Reference documentation for deal.II version 9.5.0

#include <deal.II/base/quadrature_lib.h>
Public Types  
using  SubQuadrature = Quadrature< dim==0 ? 0 :dim  1 > 
Public Member Functions  
QSimplex (const Quadrature< dim > &quad)  
template<int spacedim = dim>  
Quadrature< spacedim >  compute_affine_transformation (const std::array< Point< spacedim >, dim+1 > &vertices) const 
template<int spacedim = dim>  
Quadrature< spacedim >  mapped_quadrature (const std::vector< std::array< Point< spacedim >, dim+1 > > &simplices) const 
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  
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 
Given an arbitrary quadrature formula, return one that chops the quadrature points above the hyperplane defined by \(\sum_i x_i = 1\). In other words, it extracts those quadrature points from the base formula that satisfy \(\sum_i (\mathbf x_q)_i \le 1+10^{12}\)."
In general the resulting quadrature is not very useful, unless the quadrature you started from has been constructed specifically to integrate over triangles or tetrahedra. This class only ensures that the resulting quadrature formula only has quadrature points in the reference simplex or on its boundary.
No transformation is applied to the weights, and the weights referring to points that live outside the reference simplex are simply discarded. Because this leads to (or may lead to) a sum of quadrature weights that do not equal the area of the simplex, the resulting quadrature formula is not useful for actually computing integrals.
The main use of this quadrature formula is not to chop tensor product quadratures. Ideally you should pass to this class a quadrature formula constructed directly using points and weights in the reference simplex, capable of integrating on triangles or tetrahedra.
For finite elements based on quadrilaterals and hexahedra, a QSimplex quadrature formula is not very useful on its own. This class is typically used in conjunction with other classes, like QSplit, to patch the reference element using several QSimplex quadrature formulas.
Such quadrature formulas are useful to integrate functions with singularities at certain points, or functions that present jumps along a codimension one surface inside the reference element, like in the extended finite element method (XFEM).
Definition at line 602 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 130 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.
QSimplex< dim >::QSimplex  (  const Quadrature< dim > &  quad  ) 
Construct a quadrature that only contains the points that are in the lower left reference simplex.
[in]  quad  The input quadrature. 
Definition at line 1204 of file quadrature_lib.cc.
Quadrature< spacedim > QSimplex< dim >::compute_affine_transformation  (  const std::array< Point< spacedim >, dim+1 > &  vertices  )  const 
Return an affine transformation of this quadrature, that can be used to integrate on the simplex identified by vertices
.
Both the quadrature point locations and the weights are transformed, so that you can effectively use the resulting quadrature to integrate on the simplex.
The transformation is defined as
\[ x = v_0 + B \hat x \]
where the matrix \(B\) is given by \(B_{ij} = v[j][i]v[0][i]\).
The weights are scaled with the absolute value of the determinant of \(B\), that is \(J \dealcoloneq \text{det}(B)\). If \(J\) is zero, an empty quadrature is returned. This may happen, in two dimensions, if the three vertices are aligned, or in three dimensions if the four vertices are on the same plane. The present function works also in the codimension one and codimension two case. For instance, when dim=2
and spacedim=3
, we can map the quadrature points so that they live on the physical triangle embedded in the three dimensional space. In such a case, the matrix \(B\) is not square anymore.
[in]  vertices  The vertices of the simplex you wish to integrate on 
Definition at line 1231 of file quadrature_lib.cc.
Quadrature< spacedim > QSimplex< dim >::mapped_quadrature  (  const std::vector< std::array< Point< spacedim >, dim+1 > > &  simplices  )  const 
Given a collection of simplices, this function creates a global quadrature rule on the area covered by the simplices, by mapping the current quadrature on each simplex. A simplex is identified by its vertices, which are stored into an array of Points. Hence, this function can provide quadrature rules on polygons (or polyhedra), as they can be split into simplices.
simplices  A std::vector where each entry is an array of dim+1 points, which identifies the vertices of a simplex. 
Definition at line 1265 of file quadrature_lib.cc.

inherited 
Test for equality of two quadratures.
Definition at line 317 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 326 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 338 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.

protectedinherited 
List of quadrature points. To be filled by the constructors of derived classes.
Definition at line 333 of file quadrature.h.

protectedinherited 
List of weights of the quadrature points. To be filled by the constructors of derived classes.
Definition at line 339 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 348 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 354 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.