Reference documentation for deal.II version GIT 69313620a0 20221128 13:00:02+00:00

#include <deal.II/base/quadrature_lib.h>
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 
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  
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 
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 
A class for Gauss quadrature with arbitrary logarithmic weighting function. This formula is used to integrate \(\ln(xx_0/\alpha)\;f(x)\) 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:
\[ \int_0^1 g(x) dx = \int_0^1 f(x) \ln\left(\frac{xx_0}{\alpha}\right) dx = \sum_{i=0}^N w_i g(q_i) = \sum_{i=0}^N \bar{w}_i f(q_i) \]
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 \(\ln(xx_0/\alpha)\).
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 236 of file quadrature_lib.h.

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 0dimensional quadrature is defined as still being 0dimensional.
Definition at line 96 of file quadrature.h.

privateinherited 
The data type used in counter_map.
Definition at line 230 of file subscriptor.h.

privateinherited 
The iterator type used in counter_map.
Definition at line 235 of file subscriptor.h.
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.

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< 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.

inherited 
Test for equality of two quadratures.
Definition at line 304 of file quadrature.cc.

inherited 
Set the quadrature points and weights to the values provided in the arguments.
Definition at line 52 of file quadrature.cc.

inherited 
Number of quadrature points.

inherited 
Return the i
th quadrature point.

inherited 
Return a reference to the whole array of quadrature points.

inherited 
Return the weight of the i
th quadrature point.

inherited 
Return a reference to the whole array of weights.

inherited 
Determine an estimate for the memory consumption (in bytes) of this object.
Definition at line 313 of file quadrature.cc.

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

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

inherited 
In case the quadrature formula is a tensor product, this function returns the dim
onedimensional 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
).
Definition at line 325 of file quadrature.cc.

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.

inherited 
Unsubscribes a user from the object.
identifier
and the validity
pointer must be the same as the one supplied to subscribe(). Definition at line 156 of file subscriptor.cc.

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.

inlineinherited 
List the subscribers to the input stream
.
Definition at line 317 of file subscriptor.h.

inherited 
List the subscribers to deallog
.
Definition at line 204 of file subscriptor.cc.

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.
Definition at line 53 of file subscriptor.cc.

protected 
This is the length of interval \((0,origin)\), or 1 if either of the two extremes have been selected.
Definition at line 263 of file quadrature_lib.h.

protectedinherited 
List of quadrature points. To be filled by the constructors of derived classes.
Definition at line 292 of file quadrature.h.

protectedinherited 
List of weights of the quadrature points. To be filled by the constructors of derived classes.
Definition at line 298 of file quadrature.h.

protectedinherited 
Indicates if this object represents quadrature formula that is a tensor product of onedimensional formulas. This flag is set if dim==1 or the constructors taking a Quadrature<1> (and possibly a Quadrature<dim1> object) is called. This implies that the quadrature points are sorted lexicographically.
Definition at line 307 of file quadrature.h.

protectedinherited 
Stores the onedimensional tensor basis objects in case this object can be represented by a tensor product.
Definition at line 313 of file quadrature.h.

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 219 of file subscriptor.h.

mutableprivateinherited 
In this map, we count subscriptions for each different identification string supplied to subscribe().
Definition at line 225 of file subscriptor.h.

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.

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.

staticprivateinherited 
A mutex used to ensure data consistency when printing out the list of subscribers.
Definition at line 271 of file subscriptor.h.