Reference documentation for deal.II version 8.4.1

#include <deal.II/base/quadrature.h>
Public Types  
typedef Quadrature< dim1 >  SubQuadrature 
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 (const std::vector< Point< dim > > &points, const std::vector< double > &weights)  
Quadrature (const std::vector< Point< dim > > &points)  
Quadrature (const Point< dim > &point)  
virtual  ~Quadrature () 
Quadrature &  operator= (const Quadrature< dim > &) 
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) 
Public Member Functions inherited from Subscriptor  
Subscriptor ()  
Subscriptor (const Subscriptor &)  
virtual  ~Subscriptor () 
Subscriptor &  operator= (const Subscriptor &) 
void  subscribe (const char *identifier=0) const 
void  unsubscribe (const char *identifier=0) const 
unsigned int  n_subscriptions () const 
void  list_subscribers () const 
DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects."<< "\n\n"<< "(Additional information: "<< arg3<< ")\n\n"<< "See the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "a lot more information on what this error means and "<< "how to fix programs in which it happens.")  
DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier <"<< arg2<< "> subscribes to this object of class "<< arg1<< ". Consequently, it cannot be unsubscribed.")  
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Protected Attributes  
std::vector< Point< dim > >  quadrature_points 
std::vector< double >  weights 
Base class for quadrature formulae in arbitrary dimensions. This class stores quadrature points and weights on the unit line [0,1], unit square [0,1]x[0,1], etc.
There are a number of derived classes, denoting concrete integration formulae. Their names names prefixed by Q
. Refer to the list of derived classes for more details.
The schemes for higher dimensions are typically tensor products of the one dimensional formulae, but refer to 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.
For each quadrature formula we denote by m
, the maximal degree of polynomials integrated exactly. 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 \(m = 2N1\), 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.
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 (dim1)
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 N^{dim} quadrature points in dim
dimensions, where N is the constructor parameter of QGauss.
Definition at line 81 of file quadrature.h.
typedef Quadrature<dim1> Quadrature< dim >::SubQuadrature 
Define a typedef for a quadrature that acts on an object of one dimension less. For cells, this would then be a face quadrature.
Definition at line 88 of file quadrature.h.

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 45 of file quadrature.cc.
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.
SubQuadrature<dim>::type
expands to Quadrature<dim1>
.
Definition at line 108 of file quadrature.cc.

explicit 
Build this quadrature formula as the dim
fold tensor product of a formula in one dimension.
Assuming that the points in the onedimensional 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.
Definition at line 208 of file quadrature.cc.
Quadrature< dim >::Quadrature  (  const Quadrature< dim > &  q  ) 
Copy constructor.
Definition at line 242 of file quadrature.cc.
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 66 of file quadrature.cc.
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 79 of file quadrature.cc.
Quadrature< dim >::Quadrature  (  const Point< dim > &  point  ) 
Constructor for a onepoint quadrature. Sets the weight of this point to one.
Definition at line 91 of file quadrature.cc.

virtual 
Virtual destructor.
Definition at line 273 of file quadrature.cc.
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 252 of file quadrature.cc.
bool Quadrature< dim >::operator==  (  const Quadrature< dim > &  p  )  const 
Test for equality of two quadratures.
Definition at line 263 of file quadrature.cc.
void Quadrature< dim >::initialize  (  const std::vector< Point< dim > > &  points, 
const std::vector< double > &  weights  
) 
Set the quadrature points and weights to the values provided in the arguments.
Definition at line 55 of file quadrature.cc.
unsigned int Quadrature< dim >::size  (  )  const 
Number of quadrature points.
const Point<dim>& Quadrature< dim >::point  (  const unsigned int  i  )  const 
Return the i
th quadrature point.
const std::vector<Point<dim> >& Quadrature< dim >::get_points  (  )  const 
Return a reference to the whole array of quadrature points.
double Quadrature< dim >::weight  (  const unsigned int  i  )  const 
Return the weight of the i
th quadrature point.
const std::vector<double>& Quadrature< dim >::get_weights  (  )  const 
Return a reference to the whole array of weights.
std::size_t Quadrature< dim >::memory_consumption  (  )  const 
Determine an estimate for the memory consumption (in bytes) of this object.
Definition at line 280 of file quadrature.cc.
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.

protected 
List of quadrature points. To be filled by the constructors of derived classes.
Definition at line 217 of file quadrature.h.

protected 
List of weights of the quadrature points. To be filled by the constructors of derived classes.
Definition at line 223 of file quadrature.h.