each space direction, but they are still only of (m+1)st order.

Tensor product quadrature

At least for hypercube reference cells (i.e., squares and cubes), most integration formulae in more than one space dimension are tensor products of quadrature formulae in one space dimension, or more generally the tensor product of a formula in (dim-1) dimensions and one in one dimension. There is a special constructor to generate a quadrature formula from two others. For example, the QGauss<dim> formulae include Ndim quadrature points in dim dimensions, where \(N\) is the constructor parameter of QGauss.

Other uses of this class

Quadrature objects are used in a number of places within deal.II where integration is performed, most notably via the FEValues and related classes. Some of these classes are also used in contexts where no integrals are involved, but where functions need to be evaluated at specific points, for example to evaluate the solution at individual points or to create graphical output. Examples are the implementation of VectorTools::point_value() and the DataOut and related classes (in particular in connection with the DataPostprocessor class). In such contexts, one often creates specific "Quadrature" objects in which the "quadrature points" are simply the points (in the coordinate system of the reference cell) at which one wants to evaluate the solution. In these kinds of cases, the weights stored by the current class are not used and the name "quadrature object" is interpreted as "list of evaluation points".

Definition at line 122 of file quadrature.h.

Member Typedef Documentation

◆ SubQuadrature

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

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 229 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 234 of file subscriptor.h.

Constructor & Destructor Documentation

◆ Quadrature() [1/9]

template<int dim>
Quadrature< dim >::Quadrature ( const unsigned int  n_quadrature_points = 0)
explicit

Constructor.

This constructor is marked as explicit to avoid involuntary accidents like in hp::QCollection<dim> q_collection(3) where hp::QCollection<dim> q_collection(QGauss<dim>(3)) was meant.

Definition at line 41 of file quadrature.cc.

◆ Quadrature() [2/9]

template<int dim>
Quadrature< dim >::Quadrature ( const SubQuadrature< dim > &  q1,
const Quadrature< 1 > &  q2 
)

Build this quadrature formula as the tensor product of a formula in a dimension one less than the present and a formula in one dimension. This constructor assumes (and tests) that constant functions are integrated exactly, i.e. the sum of the quadrature weights is one.

SubQuadrature<dim>::type expands to Quadrature<dim-1>.

Definition at line 157 of file quadrature.cc.

◆ Quadrature() [3/9]

template<int dim>
Quadrature< dim >::Quadrature ( const Quadrature< dim !=1 ? 1 :0 > &  quadrature_1d)
explicit

Build this quadrature formula as the dim-fold tensor product of a formula in one dimension.

Assuming that the points in the one-dimensional rule are in ascending order, the points of the resulting rule are ordered lexicographically with x running fastest.

In order to avoid a conflict with the copy constructor in 1d, we let the argument be a 0d quadrature formula for dim==1, and a 1d quadrature formula for all other space dimensions.

This constructor does not require that constant functions are integrated exactly. Therefore, it is appropriate if the one-dimensional formula is defined with respect to a weighting function.

If dim == 0, the resulting quadrature formula will be a single Point<0> having unit weight.

Definition at line 255 of file quadrature.cc.

◆ Quadrature() [4/9]

template<int dim>
Quadrature< dim >::Quadrature ( const Quadrature< dim > &  q)

Copy constructor.

Definition at line 293 of file quadrature.cc.

◆ Quadrature() [5/9]

template<int dim>
Quadrature< dim >::Quadrature ( Quadrature< dim > &&  )
defaultnoexcept

Move constructor. Construct a new quadrature object by transferring the internal data of another quadrature object.

◆ Quadrature() [6/9]

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

Construct a quadrature formula from given vectors of quadrature points (which should really be in the unit cell) and the corresponding weights. You will want to have the weights sum up to one, but this is not checked.

Definition at line 75 of file quadrature.cc.

◆ Quadrature() [7/9]

template<int dim>
Quadrature< dim >::Quadrature ( std::vector< Point< dim > > &&  points,
std::vector< double > &&  weights 
)

Construct a quadrature formula from given vectors of quadrature points (which should really be in the unit cell) and the corresponding weights, moving the points and weights into the present object.

Definition at line 88 of file quadrature.cc.

◆ Quadrature() [8/9]

template<int dim>
Quadrature< dim >::Quadrature ( const std::vector< Point< dim > > &  points)

Construct a dummy quadrature formula from a list of points, with weights set to infinity. The resulting object is therefore not meant to actually perform integrations, but rather to be used with FEValues objects in order to find the position of some points (the quadrature points in this object) on the transformed cell in real space.

Definition at line 101 of file quadrature.cc.

◆ Quadrature() [9/9]

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

Constructor for a one-point quadrature. Sets the weight of this point to one.

Definition at line 113 of file quadrature.cc.

◆ ~Quadrature()

template<int dim>
virtual Quadrature< dim >::~Quadrature ( )
overridevirtualdefault

Virtual destructor.

Member Function Documentation

◆ operator=() [1/2]

template<int dim>
Quadrature< dim > & Quadrature< dim >::operator= ( const Quadrature< dim > &  q)

Assignment operator. Copies contents of weights and quadrature_points as well as size.

Definition at line 308 of file quadrature.cc.

◆ operator=() [2/2]

template<int dim>
Quadrature & Quadrature< dim >::operator= ( Quadrature< dim > &&  )
default

Move assignment operator. Moves all data from another quadrature object to this object.

◆ operator==()

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

Test for equality of two quadratures.

Definition at line 328 of file quadrature.cc.

◆ initialize()

template<int dim>
void Quadrature< dim >::initialize ( const ArrayView< const Point< dim > > &  points,
const ArrayView< const double > &  weights = {} 
)

Set the quadrature points and weights to the values provided in the arguments. The weights array is allowed to be empty, in which case the weights are set to infinity. The resulting object is therefore not meant to actually perform integrations, but rather to be used with FEValues objects in order to find the position of some points (the quadrature points in this object) on the transformed cell in real space.

Definition at line 51 of file quadrature.cc.

◆ size()

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

Number of quadrature points.

◆ empty()

template<int dim>
bool Quadrature< dim >::empty ( ) const

Return if quadrature is empty.

◆ point()

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

Return the ith quadrature point.

◆ get_points()

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

Return a reference to the whole array of quadrature points.

◆ weight()

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

Return the weight of the ith quadrature point.

◆ get_weights()

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

Return a reference to the whole array of weights.

◆ memory_consumption()

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

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

Definition at line 337 of file quadrature.cc.

◆ serialize()

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

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

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

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_t<dim == 1,
std::array<Quadrature<1>, dim>,
const std::array<Quadrature<1>, dim> &>
The type is abbreviated in the online documentation to improve readability of this page.

Definition at line 349 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 135 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 155 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 203 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.

Definition at line 52 of file subscriptor.cc.

Member Data Documentation

◆ quadrature_points

template<int dim>
std::vector<Point<dim> > Quadrature< dim >::quadrature_points
protected

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

Definition at line 343 of file quadrature.h.

◆ weights

template<int dim>
std::vector<double> Quadrature< dim >::weights
protected

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

Definition at line 349 of file quadrature.h.

◆ is_tensor_product_flag

template<int dim>
bool Quadrature< dim >::is_tensor_product_flag
protected

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 358 of file quadrature.h.

◆ tensor_basis

template<int dim>
std::unique_ptr<std::array<Quadrature<1>, dim> > Quadrature< dim >::tensor_basis
protected

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

Definition at line 364 of file quadrature.h.

◆ counter

std::atomic<unsigned int> Subscriptor::counter
mutableprivateinherited

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

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 218 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 224 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 240 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 248 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex
staticprivateinherited

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.


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