Reference documentation for deal.II version 9.4.1
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Public Types | Public Member Functions | Protected Attributes | List of all members
QGaussLogR< dim > Class Template Reference

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

Inheritance diagram for QGaussLogR< dim >:
[legend]

Public Types

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

Public Member Functions

 QGaussLogR (const unsigned int n, const Point< dim > &x0=Point< dim >(), const double alpha=1, const bool factor_out_singular_weight=false)
 
 QGaussLogR (QGaussLogR< dim > &&) noexcept=default
 
 QGaussLogR (const unsigned int n, const Point< 1 > &origin, const double alpha, 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
 

Protected Attributes

const double fraction
 
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 QGaussLogR< dim >

A class for Gauss quadrature with arbitrary logarithmic weighting function. This formula is used to integrate \(\ln(|x-x_0|/\alpha)\;f(x)\) on the interval \([0,1]\), where \(f\) is a smooth function without singularities, and \(x_0\) and \(\alpha\) are given at construction time, and are the location of the singularity \(x_0\) and an arbitrary scaling factor in the singularity.

You have to make sure that the point \(x_0\) is not one of the Gauss quadrature points of order \(N\), otherwise an exception is thrown, since the quadrature weights cannot be computed correctly.

This quadrature formula is rather expensive, since it uses internally two Gauss quadrature formulas of order n to integrate the nonsingular part of the factor, and two GaussLog quadrature formulas to integrate on the separate segments \([0,x_0]\) and \([x_0,1]\). If the singularity is one of the extremes and the factor alpha is 1, then this quadrature is the same as QGaussLog.

The last argument from the constructor allows you to use this quadrature rule in one of two possible ways:

\[ \int_0^1 g(x) dx = \int_0^1 f(x) \ln\left(\frac{|x-x_0|}{\alpha}\right) dx = \sum_{i=0}^N w_i g(q_i) = \sum_{i=0}^N \bar{w}_i f(q_i) \]

Which one of the two sets of weights is provided, can be selected by the factor_out_singular_weight parameter. If it is false (the default), then the \(\bar{w}_i\) weights are computed, and you should provide only the smooth function \(f(x)\), since the singularity is included inside the quadrature. If the parameter is set to true, then the singularity is factored out of the quadrature formula, and you should provide a function \(g(x)\), which should at least be similar to \(\ln(|x-x_0|/\alpha)\).

Notice that this quadrature rule is worthless if you try to use it for regular functions once you factored out the singularity.

The weights and functions have been tabulated up to order 12.

Definition at line 250 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

◆ QGaussLogR() [1/3]

template<int dim>
QGaussLogR< dim >::QGaussLogR ( const unsigned int  n,
const Point< dim > &  x0 = Point< dim >(),
const double  alpha = 1,
const bool  factor_out_singular_weight = false 
)

The constructor takes four arguments: the order of the Gauss formula on each of the segments \([0,x_0]\) and \([x_0,1]\), the actual location of the singularity, the scale factor inside the logarithmic function and a flag that decides whether the singularity is left inside the quadrature formula or it is factored out, to be included in the integrand.

◆ QGaussLogR() [2/3]

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

Move constructor. We cannot rely on the move constructor for Quadrature, since it does not know about the additional member fraction of this class.

◆ QGaussLogR() [3/3]

QGaussLogR< 1 >::QGaussLogR ( const unsigned int  n,
const Point< 1 > &  origin,
const double  alpha,
const bool  factor_out_singularity 
)

Definition at line 535 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

◆ fraction

template<int dim>
const double QGaussLogR< dim >::fraction
protected

This is the length of interval \((0,origin)\), or 1 if either of the two extremes have been selected.

Definition at line 277 of file quadrature_lib.h.

◆ 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 file:
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