Reference documentation for deal.II version 9.3.0
QGaussOneOverR< dim > Class Template Reference

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

Inheritance diagram for QGaussOneOverR< dim >:
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## Public Member Functions

QGaussOneOverR (const unsigned int n, const Point< dim > &singularity, const bool factor_out_singular_weight=false)

QGaussOneOverR (const unsigned int n, const unsigned int vertex_index, const bool factor_out_singular_weight=false)

template<>
QGaussOneOverR (const unsigned int n, const Point< 2 > &singularity, const bool factor_out_singularity)

template<>
QGaussOneOverR (const unsigned int n, const unsigned int vertex_index, const bool factor_out_singularity)

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 ::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< doubleweights

bool is_tensor_product_flag

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

## Private Member Functions

template<>
unsigned int quad_size (const Point< 2 > &singularity, const unsigned int n)

## Static Private Member Functions

static unsigned int quad_size (const Point< dim > &singularity, const unsigned int n)

## Detailed Description

### template<int dim> class QGaussOneOverR< dim >

A class for Gauss quadrature with $$1/R$$ weighting function. This formula can be used to integrate $$1/R \ f(x)$$ on the reference element $$[0,1]^2$$, where $$f$$ is a smooth function without singularities, and $$R$$ is the distance from the point $$x$$ to the vertex $$\xi$$, given at construction time by specifying its index. Notice that this distance is evaluated in the reference element.

This quadrature formula is obtained from two QGauss quadrature formulas, upon transforming them into polar coordinate system centered at the singularity, and then again into another reference element. This allows for the singularity to be cancelled by part of the Jacobian of the transformation, which contains $$R$$. In practice the reference element is transformed into a triangle by collapsing one of the sides adjacent to the singularity. The Jacobian of this transformation contains $$R$$, which is removed before scaling the original quadrature, and this process is repeated for the next half element.

Upon construction it is possible to specify whether we want the singularity removed, or not. In other words, this quadrature can be used to integrate $$g(x) = 1/R\ f(x)$$, or simply $$f(x)$$, with the $$1/R$$ factor already included in the quadrature weights.

Definition at line 300 of file quadrature_lib.h.

## Member Typedef Documentation

template<int dim>
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.

Definition at line 90 of file quadrature.h.

## ◆ QGaussOneOverR() [1/4]

template<int dim>
 QGaussOneOverR< dim >::QGaussOneOverR ( const unsigned int n, const Point< dim > & singularity, const bool factor_out_singular_weight = false )

This constructor takes three arguments: the order of the Gauss formula, the point of the reference element in which the singularity is located, and whether we include the weighting singular function inside the quadrature, or we leave it in the user function to be integrated.

Traditionally, quadrature formulas include their weighting function, and the last argument is set to false by default. There are cases, however, where this is undesirable (for example when you only know that your singularity has the same order of 1/R, but cannot be written exactly in this way).

In other words, you can use this function in either of the following way, obtaining the same result:

// This will produce the integral of f(x)/R
// And the same here
// This also will produce the integral of f(x)/R, but 1/R has to
// be specified.
for(unsigned int i=0; i<singular_quad.size(); ++i) {
}

## ◆ QGaussOneOverR() [2/4]

template<int dim>
 QGaussOneOverR< dim >::QGaussOneOverR ( const unsigned int n, const unsigned int vertex_index, const bool factor_out_singular_weight = false )

The constructor takes three arguments: the order of the Gauss formula, the index of the vertex where the singularity is located, and whether we include the weighting singular function inside the quadrature, or we leave it in the user function to be integrated. Notice that this is a specialized version of the previous constructor which works only for the vertices of the quadrilateral.

Traditionally, quadrature formulas include their weighting function, and the last argument is set to false by default. There are cases, however, where this is undesirable (for example when you only know that your singularity has the same order of 1/R, but cannot be written exactly in this way).

In other words, you can use this function in either of the following way, obtaining the same result:

// This will produce the integral of f(x)/R
// And the same here
// This also will produce the integral of f(x)/R, but 1/R has to
// be specified.
for(unsigned int i=0; i<singular_quad.size(); ++i) {
}

## ◆ QGaussOneOverR() [3/4]

template<>
 QGaussOneOverR< 2 >::QGaussOneOverR ( const unsigned int n, const Point< 2 > & singularity, const bool factor_out_singularity )

Definition at line 630 of file quadrature_lib.cc.

## ◆ QGaussOneOverR() [4/4]

template<>
 QGaussOneOverR< 2 >::QGaussOneOverR ( const unsigned int n, const unsigned int vertex_index, const bool factor_out_singularity )

Definition at line 679 of file quadrature_lib.cc.

## Member Function Documentation

template<int dim>
 static unsigned int QGaussOneOverR< dim >::quad_size ( const Point< dim > & singularity, const unsigned int n )
staticprivate

Given a quadrature point and a degree n, this function returns the size of the singular quadrature rule, considering whether the point is inside the cell, on an edge of the cell, or on a corner of the cell.

template<>
 unsigned int QGaussOneOverR< 2 >::quad_size ( const Point< 2 > & singularity, const unsigned int n )
private

Definition at line 609 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 302 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 50 of file quadrature.cc.

## ◆ size()

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

## ◆ point()

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

Return the ith quadrature point.

## ◆ get_points()

template<int dim>
 const std::vector >& 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& 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 ( ) const
inherited

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

Definition at line 311 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 >, const std::array< Quadrature< 1 >, dim > & >::type Quadrature< dim >::get_tensor_basis ( ) const
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,

Definition at line 323 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 301 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 318 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.

## Member Data Documentation

template<int dim>
protectedinherited

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

Definition at line 283 of file quadrature.h.

## ◆ weights

template<int dim>
protectedinherited

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

Definition at line 289 of file quadrature.h.

## ◆ is_tensor_product_flag

template<int dim>
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 298 of file quadrature.h.

## ◆ tensor_basis

template<int dim>
 std::unique_ptr, 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 304 of file quadrature.h.

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